# Set-builder notation: is there another symbol for “such that”?

My teacher is teaching us about sets, and he said that the '|', the ':' and the '\' symbols can be used to mean 'such that'. I'm certain of the first two, but I searched a little and couldn't find reference to the last. Does it exist for this purpose? If it's a special character, what Unicode code point does it have?

-
I've never seen it used that way, and I've read a fair amount of obscure historical material about set theory that uses obsolete notation. – MJD Aug 16 '12 at 14:36
I've never seen something like '\' used for that purpose. – Henning Makholm Aug 16 '12 at 14:36
@HenningMakholm: I guess the OP meant “/”. – PseudoNeo Aug 16 '12 at 14:43
@PseudoNeo While writing by hand, sombody writes $/$ instead of $\mid$ to denote the vertical bar. Probably because it is easier to write :-) – Siminore Aug 16 '12 at 14:57
I have seen "/" used first time in my life very recently. – timur Aug 16 '12 at 15:20

We usually use ":" and "|", as in $\{ x \in \mathbb{R} : x > 0\}$. Hope that answers your question.

-

I had a professor use a backwards "element of ($\in$) " sign to stand for "such that". He's the only one I've seen do it, and it very well could be unique to him. But there are probably many people with their own unique, preferred symbols. I wasn't a fan of it, so I stick to the basic ":" and "|", depending on how many other vertical lines are in the set description.

-
As far as I know, the "correct" symbol should be $\ni'$: the formula $(\exists x) \ni' (x>0)$ is sometimes read "there is an $x$ such that $x>0$. – Siminore Aug 16 '12 at 14:56
But surely he didn't write it as $\{ x\in X \ni \varphi(x)\}$? That would be extremely confusing. – tomasz Aug 16 '12 at 14:59
I also have seen the backwards element sign used. I used it in an assignment sometime thereafter, and got lots of comments from the grader saying "what the heck does this mean???" – Arkamis Aug 16 '12 at 15:06
I’ve been familiar with $\owns$ for such that for decades, but it’s not common, and I don’t recommend it. If I’m writing at the board, with space and and time at a premium, I prefer s.t. For sets I much prefer the colon. – Brian M. Scott Aug 16 '12 at 19:24
@Francis $\ni$ is \ni , as in \in backwards. You can also right-click any formula here and have it shown as LaTeX. – user31373 Aug 17 '12 at 4:43