Backwards epsilon

I believe the most common usage is "such that".

This seems to agree.

While this pdf seems to indicate a growing trend in using it as "contains as an element".

Historically, it was first used to mean "such that" (see the second pdf link above).

The backwards epsilon notation for "such that" was introduced by Peano in 1898, e.g. from Jeff Miller's Earliest Uses of Various Mathematical Symbols:

Such that. According to Julio González Cabillón, Peano introduced the backwards lower-case epsilon for "such that" in "Formulaire de Mathematiques vol. II, #2" (p. iv, 1898).

Peano introduced the backwards lower-case epsilon for "such that" in his 1889 "Principles of arithmetic, presented by a new method," according van Heijenoort's From Frege to Gödel: A Source Book in Mathematical Logic, 1879--1931 [Judy Green].

I have always used $\ni$ to represent "such that." Many times people do not use this notation though; rather, they use s.t. or just say "such that."

Also, you can see that Wikipedia uses the ":" notation, which is also correct; however, I usually only use that notation when in curly brackets (ie { }).

You can visit [1] to see an actual discussion of it in a list of mathematical symbols.

This was a very good question, by the way.

[1] http://www.math.ucdavis.edu/~anne/WQ2007/mat67-Common_Math_Symbols.pdf