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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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Why would you want a symbol as opposed to just saying the words themselves? – J. M. Sep 1 '11 at 22:30
I know firsthand the fever from which this user suffers: the desire to have everything in an authoritative symbolic format. Of course, it's not very useful to have formal symbols for desiderata, unless one wants to somehow approach mathematics from a design-by-contract-programming style. – Niel de Beaudrap Sep 1 '11 at 23:05
@J. M., @Niel de Beaudrap: I am a lexicographer and simply enjoy symbols. Mathematics has a particularly rich and varied inventory of them. I'm especially interested in those that have not yet made their way into standard encodings or that compete with more standard symbols. For instance, an S with a stroke through the lowermost section, for "suppose", or a reversed \in symbol (\owns in LaTeX) for "such that". – brannerchinese Sep 1 '11 at 23:38
When I become Dictator of Notation, my first decree will be to ban the usage of \owns to mean such that. Be warned! – Mariano Suárez-Alvarez Sep 2 '11 at 1:24
@Asaf: even if I had made a handwritten copy of Joyce's Ulysses in classical Mongolian script, that would not change the fact that it is notationally criminal to assign two different meanings to such similar notations! Compare $a\in A$, $A\owns a$, $1<2$ and $2>1$. – Mariano Suárez-Alvarez Sep 2 '11 at 14:50

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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As much as I like reputation points, please don't up-vote this answer. I was just amused by the idea of submitting it. ;-) – Niel de Beaudrap Sep 1 '11 at 23:36
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. – Zev Chonoles Sep 1 '11 at 23:38
@Zev Chonoles: thanks for reminding me. – Niel de Beaudrap Sep 1 '11 at 23:39
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. :) – Srivatsan Sep 1 '11 at 23:40
@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. – Niel de Beaudrap Sep 1 '11 at 23:46

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)

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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?

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I cannot see how this answers the question... – Mariano Suárez-Alvarez Sep 2 '11 at 1:23
@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. – Doug Spoonwood Sep 2 '11 at 1:26

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.

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What do you write when you want to find something? :) – t.b. Sep 2 '11 at 2:56
@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. – mixedmath Sep 2 '11 at 3:01
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... – t.b. Sep 2 '11 at 3:06
@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. – mixedmath Sep 2 '11 at 3:12

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