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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?

Thanks in advance.

SBF
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GuiRitter
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    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
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    I've never seen something like '' used for that purpose. – hmakholm left over Monica 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
  • @Siminore: Twas my point ;-) I also know of people who use “/” even when typesetting. – PseudoNeo Aug 16 '12 at 15:02
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    I have seen "/" used first time in my life very recently. – timur Aug 16 '12 at 15:20
  • I first saw this use of ‘/’ here; I find it rather disconcerting. – Brian M. Scott Aug 16 '12 at 19:25
  • @PseudoNeo: I actually meant '', as in backslash. – GuiRitter Aug 16 '12 at 20:30
  • Thanks for all of the answers, but the one that better reassured me was @Mark Dominus'. I'm terrified of teachers that present us with their own version of things and make it look like they're standard. This was not the case though. It was more like "this symbol is also used". Perhaps he meant a '|' that got inclined when written, instead of the '' character. Which is contradictory, since things get inclined to the other side in handwriting. Go figure. Glad I got this one clear: either ':' or '|' are the most common. – GuiRitter Aug 17 '12 at 00:18
  • I didn't want to post it as an answer because there's a lot of stuff I haven't seen that nevertheless exists. – MJD Aug 17 '12 at 01:56
  • I use a semicolon, like so: ${x ∈ X;; φ(x)}$. A professor of mine did so and I adapted this as well because it looks good and the semicolon is almost never used in any other way (as opposed to “$|$” or “$:$”). – k.stm Feb 13 '14 at 14:55

2 Answers2

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

anegligibleperson
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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.

Francis Adams
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  • 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???" – Emily Aug 16 '12 at 15:06
  • I have seen it used and have used it myself. But now I prefer just "s.t." in sentences and the vertical bar in set-forming brackets. – timur Aug 16 '12 at 15:11
  • Read also http://math.stackexchange.com/questions/15455/backwards-epsilon – Siminore Aug 16 '12 at 15:20
  • Apart from the use as given above in the definition of a set, I am against replacing words such as "such that" by symbols. But I not a logician! – Ronnie Brown Aug 16 '12 at 16:46
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    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
  • what is the latex for the backwards element of? – Francis Adams Aug 16 '12 at 19:35
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    @Francis $\ni $ is \ni , as in \in backwards. You can also right-click any formula here and have it shown as LaTeX. –  Aug 17 '12 at 04:43
  • For abbreviating such that, I have a professor who likes to use the dollar sign $$$. He says it looks like the letters s and t superimposed. I actually got used to it really quickly. – Christian Mann Jan 31 '14 at 09:12