set

we define a set $\text{[math]}$ to be any unordered collection of objects, e.g., $\text{[math]}$ is a set. if $\text{[math]}$ is an object, we say that $\text{[math]}$ is an element of $\text{[math]}$ or $\text{[math]}$ if $\text{[math]}$ lies in the collection; otherwise we say that $\text{[math]}$ . for instance, $\text{[math]}$ but $\text{[math]}$ .
[cite:;taken from @tao_analysis_1 chapter 3 set theory]

let $\text{[math]}$ be a set. for any object $\text{[math]}$ , and any object $\text{[math]}$ , suppose we have a statement $\text{[math]}$ pertaining to $\text{[math]}$ and $\text{[math]}$ , such that for each $\text{[math]}$ there is at most one $\text{[math]}$ for which $\text{[math]}$ is true. then there exists a set $\text{[math]}$ , such that for any object $\text{[math]}$ ,
$\text{[math]}$ [cite:@tao_analysis_1]