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This article lists mathematical properties and laws of sets, involving the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations.
Numeric literals in Python are of the normal sort, e.g. 0, -1, 3.4, 3.5e-8. Python has arbitrary-length integers and automatically increases their storage size as necessary. Prior to Python 3, there were two kinds of integral numbers: traditional fixed size integers and "long" integers of arbitrary size.
In mathematics, two sets or classes A and B are equinumerous if there exists a one-to-one correspondence (or bijection) between them, that is, if there exists a function from A to B such that for every element y of B, there is exactly one element x of A with f(x) = y. [1] Equinumerous sets are said to have the same cardinality (number of ...
Intersection (set theory) – Set of elements common to all of some sets; Iterated binary operation – Repeated application of an operation to a sequence; List of set identities and relations – Equalities for combinations of sets; Naive set theory – Informal set theories; Symmetric difference – Elements in exactly one of two sets
The empty set is a subset of every set (the statement that all elements of the empty set are also members of any set A is vacuously true). The set of all subsets of a given set A is called the power set of A and is denoted by 2 A {\displaystyle 2^{A}} or P ( A ) {\displaystyle P(A)} ; the " P " is sometimes in a script font: ℘ ( A ...
In mathematics, the symmetric difference of two sets, also known as the disjunctive union and set sum, is the set of elements which are in either of the sets, but not in their intersection. For example, the symmetric difference of the sets { 1 , 2 , 3 } {\displaystyle \{1,2,3\}} and { 3 , 4 } {\displaystyle \{3,4\}} is { 1 , 2 , 4 ...
Set-builder notation can be used to describe a set that is defined by a predicate, that is, a logical formula that evaluates to true for an element of the set, and false otherwise. [2] In this form, set-builder notation has three parts: a variable, a colon or vertical bar separator, and a predicate.
Set is the prototype of a concrete category; other categories are concrete if they are "built on" Set in some well-defined way. Every two-element set serves as a subobject classifier in Set. The power object of a set A is given by its power set, and the exponential object of the sets A and B is given by the set of all functions from A to B.