Is there a standard symbol used as shorthand for "to prove" or "need to show" in a proof? I've seen "N.T.S." but was wondering if there is anything more abstract — not bound to English.
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asked Sep 1, 2011 at 22:24
4 Answers
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Serious answer.
There isn't an actual symbol for this, at least not one in common usage.
Almost serious answer.
In published mathematics, you will usually find statements that one wants to prove (or must prove, etc.) prefaced by the symbols Lemma, Theorem, or Proposition (sometimes accompanied by a sequence of arabic numerals or roman letters denoting a serial number of sorts).
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2$\begingroup$ As much as I like reputation points, please don't up-vote this answer. I was just amused by the idea of submitting it. ;-) $\endgroup$ Commented Sep 1, 2011 at 23:36
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$\begingroup$ If you would like, I can convert the answer to "community wiki" mode, which will prevent your account from gaining any reputation from it, regardless of votes. $\endgroup$ Commented Sep 1, 2011 at 23:38
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$\begingroup$ @Zev Chonoles: thanks for reminding me. $\endgroup$ Commented Sep 1, 2011 at 23:39
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1$\begingroup$ I don't get your answer. Don't Theorem, Lemma etc. mean something that you have already proven? My feeling was that the OP wants is some notation to replace "Suffices to show that". In second thought, the wording is not clear enough. :) $\endgroup$ Commented Sep 1, 2011 at 23:40
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$\begingroup$ @Srivatsan Narayanan: they often occur before the proof, however. Chronologically, at the time of publication, they have already been shown; but in the narrative of the article or textbook, usually they are a proclamation of intent to show something later (possibly immediately). I imagine this as an opening delimiter: a Necesse Demonstrare to complement the Quod Erat Demonstrandum. $\endgroup$ Commented Sep 1, 2011 at 23:46
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Less serious answer: The most common notation is quite long, appears usually as "$\text{need to show}$".
More serious answer: One of my teachers used $\boxtimes$ for whenever he left us the proof as an exercise.
I am unaware of a standard notation for that, mostly because this is something that ought to be extremely clear. Not a hidden symbol that would get lost amidst the text. When I read a mathematical text I want to be certain which points the writer skipped and left out, for me or for himself.
For that reason I would strongly advise to avoid these sort of symbols in any, but very informal settings. (To make things compatible with how my teacher did it - we were only four people in the class, and it was quite informal)
answered Sep 1, 2011 at 23:38
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Somewhat serious answer:
If you haven't actually shown something, and want to show it, you or someone else has conjectured it. So, you simply don't know if it qualifies as provable or you don't have it in context as provable, which you need for your reader. The conjecture might even qualify as incorrect (though, incorrect conjectures, as conjectures, still can have great value). And even if someone else has proven it, you haven't proven it in the context of what you're writing where it needs to get proved. Consequently, the appropriate symbol here would be the question mark "?" So, even if it's not standard, it seems like it should, don't you think?
answered Sep 2, 2011 at 1:16
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$\begingroup$ I cannot see how this answers the question... $\endgroup$ Commented Sep 2, 2011 at 1:23
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$\begingroup$ @Mariano That seems fair. However, if there does not exist an answer to this question, the author might still want to find an appropriate symbol for such (I don't understand the motivation here, but that's beside the point). This answer tries to indicate why "?" would work as an appropriate symbol, assuming no convention exists. $\endgroup$ Commented Sep 2, 2011 at 1:26
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$\begingroup$ i think '?' would be a good symbol for the purpose $\endgroup$ Commented Dec 14, 2021 at 6:31
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I routinely use WTS for "Want to Show" - and most teachers and professors that I have come across immediately understood what it meant. I do not know if this is because they were already familiar with it, or if it was obvious to them. But I still use it all the time.
I got this from a few grad students at my undergrad, although a very funny internet commentator (Sean Plott, if you happen to know him) once mentioned that he uses it as well.
answered Sep 2, 2011 at 2:43
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1$\begingroup$ What do you write when you want to find something? :) $\endgroup$– t.b.Commented Sep 2, 2011 at 2:56
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$\begingroup$ @Theo I reference Sean Plott because he was complaining that a certain online community he was involved in routinely used WTS for "What the S**t" - and he was very confused. $\endgroup$– davidlowryduda ♦Commented Sep 2, 2011 at 3:01
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$\begingroup$ Ah, I see. So I must have read between the lines unconsciously. I'm unfamiliar with that guy and a glance at Wikipedia tells me why... $\endgroup$– t.b.Commented Sep 2, 2011 at 3:06
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$\begingroup$ @Theo: Yes, a relic of my youthful days... we moved in opposite directions - he was once a math major, but stopped. Now I do only math. $\endgroup$– davidlowryduda ♦Commented Sep 2, 2011 at 3:12
Swith a stroke through the lowermost section, for "suppose", or a reversed\insymbol (\ownsin LaTeX) for "such that". $\endgroup$\ownsto mean such that. Be warned! $\endgroup$