Meaning of set-builder notation | Babel Free

Definitions

A mathematical notation for describing a set by specifying the properties that its members must satisfy.

Examples

“With this idea for describing a finite set of sets, it is easy to generalize the concept to a certain infinite family #92;mathcal#123;S#125;#95;2 of sets #92;mathcal#123;S#125;#95;2#61;#92;#123;A#95;i#92;verti#92;inN#92;#125;#61;#92;#123;A#95;1,A#95;2,A#95;3,#92;dots,A#95;n,#92;dots#92;#125;. Once again, the power of set builder notation triumphs. The sets #92;mathcal#123;S#125;#95;1 and #92;mathcal#123;S#125;#95;2 may be described more precisely with set builder notation than by enumeration.”

“Q=a/b|a∈Iandb∈I,b ne 0 This statement is read in English as "Q is the set of all numbers of the form a/b such that a and b are both integers, but b is not equal to zero."”

“2012, Richard N. Aufmann, Joanne Lockwood, Intermediate Algebra, Cengage Learning, 8th Edition, page 6, A second method of representing a set is set-builder notation. Set-builder notation can be used to describe almost any set, but it is especially useful when writing infinite sets. In set-builder notation, the set of integers > −3 is written x|x>-3,x∈integers”

CEFR level