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I am looking for the 'such that' symbol in set theory. I don't know what it's called so I'm not sure how to look for it. For the moment, I am just using this '|'. What is the appropriate symbol?

Henry B.
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2 Answers2

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\mid, as it has the spacing of a binary relation. If you want it to resize, see “How to automatically resize the vertical bar in a set comprehension?”.

Have a look at “How to look up a math symbol?” for ideas how you can easily find a particular symbol.

Community
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Caramdir
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    If you want the vertical bar to resize, it's better, spacing-wise, to use (inside a macro, to avoid unnecessary typing) \left\{ x \in X \mathrel{}\middle|\mathrel{} x > \frac{1}{2}\right\} as mentioned in http://tex.stackexchange.com/questions/5502 – Philippe Goutet Dec 01 '10 at 09:42
  • Actually it is probably best to use the bracket package suggested by Will in the link above. – Caramdir Dec 02 '10 at 03:23
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    The problem with the bracket package is that it fiddles with the spacing in ways that may not be wanted. For example, it inserts medium space on the inside as if you typed \{\: and \:\}. This will not look good in a context like \{ x \mid x \neq 0 \}/\{x > 0\}. – Philippe Goutet Dec 03 '10 at 17:44
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Some authors use the symbol \ni (∋) (for example, Pinter's Set Theory).

tdj
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Jim
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    How is this symbol closer to the existing answer? Could you specify a context in which your suggestion has the meaning of a "such that" symbol in set theory? – cryingshadow Jan 31 '16 at 19:01
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    Hi Jim, welcome to the site! This answer is not actually correct, I don't believe. I think the OP is looking for the symbol that looks like | whereas \ni produces ∋. Not a good match at all. Do you know, I think you might be right that ∋ can be used for a similar sort of purpose, but I don't think it's the one the OP is after here. Please have a little look at the tour and perhaps visit the help centre to learn more about the site :) – Au101 Jan 31 '16 at 19:02
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    @Au101 That seems a bit unfair given that the question asked what the appropriate symbol was. I realise that it mentioned | as a workaround, but that leaves open the possibility that any standard symbol would be acceptable. So this seems reasonable to me, even if the other answer is the one the OP wanted. So long as this is a symbol for this, this is a reasonable solution. – cfr Apr 09 '16 at 02:04
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    @Au101 Though this may have been less clear when you commented - I think the edit makes the position clearer. As it currently stands, I don't think this should be deleted, though. – cfr Apr 09 '16 at 02:06
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    Hey @cfr, I guess it depends how you read the OP. I thought the OP meant, at the moment I'm typing | but I'm not sure that's the correct way to produce the symbol. Kinda like how we don't use ... we use \dots and we don't use 1. Foo \\ 2. Bar, we use an enumerate environment. And, indeed, | has incorrect spacing and, on its own, won't scale. So I guess I read the question as, I'm using a pipe but maybe there's a syntactically different such that symbol, like we don't use \Sigma for \sum – Au101 Apr 09 '16 at 02:15
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    So I don't really think the OP wanted any acceptable such that symbol, I think they had a clear one in mind, the one that looks like |, but the OP wasn't sure of the name and whether that was the correct way to produce the symbol in LaTeX, maybe the real symbol is slightly different, taller, maybe, or with serifs, maybe. But that's open to interpretation I guess :) Did I flag this post for deletion? If so, that was probably a little hasty, but the edit really has made all the difference hasn't it? :) – Au101 Apr 09 '16 at 02:16
  • @Au101 I guess my thought is that as an answer to the question this may be useful to other users even if it isn't what the OP had in mind. So it makes the thread of more general use. But, yes, I think the edit has made all the difference and I didn't realise that when I first commented. (I don't know who flagged it for deletion. Just it was flagged that way earlier and now it is not. So all is well.) – cfr Apr 09 '16 at 02:44
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    Pinter uses : not | for “such that” in set builder notation but uses ∋ for “such that” in proofs. – lukejanicke Jan 17 '21 at 05:15