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In computer science, a set is an abstract data type that can store unique values, without any particular order. It is a computer implementation of the mathematical concept of a finite set. Unlike most other collection types, rather than retrieving a specific element from a set, one typically tests a value for membership in a set.
Python sets are very much like mathematical sets, and support operations like set intersection and union. Python also features a frozenset class for immutable sets, see Collection types. Dictionaries (class dict) are mutable mappings tying keys and corresponding values. Python has special syntax to create dictionaries ({key: value})
Here, the list [0..] represents , x^2>3 represents the predicate, and 2*x represents the output expression.. List comprehensions give results in a defined order (unlike the members of sets); and list comprehensions may generate the members of a list in order, rather than produce the entirety of the list thus allowing, for example, the previous Haskell definition of the members of an infinite list.
All values of x for which the predicate holds (is true) belong to the set being defined. All values of x for which the predicate does not hold do not belong to the set. Thus {()} is the set of all values of x that satisfy the formula Φ. [3] It may be the empty set, if no value of x satisfies the formula.
In Python, == compares by value. Python's is operator may be used to compare object identities (comparison by reference), and comparisons may be chained—for example, a <= b <= c. Python uses and, or, and not as Boolean operators. Python has a type of expression named a list comprehension, and a more general expression named a generator ...
A set of polygons in an Euler diagram This set equals the one depicted above since both have the very same elements.. In mathematics, a set is a collection of different [1] things; [2] [3] [4] these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other ...
Python's tuple assignment, fully available in its foreach loop, also makes it trivial to iterate on (key, value) pairs in dictionaries: for key , value in some_dict . items (): # Direct iteration on a dict iterates on its keys # Do stuff
Here is a nonempty set, and is a set for every . In the case that the index set I {\displaystyle I} is the set of natural numbers , notation analogous to that of an infinite product may be seen: ⋂ i = 1 ∞ A i . {\displaystyle \bigcap _{i=1}^{\infty }A_{i}.}