TITLE: Notation for "such that" on a set-builder notation
QUESTION [0 upvotes]: 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.

REPLY [1 votes]: 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, $\{ x/y \ / \ 1/xy < 10 \}$.
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