Set-Builder Notation
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High Quality Content by WIKIPEDIA articles! In set theory and its applications to logic, mathematics, and computer science, set-builder notation (sometimes simply set notation) is a mathematical notation for describing a set by stating the properties that its members must satisfy. Forming sets in this manner is also known as set comprehension, set abstraction or as defining a set's intension. Let (x) be a formula in which x appears free. Set builder notation has the form {x : (x)} (some write {x (x)}, using the vertical bar instead of the colon), denoting the set of all individuals in the univ...
High Quality Content by WIKIPEDIA articles! In set theory and its applications to logic, mathematics, and computer science, set-builder notation (sometimes simply set notation) is a mathematical notation for describing a set by stating the properties that its members must satisfy. Forming sets in this manner is also known as set comprehension, set abstraction or as defining a set's intension. Let (x) be a formula in which x appears free. Set builder notation has the form {x : (x)} (some write {x (x)}, using the vertical bar instead of the colon), denoting the set of all individuals in the universe of discourse satisfying the formula (x), that is, the set whose members are every individual x such that (x) is true: formally, the extension of the predicate. Set builder notation binds the variable x and must be used with the same care applied to variables bound by quantifiers.
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