Set-builder notation

$\{n\mid \exists k\in \mathbb {Z} ,n=2k\}$

The set of all even integers,
expressed in set-builder notation.

In mathematics and more specifically in set theory, set-builder notation is a notation for specifying a set by a property that characterizes its members.^[1]

Specifying sets by member properties is allowed by the axiom schema of specification. This is also known as set comprehension and set abstraction.

^ Rosen, Kenneth (2007). Discrete Mathematics and its Applications (6th ed.). New York, NY: McGraw-Hill. pp. 111–112. ISBN 978-0-07-288008-3.

[1] Rosen, Kenneth (2007). Discrete Mathematics and its Applications (6th ed.). New York, NY: McGraw-Hill. pp. 111–112. ISBN 978-0-07-288008-3.

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