Notation for "such that" on a set-builder notation

Question

This may be a really simple question to answer, but I need to know, with references to prove my affirmation, that the actual notation for "such that" on a set builder notation is the colon or vertical line, but not the oblique line. Can anybody help me with some reference for this notation? Thank you very very much.

Answer 1

Both $\vert$ and $:$ are used.
$\vert$ perhaps, being the most historical.
For clarity of notation, $:$ is preferred.
For example imagine using $\vert$ in the definition of $\{ x : |x| < 5 \}$.

Though I don't know the source of the recent amateurish use of /, it is to be avoided since it is not accepted, causes confusion and lacks notational clarity. For example, $\{ x/y \ / \ 1/xy < 10 \}$.