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. $\endgroup$ – Daniel Fischer Jan 9 '16 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. $\endgroup$ – Daniel Fischer Jan 9 '16 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 Jan 9 '16 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 Jan 9 '16 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 Jan 9 '16 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"). $\endgroup$ – Antonio Vargas Jan 9 '16 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 Jan 9 '16 at 17:42
  • $\begingroup$ 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. $\endgroup$ – Antonio Vargas Jan 9 '16 at 17:58
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    $\begingroup$ Question marks must come cheap where you live :) $\endgroup$ – Antonio Vargas Jan 9 '16 at 18:12
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    $\begingroup$ @GyroGearloose the actual vote count is +3/-3 $\endgroup$ – Surb Jan 10 '16 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.) $\endgroup$ – Martin Sleziak Jan 24 '16 at 4:05

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 $\therefore$

  • $\begingroup$ Why not \ni for the backwards $\in$? $\endgroup$ – Asaf Karagila Jan 9 '16 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 Jan 9 '16 at 20:27
  • $\begingroup$ To add to this, I often jut get away with the "|" character for 'such that'. try shift on the "\" key $\endgroup$ – frogeyedpeas Jan 10 '16 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)? $\endgroup$ – Mario Carneiro Jan 11 '16 at 20:58
  • $\begingroup$ Please delete your answer so I can delete my (ill received) question. $\endgroup$ – Gyro Gearloose Jan 22 '16 at 22:17

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