For deletion: D2, D3, D4, D5, D6, D7, D8

Terrible self-answer to a mathematically senseless question, even excluding the silly self-promotion. (See the user's profile for more.)

^^ @Did @XanderHenderson @JoséCarlosSantos @RRL

@rschwieb @Did @XanderHenderson @RRL: Take note of yet another circular answer.

D1, D2, D3.

D4, D5, D6.

D7, D8, D9.

D10, D11, D12.

D13, D14.

C1, C2, C3.

C4, C5, C6.

C7, C8, C9.

Too broad, too.

@XanderHenderson I voted "too broad", but I think it's a fair question whether there are systematic or heuristic ways to find a proof if it exists. (Though that was not really the question, which was about a timed exam...)

(Ways that are better than just trying all possibilities, of course.)

And from the logic viewpoint of course there is, but it's too difficult to explain hahahah.

@user21820 I'm certain that example for that user has come up already in this room, but of course I have no way of remembering who brought it up :) i'm amazed it's still standing...

@user21820 Is the accepted answer any better? I haven't bothered to think through what proofs depend on what proofs, but using "basic properties" to prove other "basic properties" (as Rhys did) is an approach prone to circularity, I think...

@rschwieb The accepted answer is no better, but you know it has so many upvotes that it's impossible to get rid of it. I had downvoted it a long time ago as well.

In my opinion, only Acccumulation's answer is the best, despite not really addressing the question... Next best is Fred's, which is correct but fails to point out the fundamental error in the question (of not specifying what kind of animal x is).

C1, C2, C3, C4

@DevashishKaushik Hmm why did you ask for close-votes if you didn't vote to close them?

@user21820 Well, Fred's answer does actually prove it and Naman Kumar seems to provide some intution, but I agree- the overall quality of the answers is appalling and the OP seems to have put in no thought before asking.

@user21820 I don't have enough rep.

@DevashishKaushik Oh! That's a pity.

@DevashishKaushik It's good that Fred's answer is near the top. But Naman's answer is wrong. (−1)^4 = 1 is not equivalent to log[−1](1) = 4, even if you make senes of the latter.

@user21820 Yeah, we do need to provide proper restrictions and everything, so in the strictest sense, it is incorrect. Still, it would be useful for developing understanding.

@DevashishKaushik I agree we need to provide intuition. Though I emphasize that it is pointless to propagate the common sloppiness, because as you can see it is precisely that sloppiness that causes such questions in the first place.

If a answer was carefully written and covered both approaches, it would be useful, but then this kind of thing is probably best for textbooks, classroom discussions and blogs - not MSE.

@user21820 Agreed

@DevashishKaushik Agreed. Though some flavour of both intuition and rigour probably can be achieved satisfactorily even in Math SE. In fact, I've written on exponentiation here and at the posts linked from there. It's a pity high-school textbooks often don't do things rigorously.

@user21820 I am not a logician, but I appreciate that there is probably a nugget of a good, well refined question in there. However, it is tagged real analysis, so I don't think that this is what was being asked.

@XanderHenderson Oh it was? Sorry didn't see that.

@user21820 Yeah, it has a mass of tags, all of which indicate that the asker is struggling with homework in an introductory upper div math class (i.e. baby's first proof!). The asker doesn't have the maturity to ask about, for example, provability.

Okay... I really need to get to work...

Ok see you!

This silly answer can be deleted now (at last).

one more vote on this: math.stackexchange.com/a/3111137/29335

@JoséCarlosSantos: Done

For deletion: DA, DB, DC, DD, DE, DF, DG, DH

For undeletion: U1

@darijgrinberg Why?

reasonable question, good answer

@darijgrinberg Q is missing context IMO - second sentence is the only one that can show asker's efforts (assuming it is not copied)

it's still a reasonable question you can easily come up with (and will probably get reposted one day)

theory tells you that Z_n has nontrivial idempotents, so looking for them is natural

For deletion: DI, DJ, DK

Close or should we hope for a miracle that makes this one clear?

@darijgrinberg This Q has more potential that the previous one you suggested.

if someone edits it to make any sense :)

@darijgrinberg Is it better?

not really

still not clear what "the theorem not work" means here

@darijgrinberg U1 is ok IMHO, voting to undelete. It might be a copy (a special case rather) of this but I'm obviously not gonna vote it as such (and calling it a dupe is a stretch).

psq math.stackexchange.com/q/3113173/29335

@darijgrinberg Hmm... the question doesn't seem to contain one iota of research effort/context. It's nice that a good answer showed up, but then again the ethics of complete answers for PSQ's are questionable. It doesn't seem to fit our guidelines.

I think it's the answer that matters here.

I don't mind killing 1-liners in response to PSQs, but a lot of knowledge has been collected in PSQ answers.

Particularly back in times where there was no consensus on PSQs (if there is any now).