Meanings
- mathematicsA mathematical notation for describing a set by specifying the properties that its members must satisfy.
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."
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 notation2 more 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.
2000, Kenneth E. Hummel, Introductory Concepts for Abstract Mathematics, CRC Press (Chapman & Hall/CRC), page 1232012, 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
Cite this entry
set-builder notation. (n.d.). In WatkinsX Dictionary. Retrieved November 2, 2026, from https://dictionary.watkinsx.com/word/set-builder%20notation
“set-builder notation.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/set-builder%20notation. Accessed November 2, 2026.
WatkinsX Dictionary, s.v. “set-builder notation,” accessed November 2, 2026, https://dictionary.watkinsx.com/word/set-builder%20notation.
Source: set-builder notation on Wiktionary, CC BY-SA 4.0.