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I was wondering about the use of latex symbols \implies ($\implies$) and \therefore ($\therefore$). From the naming, I think \therefore and \implies are redundant, but I can't find a symbol for \suchthat and at university, we used $\therefore$ as a shortcut for "such that".

Question is: what should I use for what I pronounce "therefore", and what for "such that"?

Edit: as from the comments, I think I really have to clarify that my intention was to use those symbols I asked to use inside of formulas, and $\neg$ to intersperse common language with it. Good n8 $\to\forall$ of U.

(Some of you must have had really traumatic experiences with the misuse of symbols.)

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    $\begingroup$ Words. You should use words. $\endgroup$ Commented Jan 9, 2016 at 15:54
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    $\begingroup$ The bigger achievement is to see when to use symbols and when words. The right mixture of words and symbols makes things readable. $\endgroup$ Commented Jan 9, 2016 at 15:59
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    $\begingroup$ You should use the ASCII symbols "$\text{therefore}$" and "$\text{such that}$". You can even omit the LaTeX part and just write "therefore" and "such that". $\endgroup$
    – Asaf Karagila Mod
    Commented Jan 9, 2016 at 16:20
  • $\begingroup$ $\therefore$ means "therefore", and therefore it should never be used to mean "such that". And $\therefore$ is quite different from $\implies$, which means "implies" and is a verb. $\endgroup$
    – TonyK
    Commented Jan 9, 2016 at 16:26
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    $\begingroup$ "$A \therefore B\;$" means that $A$ is true, and therefore $B$ is true. "$A \implies B\;$" means that if $A$ is true, then $B$ is true. I am sure you see the difference now. $\endgroup$
    – TonyK
    Commented Jan 9, 2016 at 16:40
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    $\begingroup$ Downvotes on meta usually signify disagreement (which is very different from their meaning on the main site). On this question I would interpret downvotes to mean "please don't do that" (please don't use a symbol in place of the words "therefore" and "such that"). $\endgroup$ Commented Jan 9, 2016 at 17:29
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    $\begingroup$ @GyroGearloose I would prefer that proofs have a few explanatory words, rather than be a forest of notation. I've seen many undergrads who, upon learning a bit of elementary set theory and notation, completely give up on writing words in their mathematics; that is a bad habit. $\endgroup$
    – user296602
    Commented Jan 9, 2016 at 17:42
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    $\begingroup$ My impression of your question was that you were asking about using those symbols in paragraphs, rather than in set builder notation. If you're asking about the latter then it would help if you edited your question to clarify. $\endgroup$ Commented Jan 9, 2016 at 17:58
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    $\begingroup$ @GyroGearloose the actual vote count is +3/-3 $\endgroup$
    – Surb
    Commented Jan 10, 2016 at 12:59
  • $\begingroup$ @GyroGearloose If you wish to, you can drop me a line in chat. I have tried to explain my comments a bit better. (Of course, feel free to ignore it if you don't think that there is a need to continue the discussion. Sorry for pinging you on an unrelated post but, well, it is not possible to add a comment to a post which is deleted.) $\endgroup$ Commented Jan 24, 2016 at 4:05
  • $\begingroup$ These symbols should really only be used on blackboards, to save visual space and class time. They have no formal meaning, and one should use words. $\endgroup$ Commented Aug 11, 2022 at 0:55
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    $\begingroup$ One of my teachers, when writing on the blackboard, used "s.t." for "such that". Furthermore, that is easier to type than any LaTeX symbol. $\endgroup$
    – GEdgar
    Commented Aug 11, 2022 at 11:16

1 Answer 1

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There are multiple symbols commonly used to represent "such that"

  1. $\backepsilon$ \backepsilon or $\ni$ \ni
  2. $\mid$ \mid
  3. $:$ :

For "therefore", I usually see $\therefore$ \therefore

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    $\begingroup$ Why not \ni for the backwards $\in$? $\endgroup$
    – Asaf Karagila Mod
    Commented Jan 9, 2016 at 20:05
  • $\begingroup$ @AsafKaragila: $\ni$ is bigger than I usually see for "such that", but I guess one might include that in the multiple symbols. $\endgroup$
    – robjohn Mod
    Commented Jan 9, 2016 at 20:27
  • $\begingroup$ To add to this, I often jut get away with the "|" character for 'such that'. try shift on the "\" key $\endgroup$ Commented Jan 10, 2016 at 4:31
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    $\begingroup$ My personal experience with these symbols is that "|" is only readable as "such that" in class builders, i.e. $\{x\in A\mid P(x)\}$ is read "the set of x in A such that P of x", and ":" is only readable as such that in an existence quantifier, i.e. $\exists x\in A:P(x)$ is "there exists an x in A such that P of x" (and that last one is more commonly written with a comma or space instead). I've never seen $\backepsilon$ in use like this. Could you use it in a sentence(-like utterance)? $\endgroup$ Commented Jan 11, 2016 at 20:58
  • $\begingroup$ @MarioCarneiro Riffing off your remark: the use of : in something like $$\exists x{\in}A:P(x)\to Q(y)$$ complicates things, because it makes me wonder about the scope of the "such that"; on the other hand, without the colon, the conventional way to read the formula is simply $$[\exists x{\in}A\:P(x)]\to Q(y).$$ And of course, in something like $$\forall x{\in}A:P(x),$$ the colon doesn't even mean "such that". $\endgroup$
    – ryang
    Commented Aug 11, 2022 at 10:23
  • $\begingroup$ For"such that" I have see the backwards $\in$ with longer horizontal, $$⋺$$ Unicode calls it "CONTAINS WITH LONG HORIZONTAL STROKE" $\endgroup$
    – GEdgar
    Commented Aug 11, 2022 at 11:20

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