tea.mathoverflow.net - Discussion Feed (Why people downvote the only correct answer?)

Anixx comments on "Why people downvote the only correct answer?" (14344)

Anixx — Sat, 30 Apr 2011 02:29:01 -0700

In fact I do not think this question has much point. The very fact that differentiation in respect to a constant gives infinity just says: if you change the constant only a bit, anything else will change infinitely". I think this is the case here. If you change Pi by just a small margin, all other things will still change infinitely.

sean tilson comments on "Why people downvote the only correct answer?" (14342)

sean tilson — Fri, 29 Apr 2011 20:15:52 -0700

Another possible reason people down-voted your answer is that it totally misses the point of the question. I don't want to argue about it, it seems like the point was made quite clear in the comments on your answer.

Anixx comments on "Why people downvote the only correct answer?" (14338)

Anixx — Fri, 29 Apr 2011 16:24:36 -0700

I never said that Russian mathematicians do not understand the difference between a vertical tangent line and a cusp.

markvs comments on "Why people downvote the only correct answer?" (14335)

markvs — Fri, 29 Apr 2011 14:16:27 -0700

As a (former) Russian mathematician I confirm that Russian mathematicians understand the difference between a vertical tangent line and a cusp. Also division by 0 is not allowed in Russia (just in case, since Anixx likes dividing by zero). So Anixx's opinions about this matter are solely his/her own and in no way, shape or form reflect opinions of other Russian mathematicians.

Pete L. Clark comments on "Why people downvote the only correct answer?" (14331)

Pete L. Clark — Fri, 29 Apr 2011 12:11:44 -0700

Anixx: I'm afraid I don't believe you that Russian mathematicians (or mathematicians in any country) do not know the difference between a vertical tangent line and a cusp. This is a forum for mathematicians, and you are not writing what we recognize as correct mathematical arguments. If you are coming from some other field, like symbolic computation, then maybe your conventions are different, in which case you should probably seek a forum of like-minded people. But you are ignoring mathematical subtleties that we train our undergraduates to pay attention to, most especially to proceed from a clear definition and not make arguments like "Well, if it means anything, it must mean this..." So that's why you are getting downvotes: we don't regard your arguments as being rigorous, and in some places not meaningful at all.

If you are friendly with a mathematician, then perhaps she could help you understand why people here are objecting to what you write. Repeatedly venting your spleen with us does not seem to be helping.

Anixx comments on "Why people downvote the only correct answer?" (14330)

Anixx — Fri, 29 Apr 2011 11:47:58 -0700

"so that overall we say that the limit does not exist" - I do not know how it is in your country but in my country it is usually said that the limit is unsigned infinity. Look here for example: http://mathserfer.com/math/task.php?tname=limfun and input 1/x in the input field. Also Wolfram Alpha calls it "complex infinity".

Pete L. Clark comments on "Why people downvote the only correct answer?" (14329)

Pete L. Clark — Fri, 29 Apr 2011 11:37:28 -0700

@Anixx: It's not a question of notation. The point is that in the definition of an infinite limit, we distinguish between the limit approaching positive infinity and the limit approaching negative infinity. In the case of 1/x, the right-handed limit is + infinity and the left-handed limit is -infinity, so that overall we say that the limit does not exist, even as an extended real number. In fact in older calculus/analysis texts one often finds that the derivative of a function is allowed to be an extended real number, and in this sense something like f(x) = x^(2/3) is not differentiable at zero even in the extended sense, whereas f(x) = x^(1/2) for non-negative x and - (-x)^(1/2) for negative x is differentiable at zero in the extended sense: the derivative is positive infinity. When one thinks in terms of plane curves this becomes even more important: it is the difference between having a vertical tangent line and a cusp.

In your answer you said that a sufficient condition for the derivative to be infinity was that the function be nonconstant. You didn't say anything about differentiability at 0. My point is that for a function like x sin(1/x) the value 0 is taken infinitely many times in any neighborhood of 0, so if you are trying to impart some meaning to (f(x) - f(0))/(pi - pi), there will be infinitely many values where the numerator will also be equal to zero, so you will apparently have an indeterminate form 0/0. Perhaps according to some symbolic convention (that you have not enunciated...) this should be regarded as unsigned infinity anyway, but then why did you include the hypothesis that f be nonconstant?

Anixx comments on "Why people downvote the only correct answer?" (14326)

Anixx — Fri, 29 Apr 2011 10:13:16 -0700

...one more downvote. Why?

Anixx comments on "Why people downvote the only correct answer?" (14322)

Anixx — Fri, 29 Apr 2011 09:48:01 -0700

> calculus is not done in the one-point compactification of R, so far as I have seen, but rather in R with some appeals to the extended real numbers [-\infty,\infty]

Well in my country positive infinity is denoted as +\infty

> what if the function is something like xsin(1/x)

this function does not have non-zero derivatives in 0 as discribed in my answer.

Pete L. Clark comments on "Why people downvote the only correct answer?" (14318)

Pete L. Clark — Fri, 29 Apr 2011 09:34:36 -0700

@Anixx: I don't mean to be confrontational about this, but: yes, I certainly did claim in the comments that your answer was incorrect, at least by mathematicians' standards (and this is a forum for mathematicians). The business about \pm \infty is really the least of it, but I didn't want to get dragged into a detailed discussion of why your answer does not make sense because I began to suspect that we are simply not speaking the same language.

(If you really want to go there: calculus is not done in the one-point compactification of R, so far as I have seen, but rather in R with some appeals to the extended real numbers [-\infty,\infty]. Moreover, it's not clear where you are using the hypothesis that your function is continuous and also why nonconstant is sufficient: what if the function is something like xsin(1/x), which takes on the same value infinitely many times near the limiting point?)

Finally, no, I don't hate you. I don't understand you very well, and sometimes you say things that I wish you wouldn't, but again I am willing to ascribe this to differences of culture and/or language.

Anixx comments on "Why people downvote the only correct answer?" (14315)

Anixx — Fri, 29 Apr 2011 09:22:19 -0700

One more downvote without explanation :-(

Anixx comments on "Why people downvote the only correct answer?" (14314)

Anixx — Fri, 29 Apr 2011 09:19:31 -0700

Do you all hate me?

Anixx comments on "Why people downvote the only correct answer?" (14313)

Anixx — Fri, 29 Apr 2011 09:19:08 -0700

One more downvote. Is it going to be a record?

Anixx comments on "Why people downvote the only correct answer?" (14312)

Anixx — Fri, 29 Apr 2011 09:17:26 -0700

Note that nobody claims that the answer is incorrect.

Anixx comments on "Why people downvote the only correct answer?" (14310)

Anixx — Fri, 29 Apr 2011 09:14:21 -0700

One more downvote without explanation.

Anixx comments on "Why people downvote the only correct answer?" (14307)

Anixx — Fri, 29 Apr 2011 08:07:35 -0700

I have just received one more downvote. Why? Can anybody just explain?

Anixx comments on "Why people downvote the only correct answer?" (14306)

Anixx — Fri, 29 Apr 2011 07:53:52 -0700

> If you think that the limit of 1/x as x goes to 0 is +infinity,

No, the limit is unsigned infinity. I never wrote +infinity.

alias comments on "Why people downvote the only correct answer?" (14304)

alias — Fri, 29 Apr 2011 07:52:08 -0700

...

Andy Putman comments on "Why people downvote the only correct answer?" (14303)

Andy Putman — Fri, 29 Apr 2011 07:51:25 -0700

@Anixx : If you think that the limit of 1/x as x goes to 0 is +infinity, then you are probably participating in the wrong forum.

Anixx comments on "Why people downvote the only correct answer?" (14301)

Anixx — Fri, 29 Apr 2011 07:46:14 -0700

Why people downvote the only correct answer here: http://mathoverflow.net/questions/63127/is-this-joke-unfunny/63161#63161 ?

Do you people want to strip me of 100 rep third time in a row?