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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.
A snippet of Python code with keywords highlighted in bold yellow font. The syntax of the Python programming language is the set of rules that defines how a Python program will be written and interpreted (by both the runtime system and by human readers). The Python language has many similarities to Perl, C, and Java. However, there are some ...
A "value set" K is defined as a set of pairs, each pair consisting of a value and a set of dependent conditions. The set of dependent conditions is used by the "condition function", to determine if the value set takes that value. The condition function is defined by 3 axioms,
Executing a set of statements only if some condition is met (choice - i.e., conditional branch) Executing a set of statements zero or more times, until some condition is met (i.e., loop - the same as conditional branch) Executing a set of distant statements, after which the flow of control usually returns (subroutines, coroutines, and ...
In classical mathematics, characteristic functions of sets only take values 1 (members) or 0 (non-members). In fuzzy set theory, characteristic functions are generalized to take value in the real unit interval [0, 1], or more generally, in some algebra or structure (usually required to be at least a poset or lattice).
Python uses an English-based syntax. Haskell replaces the set-builder's braces with square brackets and uses symbols, including the standard set-builder vertical bar. The same can be achieved in Scala using Sequence Comprehensions, where the "for" keyword returns a list of the yielded variables using the "yield" keyword. [6] Consider these set ...
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As a result, there can be only one set with no elements, hence the usage of "the empty set" rather than "an empty set". The only subset of the empty set is the empty set itself; equivalently, the power set of the empty set is the set containing only the empty set. The number of elements of the empty set (i.e., its cardinality) is zero. The ...