I am looking for the 'such that' symbol in set theory. I don't know what it's called so I'm not sure how to look for it. For the moment, I am just using this '|'. What is the appropriate symbol?
\mid, as it has the spacing of a binary relation. If you want it to resize, see “How to automatically resize the vertical bar in a set comprehension?”.
Have a look at “How to look up a math symbol?” for ideas how you can easily find a particular symbol.
Some authors use the symbol
\ni (∋) (for example, Pinter's Set Theory).