**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}.

{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 | |

x^{2} | x is a real number} | the set of all real numbers greater than or equal to 0 | |

n + 1: n is an integer} | the set of all odd integers (e.g. |

**See also**

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