standard symbol for "to prove" or "need to show" in proofs?
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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$\begingroup$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).
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)
$\endgroup$ $\begingroup$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?
$\endgroup$ 3 $\begingroup$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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