###### 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 $$18$$
in-context