set-builder notation

== English == === Noun === set-builder notation (set theory) A mathematical notation for describing a set by specifying the properties that its members must satisfy. 2011, Tom Bassarear, Mathematics for Elementary School Teachers, Cengage Learning, 5th Edition, page 56, In this case, and in many other cases, we describe the set using set-builder notation: Q = { a b | a ∈ I a n d b ∈ I , b ≠ 0 } {\displaystyle Q=\left\{{\frac {a}{b}}\vert \ a\in I\ \mathrm {and} \ b\in I,\ b\neq 0\right\}} This statement is read in English as "Q is the set of all numbers of the form a b {\displaystyle {\frac {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 ∈ i n t e g e r s } {\displaystyle \left\{x\vert x>-3,\ x\in \mathrm {integers} \right\}} === Further reading === Set-builder notation on Wikipedia.Wikipedia Intension on Wikipedia.Wikipedia "Set-Builder Notation" in Mathwords.