As someone currently majoring in mathamatics, I can honestly say this is the first time I have seen ":" used in this way. The "standard" way I would expect to s

As someone currently majoring in mathamatics, I can honestly say this is the first time I have seen ":" used in this way. The "standard" way I would expect to see that would be for the first ":" to be replaced with a "|", and the second one to be replaced with a "," (or omitted entirely). The third ":" does not look out of place, although I would probably omit it, or right it as "st". EDIT: for clarity, I would right the set as: "{f : [1..N ⟶ 1..N] | ∀ y ∈ 1..N , ∃ x ∈ 1..N st f[x]=y}" The ":" in this case indicates that f has the indicated type. As long as I am commenting on my sense of "standard" notation, I should also note that the "[1..N ⟶ 1..N]" notation also seems weird (as in, I have never seen it before). I would expect it to be written as [1..N] ⟶ [1..N]. Perhaps replacing [1..N] with Z_n for the appropriate audience; however the speaker seems to be aware that this is a strange notation, as he commented about it in the beginning. In this particular case, I would probably also omit the entire predicate in favor of writing "onto" above "⟶", which I can do because the particular property being described is common enough to have a name; however this would defeat the point of showing the notion. Once I have entirely omitted the predicate like this, I would probably omit naming f entirely, giving the notation {[1..N] ⟶ [1..N]} (again, with "onto" written above the arrow). Actually, depending on audience, in this particular case I would replace the entire set with either "The symmetric group of order n", "The symmetric group S_n", or just "S_n". The f[x] notation looks a bit weird out of context, but does come up when the distinction between a function and a function application is important (often times f(x) is used as a convention to remind the reader that f is a function)