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Definition of set

 (Entry 1 of 3)

transitive verb

intransitive verb

Definition of set  (Entry 2 of 3)

called also class

Definition of set  (Entry 3 of 3)

Examples of set in a Sentence

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'set.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

Word History

Middle English setten , from Old English settan ; akin to Old High German sezzen to set, Old English sittan to sit

Middle English sett , from Old English gesett , past participle of settan

before the 12th century, in the meaning defined at transitive sense 1

14th century, in the meaning defined at sense 1a

14th century, in the meaning defined at sense 1

Phrases Containing set

• carved / etched / set / written in stone
• close - set
• dinette set
• get / set / start the ball rolling
• (get) ready, (get) set, go
• have one's heart set on (something)
• put / set one's mind to (something)
• replacement set
• set book / text
• set fire to
• set / get tongues wagging
• set / lay great store by
• set great store by / on
• set (oneself) up as (something)
• set (oneself) against
• set one's own house in order
• set one's house in order
• set pattern
• set priorities
• set / put someone's mind at ease / rest
• set / put the record straight
• set someone's mind at ease
• set something afire / aflame / ablaze
• set (something) on its ear
• set (something or someone) against
• set / start a (new) trend
• set store by
• set store on
• set the seal on
• set the wheels in motion
• set the tone
• set the world on fire
• set to music
• set the world alight
• the jet set
• dresser set
• put / set pen to paper
• chemistry set
• Mandelbrot set
• put / set (something) to rights
• point set topology
• set against
• set a precedent
• set an example
• set a record
• dead set against
• set light to
• set in one's ways
• dead set on
• set foot on
• set one's teeth on edge
• set in train
• set one's hand to
• set one's heart on
• set in motion
• set / put someone straight
• set one's sights on
• set (someone) right / straight
• set eyes on
• set for life
• set forward
• set up in (something)
• set the pattern
• set something on fire
• set up house
• the smart set
• set the scene
• set - top box
• set of pipes
• television set
• set / put (something) straight
• set the pace
• solution set
• set up in business
• set foot in
• set to work
• set up camp
• sharp - set
• set the stage
• set up housekeeping
• set up shop
• set up as (something)
• set one straight

Articles Related to set

'All Set': A Phrase Beyond "Ready"

A simple phrase with a number of possible meanings

Dictionary Entries Near set

Cite this entry.

“Set.” Merriam-Webster.com Dictionary , Merriam-Webster, https://www.merriam-webster.com/dictionary/set. Accessed 6 Apr. 2024.

Kids Definition

Kids definition of set.

Kids Definition of set  (Entry 2 of 3)

Kids Definition of set  (Entry 3 of 3)

Medical Definition

Medical definition of set.

 (Entry 1 of 2)

Medical Definition of set  (Entry 2 of 2)

More from Merriam-Webster on set

Nglish: Translation of set for Spanish Speakers

Britannica English: Translation of set for Arabic Speakers

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Python Memo 2: Dictionary vs. Set

A software architect takes a deep dive into the python language by exploring dictionaries and sets and how these two elements of the language work..

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Basis of Dictionaries and Sets

A dictionary is composed of a series of key-value mapping elements. In Python 3.7 +, a dictionary is determined to be ordered, however, before 3.6, a dictionary was disordered. Its length is mutable and elements can be deleted and changed arbitrarily. Compared with lists and tuples, the performance of dictionaries is better, especially for search, add, and delete operations. A dictionary can be completed within a constant time complexity. A set and a dictionary are basically the same, the only difference is that a set has no key-value pairing and is a series of disordered and unique element combinations. 

First, let's look at the creation of dictionaries and collections. There are usually the following ways;

Note here that dictionaries and sets in Python, whether they are keys or values, can be of mixed types. For example, in the following example, a set with elements 1, 'hello', and 5.0: 

Let's take a look at the issue of element access. Dictionaries can access an index directly; if it does not exist, an exception will be thrown:

We can also use the function get(key, default) . If the key does not exist, function get() returns a default value. For example, the following case returns 'null'.

You can also use the get(key, default) function to index. If the key does not exist, call the get() function to return a default value. For example, the following example returns 'null'.

After dictionary access, let's take a look at set again.

First of all, I'd like to emphasize that the set doesn't support index operations, because the set is essentially a hash table, which is not same with the list. Therefore, the following operation is wrong and Python will throw an exception.

To judge whether an element is in a dictionary or set, we can use value in dict/set. 

In addition to creation and access, dictionary and set also support operations such as adding, deleting and updating. 

But note, however the pop() operation of a set is to delete the last element, the set itself is disordered and you have no way of knowing which element is deleted. So the operation must be used with caution. In practical applications, in many cases, we need to sort a dictionary or a set, for example, take out the 50 pairs with the largest value.

For dictionaries, we usually sort in ascending or descending order according to the key or value:

A list is returned here. Each element in the list is a tuple composed of the keys and values of the original dictionary.

As for the set, the sorting is very similar to the lists and tuples mentioned above. Just call sorted(set) directly, and the result will return a sorted list.

Performance of Dictionaries and Sets 

As mentioned at the beginning of the article, the dictionary and set are data structures that have been highly optimized for performance, especially for search, add, and delete operations. Then, let's take a look at their performance in specific scenarios and their comparison with other data structures such as lists.

For example, the back-end of an e-commerce company stores the ID, name, and price of each product. The current demand is that, given the ID of a certain product, we want to find out its price. If we use a list to store these data structures and search them, the corresponding code is as follows:

Assuming that the list has n elements, and the search process needs to traverse the list, the time complexity is O(n). Even if we sort the list first, and then use binary search, it will require O(logn) time complexity, not to mention that the sorting of the list still needs O(nlogn) time complexity.

But if we use a dictionary to store this data, then the lookup will be very convenient and efficient, and it can be completed with only O(1) time complexity. The reason is also very simple. As we mentioned earlier, the internal composition of a dictionary is a hash table and you can find its corresponding value directly through the hash value of the key.

Similarly, we now need to find out how many different prices these commodities have. Let's compare them in the same way.

If you still choose to use the list, the corresponding code is as follows, where A and B are two-level loops. Also, assuming that the original list has n elements, then, in the worst case, O(n^2) time complexity is required.

But if we choose to use a set to store the data, because sets are a highly optimized hash table, the elements inside cannot be repeated and its addition and search operations only need O(1) complexity, thus the total time complexity is O(n).

The following code initializes a product containing 100,000 elements and calculates time needed to use lists and sets to count product prices and quantities:

As you can see, with only one hundred thousand data, the speed difference between the two is such big. In fact, the back-end data in large enterprises is often on the order of hundreds of millions or even billions. If an inappropriate data structure is used, it is easy to cause the server to crash, which not only affects the user experience, but also brings huge losses to the company.

How Dictionaries and Sets Work

We have seen the efficiency of dictionaries and sets through the above examples. But, why are dictionaries and sets so highly efficient, especially for lookup, insert, and delete operations? This is, of course, inseparable from the data structure of dictionaries and sets. Unlike other data structures, the internal structure of dictionaries and sets is a hash table.

• For a dictionary, hash tables store three elements: hash, key, and value.
• For a set, the difference is that there is no key-value pairing in the hash table, only a single element.

Let's take a look at the hash table structure of the old version of Python:

It is not difficult to imagine that as the hash table expands, it will become more and more sparse. For example, if I have the following dictionary:

Then it will be stored in a form similar to the following:

Such a design structure is obviously a waste of storage space. In order to improve the utilization of storage space, in addition to the structure of the dictionary itself, the current hash table separates the index from the hash, key, and value separately, which gives us the following new structure:

Then, the storage form used under the new hash table structure will look like:

We can clearly see that space utilization has been greatly improved. Now that we're clear on the specific design structure, let's look at the working principles of these operations.

Insert Operation

Every time an element is inserted into a dictionary or set, Python will first calculate the hash value of the key (hash(key)), and then perform an AND operation with mask = PyDicMinSize-1 to calculate the position where the element should be inserted into the hash table ( index = hash(key) & mask ). If this position in the hash table is empty, then this element will be inserted into it.

And if this position is already occupied, Python will compare the hash value and key of the two elements to see if they are equal.

• If the two are equal, it means that the element already exists. If the value is different, the value is updated.
• If the two are not equal, this situation is usually called a hash collision, which means that the keys of the two elements are not equal, but the hash values are equal. In this case, Python will continue to look for free positions in the table until it finds a position.

It is worth mentioning that, generally speaking, in this situation, the simplest way is to search linearly. That is, start from this position and look for vacancies one by one. Of course, Python has optimized this internally (you don't need to understand this deeply, you can check the source code if you are interested, I will not repeat it) to make this step more efficient.

Find Operation

Similar to the previous insert operation, Python will find the position where it should be based on the hash value; then, compare the hash value and key of the element in this position to the hash table to see if it is equal to the element that needs to be found. If they are equal, return directly; if they are not, then continue to search until a slot is found or an exception is thrown.

Delete Operation

For the delete operation, Python temporarily assigns a special value to the element at this position and then deletes it when the hash table is resized.

It is not difficult to understand that the occurrence of hash collisions tends to reduce the speed of dictionary and set operations. Therefore, in order to ensure its efficiency, the dictionary and the hash table in the collection are usually guaranteed to have at least 1/3 of the remaining space. With the continuous insertion of elements, when the remaining space is less than 1/3, Python will regain a larger memory space and expand the hash table. However, in this case, all element positions in the table will be re-arranged.

Although the hash collision and the adjustment of the size of the hash table will slow down the speed, this happens very rarely. Therefore, on average, this can still ensure that the time complexity of insert, find, and delete is O(1).

In this lesson, we have learned the basic operations of dictionaries and sets together, and have explained their high performance and internal storage structure.

The dictionary is an ordered data structure in Python 3.7+, while the set is unordered. Its internal hash table storage structure ensures the efficiency of its find, insert, and delete operations. Therefore, dictionary and set are usually used in scenarios such as efficient find and de-duplication of elements.

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Define vs. Set — What's the Difference?

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High Performance Python by Micha Gorelick, Ian Ozsvald

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Chapter 4. Dictionaries and Sets

• What are dictionaries and sets good for?
• How are dictionaries and sets the same?
• What is the overhead when using a dictionary?
• How can I optimize the performance of a dictionary?
• How does Python use dictionaries to keep track of namespaces?

Sets and dictionaries are ideal data structures to be used when your data has no intrinsic order, but does have a unique object that can be used to reference it (the reference object is normally a string, but can be any hashable type). This reference object is called the “key,” while the data is the “value.” Dictionaries and sets are almost identical, except that sets do not actually contain values: a set is simply a collection of unique keys. As the name implies, sets are very useful for doing set operations.

A hashable type is one that implements both the __hash__ magic function and either __eq__ or __cmp__ . All native types in Python already implement these, and any user classes have default values. See Hash Functions and Entropy for more details.

While we saw in the previous chapter that we are restricted to, at best, O(log n) lookup time on lists/tuples with no intrinsic order (through a search operation), dictionaries and sets give us O(n) lookups based on the arbitrary index. In addition, like lists/tuples, dictionaries and sets have O(1) insertion time. [ 4 ] As we will see in How Do Dictionaries and Sets Work? , this speed is accomplished through the use of an open address hash table as the underlying data structure.

However, there is a cost to using dictionaries and sets. First, they generally take up a larger footprint in memory. Also, although the complexity for insertions/lookups is O(1) , the actual speed depends greatly on the hashing function that is in use. If the hash function is slow to evaluate, then any operations on dictionaries or sets will be similarly slow.

Let’s look at an example. Say we want to store contact information for everyone in the phone book. We would like to store this in a form that will make it simple to answer the question, “What is John Doe’s phone number?” in the future. With lists, we would store the phone numbers and names sequentially and scan through the entire list to find the phone number we required, as shown in Example 4-1 .

We could also do this by sorting the list and using the bisect module in order to get O(log n) performance.

With a dictionary, however, we can simply have the “index” be the names and the “values” be the phone numbers, as shown in Example 4-2 . This allows us to simply look up the value we need and get a direct reference to it, instead of having to read every value in our dataset.

For large phone books, the difference between the O(1) lookup of the dictionary and the O(n) time for linear search over the list (or, at best, the O(log n) with the bisect module) is quite substantial.

Create a script that times the performance of the list- bisect method versus a dictionary for finding a number in a phone book. How does the timing scale as the size of the phone book grows?

If, on the other hand, we wanted to answer the question, “How many unique first names are there in my phone book?” we could use the power of sets. Recall that a set is simply a collection of unique keys—this is the exact property we would like to enforce in our data. This is in stark contrast to a list-based approach, where that property needs to be enforced separately from the data structure by comparing all names with all other names. Example 4-3 illustrates.

We must go over all the items in our phone book, and thus this loop costs O(n) .

Here, we must check the current name against all the unique names we have already seen. If it is a new unique name, we add it to our list of unique names. We then continue through the list, performing this step for every item in the phone book.

For the set method, instead of iterating over all unique names we have already seen, we can simply add the current name to our set of unique names. Because sets guarantee the uniqueness of the keys they contain, if you try to add an item that is already in the set, that item simply won’t be added. Furthermore, this operation costs O(1) .

The list algorithm’s inner loop iterates over unique_names , which starts out as empty and then grows, in the worst case, when all names are unique, to be the size of phonebook . This can be seen as performing a linear search for each name in the phone book over a list that is constantly growing. Thus, the complete algorithm performs as O(n log n) , since the outer loop contributes the O(n) factor, while the inner loop contributes the O(log n) factor.

On the other hand, the set algorithm has no inner loop; the set.add operation is an O(1) process that completes in a fixed number of operations regardless of how large the phone book is (there are some minor caveats to this, which we will cover while discussing the implementation of dictionaries and sets). Thus, the only nonconstant contribution to the complexity of this algorithm is the loop over the phone book, making this algorithm perform in O(n) .

When timing these two algorithms using a phonebook with 10,000 entries and 7,422 unique first names, we see how drastic the difference between O(n) and O(n log n) can be:

In other words, the set algorithm gave us a 267x speedup! In addition, as the size of the phonebook grows, the speed gains increase (we get a 557x speedup with a phonebook with 100,000 entries and 15,574 unique first names).

How Do Dictionaries and Sets Work?

Dictionaries and sets use hash tables in order to achieve their O(1) lookups and insertions. This efficiency is the result of a very clever usage of a hash function to turn an arbitrary key (i.e., a string or object) into an index for a list. The hash function and list can later be used to determine where any particular piece of data is right away, without a search. By turning the data’s key into something that can be used like a list index, we can get the same performance as with a list. In addition, instead of having to refer to data by a numerical index, which itself implies some ordering to the data, we can refer to it by this arbitrary key.

Inserting and Retrieving

In order to create a hash table from scratch, we start with some allocated memory, similar to what we started with for arrays. For an array, if we want to insert data, we simply find the smallest unused bucket and insert our data there (and resize if necessary). For hash tables, we must first figure out the placement of the data in this contiguous chunk of memory.

The placement of the new data is contingent on two properties of the data we are inserting: the hashed value of the key and how the value compares to other objects. This is because when we insert data, the key is first hashed and masked so that it turns into an effective index in an array. [ 5 ] The mask makes sure that the hash value, which can take the value of any integer, fits within the allocated number of buckets. So, if we have allocated 8 blocks of memory and our hash value is 28975 , we consider the bucket at index 28975 & 0b111 = 7 . If, however, our dictionary has grown to require 512 blocks of memory, then the mask becomes 0b111111111 (and in this case, we would consider the bucket at index 28975 & 0b11111111 ). Now we must check if this bucket is already in use. If it is empty, we can insert the key and the value into this block of memory. We store the key so that we can make sure we are retrieving the correct value on lookups. If it is in use and the value of the bucket is equal to the value we wish to insert (a comparison done with the cmp built-in), then the key/value pair is already in the hash table and we can return. However, if the values don’t match, then we must find a new place to put the data.

To find the new index, we compute a new index using a simple linear function, a method called probing . Python’s probing mechanism adds a contribution from the higher-order bits of the original hash (recall that for a table of length 8 we only considered the last 3 bits of the hash for the initial index, through the use of a mask value of mask = 0b111 = bin(8 - 1) ). Using these higher-order bits gives each hash a different sequence of next possible hashes, which helps to avoid future collisions. There is a lot of freedom when picking the algorithm to generate a new index; however, it is quite important that the scheme visits every possible index in order to evenly distribute the data in the table. How well distributed the data is throughout the hash table is called the “load factor” and is related to the entropy of the hash function. The pseudocode in Example 4-4 illustrates the calculation of hash indices used in CPython 2.7.

hash returns an integer, while the actual C code in CPython uses an unsigned integer. Because of this, this pseudocode doesn’t 100% replicate the behavior in CPython; however, it is a good approximation.

This probing is a modification of the naive method of “linear probing.” In linear probing, we simply yield the values i = (5 * i + 1) & mask , where i is initialized to the hash value of the key and the value ‘5` is unimportant to the current discussion. [ 6 ] An important thing to note is that linear probing only deals with the last several bytes of the hash and disregards the rest (i.e., for a dictionary with eight elements, we only look at the last 3 bits since at that point the mask is 0x111 ). This means that if hashing two items gives the same last three binary digits, we will not only have a collision, but the sequence of probed indices will be the same. The perturbed scheme that Python uses will start taking into consideration more bits from the items’ hashes in order to resolve this problem.

A similar procedure is done when we are performing lookups on a specific key: the given key is transformed into an index and that index is examined. If the key in that index matches (recall that we also store the original key when doing insert operations), then we can return that value. If it doesn’t, we keep creating new indices using the same scheme, until we either find the data or hit an empty bucket. If we hit an empty bucket, we can conclude that the data does not exist in the table.

Figure 4-1 illustrates the process of adding some data into a hash table. Here, we chose to create a hash function that simply uses the first letter of the input. We accomplish this by using Python’s ord function on the first letter of the input to get the integer representation of that letter (recall the hash functions must return integers). As we’ll see in Hash Functions and Entropy , Python provides hashing functions for most of its types, so typically you won’t have to provide one yourself except in extreme situations.

Insertion of the key “Barcelona” causes a collision, and a new index is calculated using the scheme in Example 4-4 . This dictionary can also be created in Python using the code in Example 4-5 .

In this case, “Barcelona” and “Rome” cause the hash collision ( Figure 4-1 shows the outcome of this insertion). We see this because for a dictionary with four elements we have a mask value of 0b111 . As a result, “Barcelona” will try to use index ord("B") & 0b111 = 66 & 0b111 = 0b1000010 & 0b111 = 0b010 = 2 . Similarly, “Rome” will try to use the index ord("R") & 0b111 = 82 & 0b111 = 0b1010010 & 0b111 = 0b010 = 2 .

Work through the following problems. A discussion of hash collisions follows:

• Finding an element —Using the dictionary created in Example 4-5 , what would a lookup on the key “Johannesburg” look like? What indices would be checked?
• Deleting an element —Using the dictionary created in Example 4-5 , how would you handle the deletion of the key “Rome”? How would subsequent lookups for the keys “Rome” and “Barcelona” be handled?
• Hash collisions —Considering the dictionary created in Example 4-5 , how many hash collisions could you expect if 500 cities, with names all starting with an uppercase letter, were added into a hash table? How about 1,000 cities? Can you think of a way of lowering this number?

For 500 cities, there would be approximately 474 dictionary elements that collided with a previous value (500–26), with each hash having 500 / 26 = 19.2 cities associated with it. For 1,000 cities, 974 elements would collide and each hash would have 1,000 / 26 = 38.4 cities associated with it. This is because the hash is simply based on the numerical value of the first letter, which can only take a value from A – Z , allowing for only 26 independent hash values. This means that a lookup in this table could require as many as 38 subsequent lookups to find the correct value. In order to fix this, we must increase the number of possible hash values by considering other aspects of the city in the hash. The default hash function on a string considers every character in order to maximize the number of possible values. See Hash Functions and Entropy for more explanation.

When a value is deleted from a hash table, we cannot simply write a NULL to that bucket of memory. This is because we have used NULL s as a sentinel value while probing for hash collisions. As a result, we must write a special value that signifies that the bucket is empty, but there still may be values after it to consider when resolving a hash collision. These empty slots can be written to in the future and are removed when the hash table is resized.

As more items are inserted into the hash table, the table itself must be resized to accommodate it. It can be shown that a table that is no more than two-thirds full will have optimal space savings while still having a good bound on the number of collisions to expect. Thus, when a table reaches this critical point, it is grown. In order to do this, a larger table is allocated (i.e., more buckets in memory are reserved), the mask is adjusted to fit the new table, and all elements of the old table are reinserted into the new one. This requires recomputing indices, since the changed mask will change the resulting index. As a result, resizing large hash tables can be quite expensive! However, since we only do this resizing operation when the table is too small, as opposed to on every insert, the amortized cost of an insert is still O(1) .

By default, the smallest size of a dictionary or set is 8 (that is, if you are only storing three values, Python will still allocate eight elements). On resize, the number of buckets increases by 4x until we reach 50,000 elements, after which the size is increased by 2x. This gives the following possible sizes:

It is important to note that resizing can happen to make a hash table larger or smaller. That is, if sufficiently many elements of a hash table are deleted, the table can be scaled down in size. However, resizing only happens during an insert .

Hash Functions and Entropy

Objects in Python are generally hashable, since they already have built-in __hash__ and __cmp__ functions associated with them. For numerical types ( int and float ), the hash is simply based on the bit value of the number they represent. Tuples and strings have a hash value that is based on their contents. Lists, on the other hand, do not support hashing because their values can change. Since a list’s values can change, so could the hash that represents the list, which would change the relative placement of that key in the hash table. [ 7 ]

User-defined classes also have default hash and comparison functions. The default __hash__ function simply returns the object’s placement in memory as given by the built-in id function. Similarly, the __cmp__ operator compares the numerical value of the object’s placement in memory.

This is generally acceptable, since two instances of a class are generally different and should not collide in a hash table. However, in some cases we would like to use set or dict objects to disambiguate between items. Take the following class definition:

If we were to instantiate multiple Point objects with the same values for x and y , they would all be independent objects in memory and thus have different placements in memory, which would give them all different hash values. This means that putting them all into a set would result in all of them having individual entries:

We can remedy this by forming a custom hash function that is based on the actual contents of the object as opposed to the object’s placement in memory. The hash function can be arbitrary as long as it consistently gives the same result for the same object. (There are also considerations regarding the entropy of the hashing function, which we will discuss later.) The following redefinition of the Point class will yield the results we expect:

This allows us to create entries in a set or dictionary indexed by the properties of the Point object as opposed to the memory address of the instantiated object:

As alluded to in the earlier note where we discussed hash collisions, a custom-selected hash function should be careful to evenly distribute hash values in order to avoid collisions. Having many collisions will degrade the performance of a hash table: if most keys have collisions, then we need to constantly “probe” the other values, effectively walking a potentially large portion of the dictionary in order to find the key in question. In the worst case, when all keys in a dictionary collide, the performance of lookups in the dictionary is O(n) and thus the same as if we were searching through a list.

If we know that we are storing 5,000 values in a dictionary and we need to create a hashing function for the object we wish to use as a key, we must be aware that the dictionary will be stored in a hash table of size 32,768, and thus only the last 15 bits of our hash are being used to create an index (for a hash table of this size, the mask is bin(32758-1) = 0b111111111111111 ).

This idea of “how well distributed my hash function is” is called the entropy of the hash function. Entropy, defined as:

where p(i) is the probability that the hash function gives hash i . It is maximized when every hash value has equal probability of being chosen. A hash function that maximizes entropy is called an ideal hash function since it guarantees the minimal number of collisions.

For an infinitely large dictionary, the hash function used for integers is ideal. This is because the hash value for an integer is simply the integer itself! For an infinitely large dictionary, the mask value is infinite and thus we consider all bits in the hash value. Thus, given any two numbers, we can guarantee that their hash values will not be the same.

However, if we made this dictionary finite, then we could no longer have this guarantee. For example, for a dictionary with four elements, the mask we use is 0b111 . Thus, the hash value for the number 5 is 5 & 0b111 = 5 and the hash value for 501 is 501 & 0b111 = 5 , and thus their entries will collide.

To find the mask for a dictionary with an arbitrary number of elements, N , we first find the minimum number of buckets that dictionary must have to still be two-thirds full ( N * 5 / 3 ). Then, we find the smallest dictionary size that will hold this number of elements (8; 32; 128; 512; 2,048; etc.) and find the number of bits necessary to hold this number. For example, if N=1039 , then we must have at least 1,731 buckets, which means we need a dictionary with 2,048 buckets. Thus, the mask is bin(2048 - 1) = 0b11111111111 .

There is no single best hash function to use when using a finite dictionary. However, knowing up front what range of values will be used and how large the dictionary will be helps in making a good selection. For example, if we are storing all 676 combinations of two lowercase letters as keys in a dictionary ( aa , ab , ac , etc.), then a good hashing function would be the one shown in Example 4-6 .

This gives no hash collisions for any combination of two lowercase letters, considering a mask of 0b1111111111 (a dictionary of 676 values will be held in a hash table of length 2,048, which has a mask of bin(2048-1) = 0b11111111111 ).

Example 4-7 very explicitly shows the ramifications of having a bad hashing function for a user-defined class—here, the cost of a bad hash function (in fact, it is the worst possible hash function!) is a 21.8x slowdown of lookups.

• Show that for an infinite dictionary (and thus an infinite mask), using an integer’s value as its hash gives no collisions.
• Show that the hashing function given in Example 4-6 is ideal for a hash table of size 1,024. Why is it not ideal for smaller hash tables?

Dictionaries and Namespaces

Doing a lookup on a dictionary is fast; however, doing it unnecessarily will slow down your code, just as any extraneous lines will. One area where this surfaces is in Python’s namespace management, which heavily uses dictionaries to do its lookups.

Whenever a variable, function, or module is invoked in Python, there is a hierarchy that determines where it looks for these objects. First, Python looks inside of the locals() array, which has entries for all local variables. Python works hard to make local variable lookups fast, and this is the only part of the chain that doesn’t require a dictionary lookup. If it doesn’t exist there, then the globals() dictionary is searched. Finally, if the object isn’t found there, the __builtin__ object is searched. It is important to note that while locals() and globals() are explicitly dictionaries and __builtin__ is technically a module object, when searching __builtin__ for a given property we are just doing a dictionary lookup inside of its locals() map (this is the case for all module objects and class objects!).

To make this clearer, let’s look at a simple example of calling functions that are defined in different scopes ( Example 4-8 ). We can disassemble the functions with the dis module ( Example 4-9 ) to get a better understanding of how these namespace lookups are happening.

The first function, test1 , makes the call to sin by explicitly looking at the math library. This is also evident in the bytecode that is produced: first a reference to the math module must be loaded, and then we do an attribute lookup on this module until we finally have a reference to the sin function. This is done through two dictionary lookups, one to find the math module and one to find the sin function within the module.

On the other hand, test2 explicitly imports the sin function from the math module, and the function is then directly accessible within the global namespace. This means we can avoid the lookup of the math module and the subsequent attribute lookup. However, we still must find the sin function within the global namespace. This is yet another reason to be explicit about what functions you are importing from a module. This practice not only makes code more readable, because the reader knows exactly what functionality is required from external sources, but it also speeds up code!

Finally, test3 defines the sin function as a keyword argument, with its default value being a reference to the sin function within the math module. While we still do need to find a reference to this function within the module, this is only necessary when the test3 function is first defined. After this, the reference to the sin function is stored within the function definition as a local variable in the form of a default keyword argument. As mentioned previously, local variables do not need a dictionary lookup to be found; they are stored in a very slim array that has very fast lookup times. Because of this, finding the function is quite fast!

While these effects are an interesting result of the way namespaces in Python are managed, test3 is definitely not “Pythonic.” Luckily, these extra dictionary lookups only start to degrade performance when they are called a lot (i.e., in the innermost block of a very fast loop, such as in the Julia set example). With this in mind, a more readable solution would be to set a local variable with the global reference before the loop is started. We’ll still have to do the global lookup once whenever the function is called, but all the calls to that function in the loop will be made faster. This speaks to the fact that even minute slowdowns in code can be amplified if that code is being run millions of times. Even though a dictionary lookup may only take several hundred nanoseconds, if we are looping millions of times over this lookup it can quickly add up. In fact, looking at Example 4-10 we see a 9.4% speedup simply by making the sin function local to the tight loop that calls it.

Dictionaries and sets provide a fantastic way to store data that can be indexed by a key. The way this key is used, through the hashing function, can greatly affect the resulting performance of the data structure. Furthermore, understanding how dictionaries work gives you a better understanding not only of how to organize your data, but also of how to organize your code, since dictionaries are an intrinsic part of Python’s internal functionality.

In the next chapter we will explore generators, which allow us to provide data to code with more control over ordering and without having to store full datasets in memory beforehand. This lets us sidestep many of the possible hurdles that one might encounter when using any of Python’s intrinsic data structures.

[ 4 ] As we will discuss in Hash Functions and Entropy , dictionaries and sets are very dependent on their hash functions. If the hash function for a particular datatype is not O(1) , any dictionary or set containing that type will no longer have its O(1) guarantee.

[ 5 ] A mask is a binary number that truncates the value of a number. So, 0b1111101 & 0b111 = 0b101 = 5 represents the operation of 0b111 masking the number 0b1111101 . This operation can also be thought of as taking a certain number of the least-significant digits of a number.

[ 6 ] The value of 5 comes from the properties of a linear congruential generator (LCG), which is used in generating random numbers.

[ 7 ] More information about this can be found at http://wiki.python.org/moin/DictionaryKeys .

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to put (something or someone) in a particular place: to set a vase on a table.

to place in a particular position or posture: Set the baby on his feet.

to place in some relation to something or someone: We set a supervisor over the new workers.

to put into some condition: to set a house on fire.

to put or apply: to set fire to a house.

to put in the proper position: to set a chair back on its feet.

to put in the proper or desired order or condition for use: to set a trap.

to distribute or arrange china, silver, etc., for use on (a table): to set the table for dinner.

to place (the hair, especially when wet) on rollers, in clips, or the like, so that the hair will assume a particular style.

to put (a price or value) upon something: He set $7500 as the right amount for the car. The teacher sets a high value on neatness.

to fix the value of at a certain amount or rate; value: He set the car at $500. She sets neatness at a high value.

to post, station, or appoint for the purpose of performing some duty: to set spies on a person.

to determine or fix definitely: to set a time limit.

to resolve or decide upon: to set a wedding date.

to cause to pass into a given state or condition: to set one's mind at rest; to set a prisoner free.

to direct or settle resolutely or wishfully: to set one's mind to a task.

to present as a model; place before others as a standard: to set a good example.

to establish for others to follow: to set a fast pace.

to prescribe or assign, as a task.

to adjust (a mechanism) so as to control its performance.

to adjust the hands of (a clock or watch) according to a certain standard: I always set my watch by the clock in the library.

to adjust (a timer, alarm of a clock, etc.) so as to sound when desired: He set the alarm for seven o'clock.

to fix or mount (a gem or the like) in a frame or setting.

to ornament or stud with gems or the like: a bracelet set with pearls.

to cause to sit; seat: to set a child in a high chair.

to put (a hen) on eggs to hatch them.

to place (eggs) under a hen or in an incubator for hatching.

to place or plant firmly: to set a flagpole in concrete.

to put into a fixed, rigid, or settled state, as the face, muscles, etc.

to fix at a given point or calibration: to set the dial on an oven; to set a micrometer.

to tighten (often followed by up ): to set nuts well up.

to cause to take a particular direction: to set one's course to the south.

Surgery . to put (a broken or dislocated bone) back in position.

(of a hunting dog) to indicate the position of (game) by standing stiffly and pointing with the muzzle.

to fit, as words to music.

to arrange for musical performance.

to arrange (music) for certain voices or instruments.

to arrange the scenery, properties, lights, etc., on (a stage) for an act or scene.

to prepare (a scene) for dramatic performance.

Nautical . to spread and secure (a sail) so as to catch the wind.

to arrange (type) in the order required for printing.

to put together types corresponding to (copy); compose in type: to set an article.

Baking . to put aside (a substance to which yeast has been added) in order that it may rise.

to change into curd: to set milk with rennet.

to cause (glue, mortar, or the like) to become fixed or hard.

to urge, goad, or encourage to attack: to set the hounds on a trespasser.

Bridge . to cause (the opposing partnership or their contract) to fall short: We set them two tricks at four spades. Only perfect defense could set four spades.

to affix or apply, as by stamping: The king set his seal to the decree.

to fix or engage (a fishhook) firmly into the jaws of a fish by pulling hard on the line once the fish has taken the bait.

to sharpen or put a keen edge on (a blade, knife, razor, etc.) by honing or grinding.

to fix the length, width, and shape of (yarn, fabric, etc.).

Carpentry . to sink (a nail head) with a nail set.

to bend or form to the proper shape, as a saw tooth or a spring.

to bend the teeth of (a saw) outward from the blade alternately on both sides in order to make a cut wider than the blade itself.

to pass below the horizon; sink: The sun sets early in winter.

to decline; wane.

to assume a fixed or rigid state, as the countenance or the muscles.

(of the hair) to be placed temporarily on rollers, in clips, or the like, in order to assume a particular style: Long hair sets more easily than short hair.

to become firm, solid, or permanent, as mortar, glue, cement, or a dye, due to drying or physical or chemical change.

to sit on eggs to hatch them, as a hen.

to hang or fit, as clothes.

to begin to move; start (usually followed by forth, out, off, etc.).

(of a flower's ovary) to develop into a fruit.

(of a hunting dog) to indicate the position of game.

to have a certain direction or course, as a wind, current, or the like.

Nautical . (of a sail) to be spread so as to catch the wind.

Printing . (of type) to occupy a certain width: This copy sets to forty picas.

Nonstandard . sit: Come in and set a spell.

the act or state of setting or the state of being set.

a collection of articles designed for use together: a set of china; a chess set.

a collection, each member of which is adapted for a special use in a particular operation: a set of golf clubs; a set of carving knives.

a number, group, or combination of things of similar nature, design, or function: a set of ideas.

a series of volumes by one author, about one subject, etc.

a number, company, or group of persons associated by common interests, occupations, conventions, or status: a set of murderous thieves; the smart set.

the fit, as of an article of clothing: the set of his coat.

fixed direction, bent, or inclination: The set of his mind was obvious.

bearing or carriage: the set of one's shoulders.

the assumption of a fixed, rigid, or hard state, as by mortar or glue.

the arrangement of the hair in a particular style: How much does the beauty salon charge for a shampoo and set?

a plate for holding a tool or die.

an apparatus for receiving radio or television programs; receiver.

Philately . a group of stamps that form a complete series.

Tennis . a unit of a match, consisting of a group of not fewer than six games with a margin of at least two games between the winner and loser: He won the match in straight sets of 6–3, 6–4, 6–4.

a construction representing a place or scene in which the action takes place in a stage, motion-picture, or television production.

Machinery .

the bending out of the points of alternate teeth of a saw in opposite directions.

a permanent deformation or displacement of an object or part.

a tool for giving a certain form to something, as a saw tooth.

a chisel having a wide blade for dividing bricks.

Horticulture . a young plant, or a slip, tuber, or the like, suitable for planting.

the number of couples required to execute a quadrille or the like.

a series of movements or figures that make up a quadrille or the like.

a group of pieces played by a band, as in a night club, and followed by an intermission.

the period during which these pieces are played.

Bridge . a failure to take the number of tricks specified by one's contract: Our being vulnerable made the set even more costly.

the direction of a wind, current, etc.

the form or arrangement of the sails, spars, etc., of a vessel.

suit (def. 12) .

Psychology . a temporary state of an organism characterized by a readiness to respond to certain stimuli in a specific way.

Mining . a timber frame bracing or supporting the walls or roof of a shaft or stope.

Carpentry . nail set .

Mathematics . a collection of objects or elements classed together.

Printing . the width of a body of type.

sett (def. 3) .

fixed or prescribed beforehand: a set time; set rules.

specified; fixed: The hall holds a set number of people.

deliberately composed; customary: set phrases.

fixed; rigid: a set smile.

resolved or determined; habitually or stubbornly fixed: to be set in one's opinions.

completely prepared; ready: Is everyone set?

Also get set! (in calling the start of a race): Ready! Set! Go!

to begin on; start.

to undertake; attempt.

to assault; attack.

set against,

to cause to be hostile or antagonistic.

to compare or contrast: The advantages must be set against the disadvantages.

set ahead, to set to a later setting or time: Set your clocks ahead one hour.

to reserve for a particular purpose.

to cause to be noticed; distinguish: Her bright red hair sets her apart from her sisters.

to put to one side; reserve: The clerk set aside the silver brooch for me.

to dismiss from the mind; reject.

to prevail over; discard; annul: to set aside a verdict.

to hinder; impede.

to turn the hands of (a watch or clock) to show an earlier time: When your plane gets to California, set your watch back two hours.

to reduce to a lower setting: Set back the thermostat before you go to bed.

set by, to save or keep for future use.

to write or to copy or record in writing or printing.

to consider; estimate: to set someone down as a fool.

to attribute; ascribe: to set a failure down to bad planning.

to put in a position of rest on a level surface.

to humble or humiliate.

to land an airplane: We set down in a heavy fog.

(in horse racing) to suspend (a jockey) from competition because of some offense or infraction of the rules.

to give an account of; state; describe: He set forth his theory in a scholarly report.

to begin a journey; start: Columbus set forth with three small ships.

to begin to prevail; arrive: Darkness set in.

(of winds or currents) to blow or flow toward the shore.

to cause to become ignited or to explode.

to begin; start.

to intensify or improve by contrast.

to begin a journey or trip; depart.

Also set upon. to attack or cause to attack: to set one's dog on a stranger.

to instigate; incite: to set a crew to mutiny.

to begin a journey or course: to set out for home.

to undertake; attempt: He set out to prove his point.

to design; plan: to set out a pattern.

to define; describe: to set out one's arguments.

to plant: to set out petunias and pansies.

to lay out (the plan of a building) in actual size at the site.

to lay out (a building member or the like) in actual size.

to make a vigorous effort; apply oneself to work; begin.

to begin to fight; contend.

to put upright; raise.

to put into a high or powerful position.

to construct; assemble; erect.

to be assembled or made ready for use: exercise equipment that sets up in a jiffy.

to inaugurate; establish.

to enable to begin in business; provide with means.

Informal . to make a gift of; treat, as to drinks.

Informal . to stimulate; elate.

to propound; plan; advance.

to bring about; cause.

to become firm or hard, as a glue or cement: a paint that sets up within five minutes.

to lead or lure into a dangerous, detrimental, or embarrassing situation, as by deceitful prearrangement or connivance.

to entrap or frame, as an innocent person in a crime or a criminal suspect in a culpable circumstance in order to achieve an arrest.

to arrange the murder or execution of: His partner set him up with the mob.

Bridge . to establish (a suit): to set up spades.

Idioms about set

all set , Informal . in readiness; prepared: They were at the starting line and all set to begin.

set forward , to turn the hands of (a watch or clock) to show a later time: When your plane lands in New York, set your watch forward two hours.

set one's face against . face (def. 58) .

set store by . store (def. 16) .

Origin of set

Synonym study for set, confusables note for set, other words for set, other words from set.

• in·ter·set, verb (used with object), in·ter·set, in·ter·set·ting.
• mis·set, verb, mis·set, mis·set·ting.
• self-set, adjective

Words that may be confused with set

• set , sit (see confusables note at the current entry)

Words Nearby set

• Sesto San Giovanni
• set against
• set an example

Other definitions for Set (2 of 2)

the brother and murderer of Osiris, represented as having the form of a donkey or other mammal and regarded as personifying the desert.

• Also Seth [seyt] /seɪt/ .

Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2024

How to use set in a sentence

That means something focused on one exercise, with a clear number of sets and reps.

“He spent more time about who was going to call Fox and yell at them to set them straight than he did on the virus,” she said.

If you’re using it in arid regions, or mostly on smooth trails, you might not get your money’s worth out of a good set of aftermarket tires.

When we look at Threads business model we’re set up to respond very quickly and we have had a strong year.

set a trapThe next skill set down from hunting with primitive archery tools is trapping.

When cities started adding chlorine to their water supplies, in the early 1900s, it set off public outcry.

Submission is set in a France seven years from now that is dominated by a Muslim president intent on imposing Islamic law.

In the last year, her fusion exercise class has attracted a cult following and become de rigueur among the celebrity set .

I wonder what that lady is doing now, and if she knows what she set in motion with Archer?

Empire will be hate-watched and may set off some conversations on its way from fading from our minds.

You would not think it too much to set the whole province in flames so that you could have your way with this wretched child.

I take the Extream Bells, and set down the six Changes on them thus.

She set off down Trafalgar Road in the mist and the rain, glad that she had been compelled to walk.

Good is set against evil, and life against death: so also is the sinner against a just man.

He set down as the second the golden rule, “Whatsoever ye would that men should do unto you, do ye even so to them.”

British Dictionary definitions for set (1 of 2)

/ ( sɛt ) /

to put or place in position or into a specified state or condition : to set a book on the table ; to set someone free

(also intr; foll by to or on) to put or be put (to); apply or be applied : he set fire to the house ; they set the dogs on the scent

to put into order or readiness for use; prepare : to set a trap ; to set the table for dinner

(also intr) to put, form, or be formed into a jelled, firm, fixed, or rigid state : the jelly set in three hours

(also intr) to put or be put into a position that will restore a normal state : to set a broken bone

to adjust (a clock or other instrument) to a position

to determine or establish : we have set the date for our wedding

to prescribe or allot (an undertaking, course of study, etc) : the examiners have set ``Paradise Lost''

to arrange in a particular fashion, esp an attractive one : she set her hair ; the jeweller set the diamonds in silver

(of clothes) to hang or fit (well or badly) when worn

Also: set to music to provide music for (a poem or other text to be sung)

Also: set up printing to arrange or produce (type, film, etc) from (text or copy); compose

to arrange (a stage, television studio, etc) with scenery and props

to describe or present (a scene or the background to a literary work, story, etc) in words : his novel is set in Russia

to present as a model of good or bad behaviour (esp in the phrases set an example, set a good example, set a bad example )

(foll by on or by ) to value (something) at a specified price or estimation of worth : he set a high price on his services

( foll by at) to price (the value of something) at a specified sum : he set his services at £300

(also intr) to give or be given a particular direction : his course was set to the East

(also intr) to rig (a sail) or (of a sail) to be rigged so as to catch the wind

(intr) (of the sun, moon, etc) to disappear beneath the horizon

to leave (dough, etc) in one place so that it may prove

to sharpen (a cutting blade) by grinding or honing the angle adjacent to the cutting edge

to displace alternate teeth of (a saw) to opposite sides of the blade in order to increase the cutting efficiency

to sink (the head of a nail) below the surface surrounding it by using a nail set

computing to give (a binary circuit) the value 1

(of plants) to produce (fruits, seeds, etc) after pollination or (of fruits or seeds) to develop after pollination

to plant (seeds, seedlings, etc)

to place (a hen) on (eggs) for the purpose of incubation

(intr) (of a gun dog) to turn in the direction of game, indicating its presence

Scot and Irish to let or lease : to set a house

bridge to defeat (one's opponents) in their attempt to make a contract

a dialect word for sit

set eyes on to see

the act of setting or the state of being set

a condition of firmness or hardness

bearing, carriage, or posture : the set of a gun dog when pointing

the fit or hang of a garment, esp when worn

the scenery and other props used in and identifying the location of a stage or television production, film, etc

Also called: set width printing

the width of the body of a piece of type

the width of the lines of type in a page or column

the cut of the sails or the arrangement of the sails, spars, rigging, etc, of a vessel

the direction from which a wind is blowing or towards which a tide or current is moving

psychol a temporary bias disposing an organism to react to a stimulus in one way rather than in others

a seedling, cutting, or similar part that is ready for planting : onion sets

a blacksmith's tool with a short head similar to a cold chisel set transversely onto a handle and used, when struck with a hammer, for cutting off lengths of iron bars

See nail set

the direction of flow of water

a mechanical distortion of shape or alignment, such as a bend in a piece of metal

the penetration of a driven pile for each blow of the drop hammer

a variant spelling of sett

fixed or established by authority or agreement : set hours of work

(usually postpositive) rigid or inflexible : she is set in her ways

unmoving; fixed : a set expression on his face

conventional, artificial, or stereotyped, rather than spontaneous : she made her apology in set phrases

(postpositive; foll by on or upon) resolute in intention : he is set upon marrying

(of a book, etc) prescribed for students' preparation for an examination

• See also set about, set against, set aside , set back , set down, set forth, set in , set off, set on, set out, set to , set up , set upon

British Dictionary definitions for set (2 of 2)

a number of objects or people grouped or belonging together, often forming a unit or having certain features or characteristics in common : a set of coins ; John is in the top set for maths

a group of people who associate together, esp a clique : he's part of the jet set

maths logic

Also called: class a collection of numbers, objects, etc, that is treated as an entity: 3, the moon is the set the two members of which are the number 3 and the moon

(in some formulations) a class that can itself be a member of other classes

any apparatus that receives or transmits television or radio signals

tennis squash badminton one of the units of a match, in tennis one in which one player or pair of players must win at least six games : Graf lost the first set

the number of couples required for a formation dance

a series of figures that make up a formation dance

a band's or performer's concert repertoire on a given occasion : the set included no new numbers

a continuous performance : the Who played two sets

(intr) (in square dancing and country dancing) to perform a sequence of steps while facing towards another dancer : set to your partners

(usually tr) to divide into sets : in this school we set our older pupils for English

Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

Scientific definitions for set

A collection of distinct elements that have something in common. In mathematics, sets are commonly represented by enclosing the members of a set in curly braces, as {1, 2, 3, 4, 5}, the set of all positive integers from 1 to 5.

The American Heritage® Science Dictionary Copyright © 2011. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

Other Idioms and Phrases with set

In addition to the idioms beginning with set

• set a precedent
• set at rest
• set back on one's heels
• set back the clock
• set eyes on
• set fire to
• set forward
• set in motion
• set in one's ways, be
• set on a pedestal
• set one back
• set one back on one's feet
• set one's back up
• set one's cap for
• set one's face against
• set one's heart on
• set one's mind at rest
• set one's mind on
• set one's seal on
• set one's sights on
• set one's teeth on edge
• set on fire
• set store by
• set straight
• set the pace
• set the record straight
• set the scene for
• set the table
• set the wheels in motion
• set the world on fire
• set tongues wagging
• set to rights
• set up housekeeping
• set up shop
• dead set against
• get (set) someone's back up
• get (set) the ball rolling
• lay (set) eyes on
• on a pedestal, set
• tongues wagging, set

Also see underput.

The American Heritage® Idioms Dictionary Copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.

• Cambridge Dictionary +Plus

Meaning of set in English

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set verb ( POSITION )

• He set the books down on the table .
• She set the tray down beside me.
• Finish chopping the onions and set them to one side .
• The building itself is set back from the street .
• The mansion is set in 90 acres of beautiful , unspoilt countryside .
• change something around
• pile (something) up
• reinstallation
• reorientate
• superimpose
• transposition

You can also find related words, phrases, and synonyms in the topics:

set verb ( CONDITION )

• We watched as demonstrators doused a car with petrol and set it alight .
• A peace campaigner had set herself on fire in protest at the government's involvement in the war .
• Rioters armed with firebombs set light to police barricades .
• The new government has decided to set all political prisoners free .
• The lamp caught fire and set light to the curtains .
• attribute something to someone
• hyperstimulation
• implementation
• Pygmalion effect
• realization
• reattribute

set verb ( ESTABLISH )

• We're not in a position to set any conditions - we'll have to accept what they offer us.
• They need to set some boundaries of behaviour for that child .
• My brother set the academic standards we all had to follow .
• We have set ourselves a limit for our spending .
• He sets us a great example by cycling to work every day .

set verb ( GET READY )

• She set her clock by the time on the computer .
• I've set the alarm for 7.30.
• I set the heating to come on at six.
• The oven is set to come on automatically .
• I set the washing machine for a delicate wash .
• batten down the hatches idiom
• break someone in
• bug-out bag
• build (someone/something) up
• gear (someone/something) up
• get/have your ducks in a row idiom
• gird your self idiom
• roll up your sleeves idiom
• set something up
• set the scene/stage idiom

set verb ( FIX )

• decide I've decided to move to Sweden.
• fix UK The price has been fixed at £10.
• set Have you set a date for the wedding?
• finalize We've chosen a venue for the wedding, but we haven't finalized the details yet.
• settle OK then, we're going to Spain. That's settled.
• settle on/upon Have you settled on a place to live yet?
• We set a date for a follow-up meeting .
• Have you set a time for the next appointment ?
• The price of the boat was set too high for us.
• be make or break for someone/something idiom
• be on the horns of a dilemma idiom
• flip a coin idiom
• get it together idiom
• get something into your head idiom
• hammer something out
• have a, some, etc. say in something idiom
• swing the balance idiom
• take it into your head to do something idiom
• take the plunge idiom

set verb ( GIVE WORK )

• accommodate
• accommodate someone with something
• administration
• arm someone with something
• hand something back
• hand something down
• hand something in
• hand something out
• re-equipment
• reassignment

set verb ( MUSIC )

• acciaccatura
• hemidemisemiquaver
• key signature
• secco recitative

set verb ( SUN )

• geostationary
• geosynchronous
• observatory
• the North Star

Phrasal verbs

Set noun ( group ).

• Government by coalition has its own peculiar set of problems .
• A set of stamps has been commissioned in commemoration of Independence Day .
• He only needs two more cards to complete the set.
• Cross the bridge and turn right at the first set of traffic lights .
• They got an entire set of silver cutlery as a wedding present .
• age bracket
• agglomerate
• agglomeration
• Aladdin's cave
• starter pack
• store cupboard

set noun ( FILM/PLAY )

• He designs the sets for the local drama group .
• She was famous for throwing tantrums on set.
• They met on the set of 'Titanic'.
• stage right

set noun ( PART )

• I played a couple of sets with Alfie.
• He won the match by five sets to three.
• approach shot
• mixed doubles
• passing shot
• shuttlecock
• table tennis

set noun ( POSITION )

• coign of vantage
• crime scene
• multi-location
• technology park
• World Heritage Site

set noun ( TELEVISION )

• breakfast television
• ghost image
• plasma screen
• square-eyed
• the small screen phrase

set adjective ( READY )

• action stations
• at someone's beck and call idiom
• at your command idiom
• be chafing at the bit idiom
• concert pitch

set adjective ( SAME )

• average Joe
• bog-standard
• conformance
• conventionalized
• institutionalize
• regularization
• the/your average bear idiom
• unchallenging
• unextraordinary
• unspectacular

set adjective ( STUDY )

• academic year
• access course
• Advanced Placement
• asynchronous
• foundation course
• immersion course
• on a course
• open admissions
• the national curriculum
• work placement

set | American Dictionary

Set verb ( put ), set verb ( cause a condition ), set verb ( arrange ), set verb ( become fixed ), set verb ( move down ), set noun ( play background ), set adjective [not gradable] ( ready ), set adjective [not gradable] ( fixed ), set | business english, examples of set, collocations with set.

These are words often used in combination with set .

Click on a collocation to see more examples of it.

Translations of set

Get a quick, free translation!

Word of the Day

your bread and butter

a job or activity that provides you with the money you need to live

Shoots, blooms and blossom: talking about plants

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• set (POSITION)
• set (CONDITION)
• set someone/something doing something
• set someone to work
• set (ESTABLISH)
• set (GET READY)
• set into something /be set with something
• set (GIVE WORK)
• set (MUSIC)
• set (GROUP)
• set (FILM/PLAY)
• the set of something
• set (TELEVISION)
• set (READY)
• set expression/phrase
• set (STUDY)
• set (CAUSE A CONDITION)
• set (ARRANGE)
• set (BECOME FIXED)
• set (MOVE DOWN)
• set (PLAY BACKGROUND)
• set (FIXED)
• set up shop
• Collocations
• Translations
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Dictionary vs Set

This lesson will discuss the key difference between Dictionary and Set in python.

Introduction

Member functions.

Before solving any challenges regarding Hash Tables, it is necessary to look at the implementations of dict , and set and see how they are different. Both are implemented in Python. It is also a common misconception that these two structures are the same, but they are very different from each other.

dict or dictionary is a Mapping Type object which maps hashable values to arbitrary objects. It stores an element in the form of key-value pairs.

It provides the basic functionality of hashing along with some helper functions that help in the process of insertion, deletion, and search.

Some of the key features of dict are given below:

• An dict stores key-value pairs (examples given below) to map a key to the value:

a b c − > 123 abc->123 ab c − > 123

x y z − > 456 xyz->456 x yz − > 456

• dict cannot contain duplicate keys. It can, however, have duplicate values.
• dict does not store elements in any order either by the key or the value .

Note : The insert order is maintained from Python 3.7 and above.

• dict uses a hash table for its implementation. It takes the key and then maps it into the range of hash table using the hash function.
• On average, the complexity of the basic operation is O ( 1 ) O(1) O ( 1 ) . It will go up to O ( n ) O(n) O ( n ) in the worst-case.

set is a container in Python which has no duplicates. It consists of elements in no specific order. It is also built in the same way as dict , i.e., using the Hash Table, but it is still quite different from the dict .

Some of the key features of set are listed below:

• set is a container that implements the Set interface, and this interface only stores values, not a key-value pair. The value of an element will be its key at the same time.

1 − > 1 1->1 1 − > 1

a b c − > a b c abc->abc ab c − > ab c

• set does not allow storing duplicate elements as a set can only contain unique elements.

Some of the commonly used member functions of set are given below:

Some of the commonly used member functions of dict are given below:

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Set vs Dictionary Python: Understanding the Differences

Discover the nuanced differences between Python's sets and dictionaries, each offering unique advantages for managing and manipulating data.

In the realm of Python programming, data structures play a crucial role in managing and manipulating data efficiently. Two fundamental data structures, sets, and dictionaries, offer distinct functionalities that cater to different needs. Let’s delve into the differences between sets and dictionaries in Python and explore their appropriate use cases.

Sets and Dictionaries in Python: Sets in Python are unordered collections of unique elements, while dictionaries are collections of key-value pairs. Sets do not allow duplicate elements, making them ideal for tasks that involve checking for membership or eliminating duplicates. On the other hand, dictionaries provide a mapping between unique keys and corresponding values, facilitating fast lookups and efficient data retrieval.

Characteristics of Sets and Dictionaries:

• Sets: Unordered, mutable, unique elements
• Dictionaries: Unordered, mutable, key-value pairs

Usage and Appropriate Use Cases: Sets are commonly used when dealing with collections of unique elements or performing mathematical set operations like union, intersection, or difference. They excel at membership testing and eliminating duplicates from a dataset. On the other hand, dictionaries are preferred for mapping relationships between keys and values, enabling quick access to values based on unique keys.

Differences Between Sets and Dictionaries:

• Sets store unique elements.
• Dictionaries store key-value pairs.
• Sets focus on membership testing.
• Dictionaries allow access to values based on keys.
• Sets are suitable for handling collections of unique elements.
• Dictionaries are ideal for mapping relationships between keys and values.

Examples of Set and Dictionary Operations in Python:

In conclusion, understanding the differences between sets and dictionaries in Python is essential for optimizing your data management strategies. By leveraging the unique functionalities of sets and dictionaries based on your specific requirements, you can enhance your programming capabilities and efficiently handle diverse data structures in your Python projects. Experiment with sets and dictionaries to unlock their full potential and streamline your data manipulation processes effectively.

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Definition of set adjective from the Oxford Advanced Learner's Dictionary

in position

• a house set in 40 acres of parkland
• He had close-set eyes.
• The holiday homes are set in pleasant grounds.
• Their house was set back from the road.

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• Each person was given set jobs to do.
• The school funds a set number of free places.
• Mornings in our house always follow a set pattern.
• New vehicles must comply with set safety standards.

opinions/ideas

• set ideas/opinions/views on how to teach
• As people get older, they get set in their ways .
• He had very set ideas of what he wanted.
• a set dinner/lunch/meal
• Shall we have the set menu ?

likely/ready

• set for something The team looks set for victory.
• set to do something Interest rates look set to rise again.
• Be set to leave by 10 o'clock.
• Get set… Go!
• By 2050, one in six people on the planet will be aged 65 or over.
• The number of people globally aged 65 and over is expected / likely to double by 2050.
• It is predicted that the over-65s will make up 17 per cent of the global population by 2050.
• Experts have forecast that the number of people over 65 will rise to 1.6 billion by 2050.
• World population is set to reach 9.7 billion by 2050.
• Net migration into the UK over the last decade was higher than expected .
• Overall population growth in the UK has been in line with predictions .
• a set smile
• His face took on a set expression.
• Why are you so dead set against the idea?
• Her father is dead set against the marriage.
• She’s set on a career in medicine.
• He’s set on getting a new car
• The council is now set on expanding the sports centre.
• The government is now set on increasing taxes.
• used to tell runners in a race to get ready and then to start
• what you say to tell people to start a race

Other results

• set on somebody
• set about somebody
• set somebody down
• set something off
• set upon somebody
• set something out
• set somebody up
• set something up
• set something aside
• set something down
• set something forth
• set somebody back something
• set something in something
• set something into something
• set somebody against somebody
• set the bar
• set up home
• set up house
• set the pace
• set up shop
• set tongues wagging
• carved/set in stone
• set light to something
• set sail (from/for…)
• set something in train
• be set in your ways
• go/set about your work
• set foot in/on something
• set your heart on something
• set your mind on something
• set/put something in motion
• put/set the record straight
• set the seal on something
• set the stage for something
• set somebody’s teeth on edge

Nearby words

Differences Between List, Tuple, Set and Dictionary in Python

Data structures in python provide us with a way of storing and arranging data that is easily accessible and modifiable. These data structures include collections. Some of the most commonly used built-in collections are lists, sets, tuples and dictionary.

Introduction

Having a hard time understanding what Lists, tuples, sets and dictionaries are in python? Everyone who works on python at least once has been confused about the differences between them or when to use them. Well, say no more, as we'll break down these Data structure collections' differences and understand them so that we may never forget them!

Let’s take a closer look at what each of these collections are :

Key Difference Between List, Tuple, Set, and Dictionary in Python

Mutability:.

• List: Mutable (modifiable).
• Tuple: Immutable (non-modifiable).
• Set: Mutable, but elements inside must be immutable.
• Dictionary: Mutable; keys are immutable, but values can change.
• List: Maintains order of elements.
• Tuple: Maintains order of elements.
• Set: No guaranteed order.
• Dictionary: As of Python 3.7+, insertion order is preserved.

Uniqueness:

• List: Allows duplicates.
• Tuple: Allows duplicates.
• Set: Only unique elements.
• Dictionary: Unique keys, values can be duplicated.

Data Structure:

• List: Ordered collection.
• Tuple: Ordered collection.
• Set: Unordered collection.
• Dictionary: Collection of key-value pairs.

Difference Between List VS Tuple VS Set VS Dictionary in Python

Let us know more about Lists, Tuples, Sets and Dictionaries in following topics:

Lists are one of the most commonly used data structures provided by python; they are a collection of iterable, mutable and ordered data. They can contain duplicate data.

Certainly! Here are the code snippets extracted and organized with suitable subheadings for each data structure:

Adding New Element

Deleting element, sorting elements, searching elements, reversing elements, counting elements.

Tuples are similar to lists. This collection also has iterable, ordered, and (can contain) repetitive data, just like lists. But unlike lists , tuples are immutable.

Set is another data structure that holds a collection of unordered, iterable and mutable data. But it only contains unique elements.

Certainly! Here are the code snippets for the "Set" section of the table, including the Syntax and Searching Elements sections:

Unlike all other collection types, dictionaries strictly contain key-value pairs.

• In Python versions < 3.7: is an unordered collection of data.
• In Python v3.1: a new type of dictionary called ‘OrderedDict’ was introduced, which was similar to dictionary in python; the difference was that orderedDict was ordered (as the name suggests)
• In the latest version of Python, i.e. 3.7 : Finally, in python 3.7, dictionary is now an ordered collection of key-value pairs. The order is now guaranteed in the insertion order, i.e. the order in which they were inserted.

If you’re questioning if both orderedDict and dict are ordered in python 3.7. Then why are there two implementations? Is there any difference?

We can leave that for when we talk about dictionaries in detail. But until then, we should know what dictionaries are, and their purpose, as that is something that will never change.

NOTE: An ordered collection is when the data structure retains the order in which the data was added, whereas such order is not retained by the data structure in an unordered collection .

• Sets, on one hand, are an unordered collection, whereas a dictionary (in python v3.6 and before) on the other may seem ordered, but it is not. It does retain the keys added to it, but at the same time, accessibility at a specific integer index is not possible; instead, accessibility via the key is possible.
• Each key is unique in a dictionary and acts as an index as you can access values using it. But the order in which keys are stored in a dictionary is not maintained, hence unordered. Whereas python 3.7’s Dictionary and ‘OrderedDict’ introduced in python 3.1 are ordered collections of key-value data as they maintain the insertion order.

Let’s dig deeper into the differences between these collections :

Key Differences Between Dictionary, List, Set, and Tuple

• Dictionary: Uses curly brackets { } with key-value pairs separated by commas.
• List: Employs square brackets [ ] with comma-separated elements.
• Set: Utilizes curly brackets { } with comma-separated elements.
• Tuple: Employs parentheses ( ) with comma-separated elements.
• Dictionary: Maintains order in Python 3.7+ but is unordered in Python 3.6.
• List: Maintains order.
• Set: Unordered.
• Tuple: Maintains order.

Duplicate Data

• Dictionary: Keys are unique, values can be duplicated.
• List: Allows duplicate elements.
• Set: Does not allow duplicate elements.
• Tuple: Allows duplicate elements.
• Dictionary: Key-based indexing.
• List: Integer-based indexing starting from 0.
• Set: No index-based mechanism.
• Tuple: Integer-based indexing starting from 0.

Adding Elements

• Dictionary: Uses key-value pairs.
• List: New items can be added using append() method.
• Set: Uses add() method.
• Tuple: Being immutable, new data cannot be added.

Deleting Elements

• Dictionary: Uses pop(key) method to remove specified key and value.
• List: Uses pop() method to delete an element.
• Set: Uses pop() method to remove an element.
• Tuple: Being immutable, no data can be popped or deleted.
• Dictionary: Keys can be sorted using the sorted() method.
• List: Uses sort() method to sort elements.
• Set: Unordered, so sorting is not applicable.
• Tuple: Being immutable, data cannot be sorted.
• Dictionary: Uses the get(key) method to retrieve value for a specified key.
• List: Uses index() method to search and return index of first occurrence.
• Set: Unordered, so searching is not applicable.
• Tuple: Uses index() method to search and return index of first occurrence.
• Dictionary: No integer-based indexing, so no reversal.
• List: Uses reverse() method to reverse elements.
• Set: Unordered, so reversing is not advised.
• Tuple: Being immutable, reverse method is not applicable.
• Dictionary: count() not defined for dictionaries.
• List: Uses count() method to count occurrence of a specific element.
• Set: count() is not defined for sets.
• Tuple: Uses count() method to count occurrence of a specific element.
• Lists and Tuples vary in mutability as lists are mutable, whereas tuples are not.
• Set is the only unordered collection in python 3.7 .
• Dictionaries store data in the form of key-value pairs in python and remain a controversy when it comes to whether they’re ordered or unordered. As this varies with multiple versions of python. Python v<=3.6 has dictionaries as unordered, but at the same time, orderedDict was introduced in python 3.1 , and then finally python 3.7 has both orderedDict and Dictionary and now both are ordered.

Hope this information gives more clarity on what are the differences between list, tuple, set and dictionary in python. And what use cases do they serve and hope it gives you clarity on when to use which collection.

‘Set' vs 'Sit': What's the Difference?

‘Set’ and ‘sit’ sound very similar, but what’s the difference between these words? Below, we’ll go over the definition and meanings of both words. Plus, you’ll learn how to pronounce and use both words in a sentence correctly.

Need a quick answer?

Here it is:

• ‘Set’ is a verb that means to place something somewhere.
• ‘Sit’ is a transitive verb that means to be seated.

These words might look similar, but they have different meanings. So, avoid using them interchangeably in your writing.

When to Use ‘Sit’ vs. ‘Set’

As you learned , ‘ sit ’ means to be seated, and ‘ set ’ means to place something down. But you might have heard someone tell you to ‘ sit ’ something down on the table.

So, how do you know which to use and when?

• Use ‘ sit ’ when you’re referring to people.

For example, you might hear someone say:

Go over there and sit down. You’ve got too much energy!

• Use ‘ set ’ when you’re referring to objects .

We’re going to set up your new account login today.

Basically, use ‘set’ with things and ‘sit’ when it comes to people.

How to Use ‘Sit’ vs. ‘Set’ Correctly

We learned that both words are verbs , but the first one means to be seated (usually in a chair, on a couch, or on a bench).

For example:

• You ‘ sit ’ down at the table for dinner.

The second one means to place something somewhere.

For example, you might:

• ‘ S et ’ the table by setting dishes and silverware down on the table.

In popular sitcoms from the 80s and 90s, such as The Nanny and Full House , you might see the families ‘ sit ’ down to eat dinner together.

• One of them might ‘ set’ the table before everyone eats .

In the case of The Nanny , it was usually Niles, the butler, who ‘set’ the table.

Definition of ‘Set’: What Does ‘Set’ Mean?

The Merriam-Webster definition of ‘ set ’ is:

• To cause to sit (place in or on a seat).

It could also mean:

• To put (a fowl) on eggs to hatch them
• To put (egg) for hatching under a fowl or into an incubator
• To place (oneself) in a position to start running in a race
• To place with care or deliberate purpose with relative stability
• To make (a trap) ready to catch prey
• To fix (a hook) firmly into the jaw of a fish
• To put aside (something, such as dough containing yeast) for fermenting
• To direct with fixed attention
• To cause to assume a specified condition, relation, or occupation
• To cause the start of
• To appoint or assign to an office or duty
• Post or station
• To cause to assume a specified posture or position
• To fix as a distinguishing imprint, sign, or appearance
• To fix or decide as a time, limit, or regulation (prescribe)
• To establish the highest level or best performance
• To furnish as a pattern or model
• To allot as a task
• To adjust (a device and especially a measuring device) to a desired position
• To restore to normal position or connection when dislocated or fractured
• To spread to the wind
• To put in order for use
• To make scenically ready for a performance
• To arrange (type) for printing
• To put into type or its equivalent (as on film)
• To put a fine edge on by grinding or honing
• To bend the tooth points of (a saw) slightly alternately in opposite directions
• To fix in a desired position (as by heating or stretching)
• The act or action of setting
• Direction of flow
• The manner of fitting or of being placed or suspended
• Intent, determined
• Intentional, premeditated

Phrases Containing ‘Set’

• Set foot on
• Set eyes on
• Set forward
• Set in motion
• Set one’s heart on
• Set one’s sights on
• Set one straight
• Set the stage
• Set to music

Definition of ‘Sit’: What Does ‘Sit’ Mean?  

The same dictionary defines ‘ sit ’ as:

• To rest on the buttocks or haunches.
• Perch, roost
• To occupy a place as a member of an official body
• To hold a session (be in session for official business)
• To cover eggs for hatching (brood)
• To take a position for having one’s portrait painted or for being photographed
• To serve as a model
• To lie or hang relative to a wearer
• To affect one with or as if with weight
• To have a location
• Of wind: to blow from a certain direction
• To remain inactive or quiescent
• To take an examination
• To please or agree with one (used with and an adverb)
• To cause to be seated (place on or in a seat – often used with down )
• To sit on (eggs)
• To keep one’s seat on
• To provide seats or seating room for
• The manner in which a garment fits
• An act or period of sitting

Phrases Containing ‘Sit’

• Sit on one’s hands

Pronunciation: How to Pronounce ‘Set’ and ‘Sit’

Are you wondering how to pronounce these words?

Here’s a short guide.

To pronounce ‘ set ’ correctly, here’s the phonetic spelling:

To pronounce ‘ sit ’ correctly, here’s the phonetic spelling:

How to Use ‘Set’ and ‘Sit’ in a Sentence  

Now that you know what the words mean and how to pronounce them, let’s see some examples of how to use them in sentences.

• Can you set those brightly colored plates down on that table over there? I need to start getting everything ready for the Mommy and Me Luncheon.
• We were just about to help you get everything set up for the assembly. Do you think we need more chairs on stage for the speakers?
• Let’s get your new account set up. We’re so glad you’ve decided to partner with our company. I just know that we’re going to do great things together.
• We have a set of China I think you’d love . Come with me, and we can take a look at a few sets we have in stock. They’re a bit on the higher end, but that’s not an issue, right?
• I don’t like the way this dress sits on me. I think I should try another one. I need to see some other options, please.
• We don’t have to sit here . This is a big theater , and no one else is here. Let’s go to the back and get the best seats at the top.
• Can we sit down for a minute? We’ve been shopping sales all day long. I’m tired, and I think I need some food .
• My teacher always tells us to sit down because we’re constantly getting out of our seats to do things.

Final Thoughts on ‘Set’ and ‘Sit’

To recap, we learned the following:

• ‘ Set ’ is a verb that means to place something somewhere.
• ‘ Sit ’ is a transitive verb that means to be seated.

If you ever get stuck on anything, feel free to come back here to review what you learned. We’ve also got a ton of other content on confusing words and phrases. You might find it helpful as you’re learning the language. Go check it out anytime.

Learn More:

• 'Sit in a Chair' or 'Sit on a Chair': Which is Correct?
• 'Assure' vs. 'Ensure' vs 'Insure': What's the Difference?
• ‘Sale’ or ‘Sail’: What’s the Difference?
• ‘Sell’ or ‘Sale’: What’s the Difference?
• 'All Is' vs 'All Are': Which is Correct
• 'Imitated' vs 'Intimated': What's the Difference?
• ‘Threw' vs 'Through': What's the Difference Between the Two?
• 'Appraise' vs 'Apprise': What's the Difference?
• ‘Emigrate' vs 'Immigrate': What's the Difference?
• 'Hoping' vs 'Hopping': What's the Difference?
• ‘Prove' vs 'Proof': What's the Difference Between the Two?
• ‘Right’ vs ‘Write’ vs ‘Rite’ vs ‘Wright’: What’s the Difference?
• ‘Knew’ vs ‘New’: What’s the Difference?
• 'Farther' vs 'Further': What's the Difference?
• ‘For’ vs ‘Four’ vs ‘Fore’: What’s the Difference Between Them?

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Set in Math – Definition, Types, Properties, Examples

What is a set, elements of a set, types of sets, solved examples, practice problems, frequently asked questions.

We commonly use the terms like ‘a complete set of novels’ or ‘a set of cutlery’ in day-to-day life. What do we mean by the term ‘set’ here? It simply defines a collection of objects or things of the same type. Sets in math are also defined in the similar context.

Set Definition

In mathematics, a set is defined as a collection of distinct, well-defined objects forming a group. There can be any number of items, be it a collection of whole numbers, months of a year, types of birds, and so on. Each item in the set is known as an element of the set. We use curly brackets while writing a set.

Consider an example of a set.

$\text{A} = \left\{1, 3, 5, 7, 9\right\}$.

It has five elements. It is a set of odd numbers less from 1 to 10.

What do we mean by ‘well-defined’ objects?

Consider an example. A collection of odd natural numbers less than 20 is defined, but a collection of brave students in a class is not defined.

We can represent a collection of odd natural numbers less than 20 in the form of a set as

$\text{B} = \left\{1, 3, 5, 7, 9, 11, 13, 15, 17, 19\right\}$. 

The number of elements in the set are denoted by n(A) where A is a set. 

Example: $\text{A} = \left\{1, 4, 9, 16, 25, 36, 49, 64, 81, 100\right\}$.

$n(A) = 10$. 

The other word used for the number of elements in the set is called its cardinality. 

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Elements or members are the terms or items present in a set. They are enclosed in curly brackets and separated by commas. To represent that an element is contained in a set, we use the symbol “$\in$.” It is read as ‘belongs to.’

Suppose we have a set of even natural numbers less than 10.

$\text{A} = \left\{2, 4, 6, 8\right\}$ .

Here, $2 \in A$ but $3 \notin A$.

Representation of Sets

We represent the sets in different ways. The only difference is in the way in which the elements are listed. The different forms of representing sets are discussed below.

Roster Form

The most familiar and easy form used to represent sets is the roster form, in which the elements are enclosed in curly brackets and are separated by commas such as $\text{B} = \left\{1, 4, 9, 16, 25\right\}$, which is the collection of the square of consecutive numbers less than 30. The order of the elements does not matter and there can be an infinite number of elements in a set, which we define using a series of dots at the end of the last element. There are two types of sets in Roster Form:

Finite Roster Notation of Sets in which there are elements that can be counted, such as $\text{A} = \left\{5, 10, 15, 20, 25\right\}$ (The multiples of 5 less than 30.)

Infinite Roster Notation of Sets in which the elements can not be counted, such as $\text{B} = \left\{4, 8, 12, 16 …\right\}$ (The multiples of 4)

Set Builder Form

The set builder notation has a particular rule that describes the common feature of all the elements of a set. It uses a vertical bar in its representation along with a text describing the character of the elements, such as $\text{A} = \left\{ \text{x}\; |\; \text{x} \; \text{is a prime number}, x \le 20\right\}$. According to the statement, all the elements of the set are prime numbers less than or equal to 20. We use “:” place of the “|” sometimes. 

Let’s discuss different types of sets. 

Singleton Sets

When a set has only one element, it is known as a singleton set.

Set $\text{A} = \left\{ \text{x}\; |\; \text{x}\; \text{is a whole number between}\;12\; \text{and}\;14\right\} = \left\{13\right\}$.

Null or Empty Sets

When a set does not contain any element, it is known as a null or an empty set. It is denoted by the symbol “$\Phi$” and it is read as “phi.” 

Set $\text{B} = =$ Integers between 1 and $2 = \Phi$

Two sets are said to be equal if they have the same elements in them. Suppose there are two sets $\text{A} = \left\{1, 4, 5\right\}$ and $\text{B} = \left\{1, 4, 5\right\}$. Here, $\text{A} = \text{B}$ because each element is the same. 

Unequal Sets

Two sets are said to be unequal if they have at least one different element. Suppose we have two sets $\text{A} = \left\{1, 2, 5\right\}$ and $\text{B} = \left\{1, 2, 4\right\}$. Here, $\text{A} \neq \text{B}$ as $5 \in \text{A}$ but $5 \notin \text{B}$.  

Equivalent Sets

Equivalent sets are the two sets that have the same number of elements, even if the elements are different. Suppose we have two sets $\text{A} = \left\{10, 11, 12, 13\right\}$ and $\text{B} = \left\{January, February, March, April\right\}$. Since $n(A) = n(B)$, A and B are equivalent sets. 

Overlapping Sets

If at least one element from set A is present in set B, then the sets are said to be overlapping. Example: $\text{A} = \left\{2, 3, 6\right\} \text{B} = \left\{6, 8, 12\right\}$. 6 is present in set A and set B. So, A and B are overlapping sets.

Subset and Superset

If every element in set A is also present in set B, then set A is known as the subset of set B, which is denoted by $\text{A} \subseteq \text{B}$ and B is known as the superset of set A, which is denoted by $\text{B} \supseteq \text{A}$.

Example: $\text{A} = \left\{1, 4, 7, 10, 12\right\}\; \text{B} = \left\{1, 4, 6, 7, 8, 10, 11, 12, 13\right\}$

$\text{A} \subseteq \text{B}$, since all the elements of A are present in B.

Also, set B is the superset of set A.

Universal Set

The collection of all the elements in regard to a particular subject is known as a universal set which is denoted by the letter “U.” Suppose we have a set U as the set of all the natural numbers. So, the set of even numbers, set of odd numbers, set of prime numbers is a subset of the universal set.

Disjoint Sets

Two sets are known as disjoint sets if they have no common elements in both sets. Consider two sets – $\text{A} = \left\{5, 6, 7\right\}$ and $\text{B} = \left\{2, 3, 4\right\}$. Here, set A and set B are disjoint sets as they have no elements in common. 

The set of all subsets that a set could contain is known as the power set. Suppose we have a set $\text{A} = \left\{2, 3\right\}$. Power set of A is $= \left\{\left\{\varnothing\right\}, \left\{2\right\}, \left\{3\right\}, \left\{2,3\right\}\right\}$.

If n is the number of elements in a set, then the number of subsets $=2^{n}$.

Visual Representation of Sets Using Venn Diagram

The pictorial representation of sets represented as circles is known as the Venn diagram. The elements of the sets are inside the circles. The rectangle that encloses the circles represents the universal set. The Venn diagram represents how the sets are related to each other. 

Operations on Sets

There are some operations on sets given below: 

Union of Sets

B. Suppose we have two sets $\text{A} = \left\{1, 2, 3\right\}$ and $\text{B} = \left\{3, 4, 5\right\}$

$\text{A}\; \text{U}\; \text{B} = \left\{1, 2, 3, 4, 5\right\}$

Intersection of Sets

The intersection of sets is denoted by $\text{A} \cap \text{B}$ has the elements which are common in both set A and set B. Suppose we have two sets $\text{A} = \left\{1, 3\right\}$ and $\text{B} = \left\{3, 4\right\}$

$\text{A} \cap \text{B} = {3}$

Difference of Sets

We denote the set difference by $\text{A} – \text{B}$, which has the elements in set A that are not present in set B. Suppose we have two sets, i.e.,  $\text{A} = \left\{3, 4, 5\right\}$ and $\text{B} = \left\{5, 6, 7\right\}$

$\text{A} \;–\; \text{B} = \left\{3, 4\right\}$

Complement of a Set

The complement of a set A is denoted by A’, which is the set of all elements in the universal set that are not present in set A. A’ can also be represented as $\text{U} \;–\; \text{A}$, i.e., the difference in the elements of the universal set and set A.

Suppose $\text{U} =$ Set of Natural Numbers and $\text{A} =$ Set of Prime Numbers

So, $\text{U} \;–\; \text{A} =$ Set of all Non-prime Numbers.

Sets Formulas

There are some set formulas that we can use to find the number of elements. 

For sets A and B,

• $n(A\; U\; B) = n(A) + n(B) – n(A \cap B)$
• $n(A − B) = n(A U B) − n(B)$
• $n(A − B) = n(A) − n(A \cap B)$

Properties of Sets

Here are the properties of sets:

1. How many elements are there in the set $\text{A} = \left\{ \text{x}\; : \text{x}\; \text{is a perfect square less than 30}\right\}$ ?

Solution: $\text{A} = \left\{1, 4, 9, 16, 25\right\}$

2. Arrange the set $A = \left\{ y : y^{2} = 36 ; y\; \text{is an integer}\right\}$ in roster form.

Solution: $y^{2} = 36 \Rightarrow y^{2} − 36 = 0 \Rightarrow y = \pm 6$

$\text{A} = { –\; 6, 6}$

3. Write the set $\text{B} = \left\{1, 2, 5, 10, 17\right\}$ in set builder form.

Solution: $0^{2} + 1 = 1$

$1^{2} + 1 = 2$

$2^{2} + 1 = 5$

$3^{2} + 1 = 10$

$4^{2} + 1 = 17$

So, in roaster form $\text{B} = \left\{y : y^{2} + 1, y \lt 5\right\}$ 

4. If A is a set of prime numbers and B is a set of even numbers. What will be $\text{A} \cap \text{B}$ ?

Solution: Only 2 is the number, which is a prime number as well as an even number. So,  $\text{A} \cap \text{B} = {2}$.

5. Draw a Venn diagram for the sets $\text{A} = \left\{1, 3, 6, 9, 11, 15, 17\right\}$ and $\text{B} = \left\{2, 4, 9, 11, 13, 17\right\}$ . 

Solution: 

What is a Set in Math

Attend this quiz & Test your knowledge.

Which of the following sets denotes $\left\{\right\}$?

If $\text{a} = \left\{\;–\; 1, 0, 2, 3, 5, 7\right\}$ and $\text{b} = \left\{0, 1, 2, 3, 5, 6\right\}$, then what is $\text{a}\; \text{u}\; \text{b}$, if $\text{p} = \left\{ \;–\; 10, \;–\; 7, \;–\; 4, \;–\; 3, \;–\; 2, \;–\; 1\right\}$ and $\text{q} = \left\{ \;–\; 9, \;–\; 8, \;–\; 7, \;–\; 6, \;–\; 4, \;–\; 2\right\}$ then __ denotes $\left\{ \;–\; 10, \;–\; 3, \;–\; 1\right\}$, how many subsets will be there if $n(a) = 3$ where a is a set, if $n(a)$ = $16,n (b) = 18$ and $n(a \cup b) = 7$, then what is the value of $n(a \cup b)$.

What are sets formula if sets are disjoint?

For disjoint sets A and B;

• $n(A U B) = n(A) + n(B)$
• $A \cap B = \varnothing$
• $n(A − B) = n(A)$

Is {0} a null set ?

No. There is one element inside the brackets. So, it is a singleton set, not a null set.

What is a Cartesian Product in sets?

Cartesian Product of Set A and B is defined as an ordered pair $(x, y)$ where $x \in A$ and $y \in B$.

How is set theory applicable in daily lives?

In real life, sets are used in bookshelves while arranging the books according to alphabetic order or genre; closets where dresses, tops, jeans are kept as a set, etc.

Does the union of two sets include the intersection of the sets?

Yes, the union of two sets includes the intersection of the sets. Union of set A and B includes the elements either in set A or in set B or in both set A and B.

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Python Set VS List – Sets and Lists in Python

In Python, set and list are both data structures for storing and organizing any values. Those values could be numbers, strings, and booleans.

In this article, we'll look at the differences between set and list . But before that, let's take a look at what both set and list are.

What We'll Cover

What is a python set , how to create a set in python, what is a python list , how to create a list in python, what is the difference between a set and a list.

A set is a collection of unordered and unique values. The values in a set are unique because there cannot be any duplicates.

The items in a set are also immutable – you can't change them. But you can still add and remove from the collection.

In short, a set stores multiple values in curly braces or inside the set() constructor.

To create a set in Python, you can use the set() constructor or curly braces.

Set with the set() constructor:

Notice I used two parentheses to create the list. That's because the set() constructor expects one argument. Putting all the values in another set of parentheses makes all the values a single argument.

The set can also contain multiple data types – strings, numbers, or booleans:

You can also create a set with curly braces like this:

And you can include multiple data types in a set created with curly braces:

A list is a variable for storing multiple values in Python. It's one of the built-in data structures in Python along with sets, tuples, and dictionaries. If you're familiar with JavaScript, a Python list is like a JavaScript array.

You can create a Python list with the list() constructor or square brackets:

Sets and lists are built-in data structures you can use to store and arrange values in Python.

If you're wondering which to use, it depends on the use case. If you don’t want the values in the data to change, you can use a set. But if you want the items to change, you can use a list. You can also take into account whether the order of the items matters to you or not.

That's why this article took you through what set and list are, how to create them, and most importantly the differences between the two of them.

Thanks for reading.

Web developer and technical writer focusing on frontend technologies. I also dabble in a lot of other technologies.

If you read this far, thank the author to show them you care. Say Thanks

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AT&T says a data breach leaked millions of customers’ information online. Were you affected?

FILE - The sign in front of an AT&T retail store is seen in Miami, July 18, 2019. The theft of sensitive information belonging to millions of AT&T’s current and former customers has been recently discovered online, the telecommunications giant said Saturday, March 30, 2024. In an announcement addressing the data breach, AT&T said that a dataset found on the dark web contains information including some Social Security numbers and passcodes for about 7.6 million current account holders and 65.4 million former account holders. (AP Photo/Lynne Sladky, File)

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NEW YORK (AP) — The theft of sensitive information belonging to millions of AT&T’s current and former customers has been recently discovered online, the telecommunications giant said this weekend.

In a Saturday announcement addressing the data breach, AT&T said that a dataset found on the “dark web” contains information including some Social Security numbers and passcodes for about 7.6 million current account holders and 65.4 million former account holders.

Whether the data “originated from AT&T or one of its vendors” is still unknown, the Dallas-based company noted — adding that it had launched an investigation into the incident. AT&T has also begun notifying customers whose personal information was compromised.

Here’s what you need to know.

WHAT INFORMATION WAS COMPROMISED IN THIS BREACH?

Although varying by each customer and account, AT&T says that information involved in this breach included Social Security numbers and passcodes — which, unlike passwords, are numerical PINS that are typically four digits long.

Full names, email addresses, mailing address, phone numbers, dates of birth and AT&T account numbers may have also been compromised. The impacted data is from 2019 or earlier and does not appear to include financial information or call history, the company said.

HOW DO I KNOW IF I WAS AFFECTED?

Consumers impacted by this breach should be receiving an email or letter directly from AT&T about the incident. The email notices began going out on Saturday, an AT&T spokesperson confirmed to The Associated Press.

WHAT ACTION HAS AT&T TAKEN?

Beyond these notifications, AT&T said that it had already reset the passcodes of current users. The company added that it would pay for credit monitoring services where applicable.

AT&T also said that it “launched a robust investigation” with internal and external cybersecurity experts to investigate the situation further.

HAS AT&T SEEN DATA BREACHES LIKE THIS BEFORE?

AT&T has seen several data breaches that range in size and impact over the years .

While the company says the data in this latest breach surfaced on a hacking forum nearly two weeks ago, it closely resembles a similar breach that surfaced in 2021 but which AT&T never acknowledged, cybersecurity researcher Troy Hunt told the AP Saturday.

“If they assess this and they made the wrong call on it, and we’ve had a course of years pass without them being able to notify impacted customers,” then it’s likely the company will soon face class action lawsuits, said Hunt, founder of an Australia-based website that warns people when their personal information has been exposed.

A spokesperson for AT&T declined to comment further when asked about these similarities Sunday.

HOW CAN I PROTECT MYSELF GOING FORWARD?

Avoiding data breaches entirely can be tricky in our ever-digitized world, but consumers can take some steps to help protect themselves going forward.

The basics include creating hard-to-guess passwords and using multifactor authentication when possible. If you receive a notice about a breach, it’s good idea to change your password and monitor account activity for any suspicious transactions. You’ll also want to visit a company’s official website for reliable contact information — as scammers sometimes try to take advantage of news like data breaches to gain your trust through look-alike phishing emails or phone calls.

In addition, the Federal Trade Commission notes that nationwide credit bureaus — such as Equifax, Experian and TransUnion — offer free credit freezes and fraud alerts that consumers can set up to help protect themselves from identity theft and other malicious activity.

AP Reporter Matt O’Brien contributed to this report from Providence, Rhode Island.

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Difference between set() and frozenset() in Python

Learn the difference between set() and frozenset() function in Python.

Python provides two built-in functions which are set() and frozenset(). These two functions are used for creating sets but come with a few differences. Let’s see how you can use them.

Python set() ¶

A set is an unordered and unindexed collection of unique elements. Sets are mutable, you can change the elements using a built-in function like add(), remove(), etc. Since the elements are mutable and not in order, they don’t have hash values. So you can’t access the elements with the help of index numbers.

Note: Sets can’t be used as a dictionary key or as elements of another set. They can be used as a dictionary value.

Set is represented by curly braces like this {} or you can use set() . You can’t use only curly braces to create an empty set, this will create a dictionary. You can use set() if you want to create an empty set. Sets can include any immutable data type like string, number, tuple, etc. You can also include mutable data type like list, dictionary, etc.

Let’s go through some examples and see some of the operations you can perform on sets:

The output of the above code is as follows:

In the above example, some of the built-in functions have been used. There exists two functions remove() and discard() which help to remove the element from the set. They both remove the element from the set if there is an element present in the set but there is a difference between them.

If the element is not in the set which you want to remove then discard() returns none while remove() will raise an error. You can learn more about the operations from their official documentation .

Python frozenset() ¶

A frozenset is an unordered and unindexed collection of unique elements. It is immutable and it is hashable. It is also called an immutable set. Since the elements are fixed, unlike sets you can't add or remove elements from the set.

Frozensets are hashable, you can use the elements as a dictionary key or as an element from another set. Frozensets are represented by the built-in function which is frozenset() . It returns an empty set if there are no elements present in it. You can use frozenset() if you want to create an empty set.

Let's go through some examples to understand more about frozenset:

The above example shows you can't add a new element to the frozenset.

Let's see how can use a dictionary with frozenset:

Let's see other operations that you can perform on frozenset, you can also perform these operations on normal sets:

You can learn more about the operations from their official documentation .

Conclusion ¶

So far we have learned about sets and frozensets. We have also learned about the operations that you can perform on sets and frozensets. We have also learned about the difference between sets and frozensets. You can learn more about them from their official documentation .

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