Set-Builder Notation

A shorthand used to write sets, often sets with an infinite number of elements.

Note: The set {x : x > 0} is read aloud, "the set of all x such that x is greater than 0." It is read aloud exactly the same way when the colon : is replaced by the vertical line | as in {x | x > 0}.

General Form:	{formula for elements: restrictions} or {formula for elements| restrictions}
Examples:	{x: x ≠ 3}	the set of all real numbers except 3
	{x | x < 5}	the set of all real numbers less than 5
	{x2 | x is a real number}	the set of all real numbers greater than or equal to 0
	{2n + 1: n is an integer}	the set of all odd integers (e.g. ..., -3, -1, 1, 3, 5,...).

 

See also

Interval notation, real numbers, integers, cardinality