@amWhy @Did @Jack @SimplyBeautifulArt @Xam @LeakyNun @MartinSleziak: Please help! This and this are utter rubbish. We're going to need all the downvotes we can throw at them to be able to delete them.
@user21820 I wonder whether the latter might be actually useful - if the comment saying that this is circular were more visible. Basically what I am saying is that L'Hospital might be the first idea that comes to mind for many users. If they see somewhere that this is incorrect and why, that is useful information.
So I wouldn't mind the L.H. answer to stay if it is clearly marked that it is incorrect with explanation why. (For example, starting by EDIT: This is actually circular, because ....)
There are occasions when the use of l'Hopital is circular. E.g., when using l'H on $$\lim_{x\to0}{\sin x\over x}$$ you have to differentiate $\sin x$, but to differentiate $\sin x$, you have to evaluate $\lim_{x\to0}{\sin x\over x}$.
@user21820 That sounds like a reasonable link for this purpose, adding it both to the question and to the answer seems like a reasonable thing to do. (A question on the main would be even better - I will be busy today, so I do not have much time for searching.)
@user21820 Just one more comment on rewarding the poster. I do see upvotes/downvotes mainly as tool to help showing how useful post is, whether it is correct etc. - not mainly as a reward for the poster. (Which is why I downvoted this one after your ping.) In this case - as you probably know - even if the answer is deleted, the OP keeps the reputation gain from this answer.
@MartinSleziak As I said I do not agree with editing that wrong answer. We've been through this kind of issue many times. While you prefer editing an incorrect answer to make it correct, I prefer deleting it to send a strong signal that nonsense is not tolerated on Math SE. I think the deletion is sufficient despite the reputation being kept for posts with score ≥ 3.
I do agree that your rationale (upvotes for showing usefulness rather than for rewarding poster) is consistent with your actions.
As I said, I'm going to be busy today (and probably during the weekend). If I don't forget (and if the answer is not deleted by then) I will look again at this issue.
I reacted to the part about rewarding the OP mainly to mention that even after deletion they keep the reputation - but I assume you know that, this was mentioned a few times here.
As for the first link, I did not actually look at that one, so I'll reserva my judgement after I read it.
This shows how addictive this site is - I should head for work and since I am travelling this evening, I should make sure I do not forget anything I need to take with me. Yet, I did not resist checking whether there is something new in chat. :-)
I should probably try to change my focus a bit - less activity in meta and janitorial rooms; more time spent asking and answering math questions. Fingers crossed. (Sorry for veering off to things which are off-topic in this room.)
@Did @Xam @amWhy: Unless I'm seriously mistaken, this and this are totally bogus answers and should be deleted. Unfortunately, the asker failed to notice the logical errors.
@user170039 This is basic logic. The question is using a convention common to many textbooks that I severely dislike, for pedagogical reasons, but you have to be aware of it; namely that phrasing means "∀t∈R ∀a,b∈N ( t^2 = at+b ⇒ t^3 ≠ ? )". It should then be clear why those two answers are bogus while Robert Israel's answer is correct.
If it's not clear what I dislike, it is the use of the word "let" for universal quantification, since the quantified object may not exist, and since they also use it for existential instantiation such as "Let δ = min(1,sqrt(ε))." and for definitions such as "Let #(S) be the minimum ordinal k such that there is a bijection from k to S."
@user21820 The question itself is difficult to decipher since it mixes English and mathematical symbols in a way that makes it impossible (at least, to me) to determine what the hypothesis really is. (And anyway, what can the sentence "Then, for any choice of $a,b\in \mathbb{N}$." (note the period at the end) even mean?)
@Did Blame the text (or asker's transcription errors) from which that question came. However, I've given 3 comments up the only natural interpretation of that question.
The question's logical structure is actually clearer than the grammar makes it look, because of the use of "never" and "any".
Maybe the asker wanted to mean something like the following: "Let $t^2=at+b$ with $t \in \mathbb{R}$ and $a,b\in \mathbb{N}$. Then, for any choice of $c,d\in \mathbb{N}$. Then $t^3$ is never equal to..."
@user21820 That's why I said "Maybe the asker wanted to mean something like the following..." and not something like "The asker meant something like the following...".
@user170039 It's not possible for the asker to mean what you suggested because c,d are not used anywhere. And the fact that Robert and Raffaele both understood the question in exactly the same way as I did (and are familiar with abstract algebra unlike the other two and the asker) shows something.
@user170039: Oh and note that Robert Z just deleted his answer after my comment.
user131753
@user21820 Robert Israel also used $c,d$ in his answer.
@user170039 Please read his answer carefully. If you do not understand abstract algebra, please refrain from criticizing it. His interpretation is exactly the same as mine.
user131753
@user21820 I don't understand where in my comments you find me criticizing him. If you do not understand what I mean, please refrain from criticizing it without understanding it first.
@user170039 You claim "Robert Israel also used $c,d$ in his answer" as if it is the same kind of c,d as in your comment on the question.
That is wrong.
user131753
3:58 PM
@user21820 What do you mean by "the same kind" here? Do you mean that $c,d$ here are integer variables in Robert's answer and not in my suggested modification of OP's question?
You said you thought the question could mean "Let t^2=at+b with t∈R and a,b∈N. Then, for any choice of c,d∈N. Then t^3 is never equal to...". This is definitely not what Robert Israel is answering to. He is answering to my interpretation of the question. I will not entertain any further doubt about that.
user131753
@user21820 Anyway, I don't find your interpretation to be convincing either (possibly my mistake but since you won't entertain any further doubt about "that", let's just stop here).
There are occasions when the use of l'Hopital is circular. E.g., when using l'H on $$\lim_{x\to0}{\sin x\over x}$$ you have to differentiate $\sin x$, but to differentiate $\sin x$, you have to evaluate $\lim_{x\to0}{\sin x\over x}$.
