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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. Thus there is a variable on the left of the ...
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 ...
This notation is called set-builder notation (or "set comprehension", particularly in the context of Functional programming). Some variants of set builder notation are: {x ∈ A | P(x)} denotes the set of all x that are already members of A such that the condition P holds for x. For example, if Z is the set of integers, then {x ∈ Z | x is ...
In set-builder notation, it is used as a separator meaning "such that"; see { | }. 3. Restriction of a function : if f is a function , and S is a subset of its domain , then f | S {\displaystyle f|_{S}} is the function with S as a domain that equals f on S .
Shqip; سنڌي ... Educational media awards (6 P) C. ... Pages in category "Educational materials" The following 61 pages are in this category, out of 61 total.
More generally, a collection of any sets whatsoever is called a family of sets, set family, or a set system. Additionally, a family of sets may be defined as a function from a set , known as the index set, to , in which case the sets of the family are indexed by members of . [1]
Universe set and complement notation The notation L ∁ = def X ∖ L . {\displaystyle L^{\complement }~{\stackrel {\scriptscriptstyle {\text{def}}}{=}}~X\setminus L.} may be used if L {\displaystyle L} is a subset of some set X {\displaystyle X} that is understood (say from context, or because it is clearly stated what the superset X ...
Naive set theory is the original set theory developed by mathematicians at the end of the 19th century, treating sets simply as collections of things. Axiomatic set theory is a rigorous axiomatic theory developed in response to the discovery of serious flaws (such as Russell's paradox ) in naive set theory.