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Set-Builder Notation


Set-builder notation specifies a set by a property satisfied by its elements. The expression

 {x in A:P(x)}

denotes the subset of A consisting of precisely those x for which the predicate P(x) is true. The restriction x in A supplies an ambient set and avoids treating an unrestricted condition as though it automatically defined a set. A vertical bar is also commonly used in place of the colon between an element and its condition.


See also

Set

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References

Halmos, P. R. Naive Set Theory. New York: Springer-Verlag, 1974.

Cite this as:

Weisstein, Eric W. "Set-Builder Notation." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Set-BuilderNotation.html

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