###### Definition1.7.2Set-Builder Notation

Set-builder notation attempts to directly say the condition that numbers in the interval satisfy. In general, write set-builder notation like:

\begin{equation*} \left\{x\mid\text{condition on }x\right\} \end{equation*}and read it out loud as “the set of all \(x\) such that ….” For example,

\begin{equation*} \left\{x\mid x\geq18\right\} \end{equation*}is read out loud as “the set of all \(x\) such that \(x\) is greater than or equal to \(18\text{.}\)” The breakdown is as follows.

\(\highlight{\{}\lowlight{x\mid x\geq18}\highlight{\}}\) | the set of |

\(\lowlight{\{}\highlight{x}\lowlight{{}\mid x\geq18\}}\) | all \(x\) |

\(\lowlight{\{x}\highlight{{}\mid{}}\lowlight{x\geq18\}}\) | such that |

\(\lowlight{\{x\mid{}}\highlight{x\geq18}\lowlight{\}}\) | \(x\) is greater than or equal to \(18\) |