@CarlMummert Curious tag selection. Almost half are "modular-arithmetic" one of my top tags, but very, very far from the top of yours. Also includes some of my answers too. How did you select these questions?
The nice thing about the new tools is that it makes targeting abuses obvious
@BillDubuque That is both inherently non-sequitur and also seems to be a non-sequitur response to the questions posed in the chat comment link. I'd prefer to let the matter rest for a while, in deference to the hint Carl was giving.
@CarlMummert I don't think that c7 is a great question, but I am willing to leave it alone on the grounds that a minimal amount of effort is made by demonstrating two solutions. While I believe that effort shown is poor context at best, it still puts the question slightly ahead of the majority of the questions that pop up here.
@XanderHenderson I'm curious to know what you (and others) think about the points raised in my prior comments given that you seem to care about such matters given your prior comments on transparency. Do you condone targeted voting?
@XanderHenderson: thanks - that's OK with me, I don't mind if other people don't vote for the questions. In my thoughts, I would like to see the actual context of the problem, and maybe some motivation. It seems like some kind of "made up" problem without an explanation of the motivation.
Can y'all have a look at this question? The asker is trying to bring back a question which was closed for lack of context (and which they answered).
Personally, I don't find the question that interesting (but I don't really like competition math all that much). I also don't see much context---as it stands, the question is "Here's my solution. Are there other solutions?"
That being said, I respect the attempt to turn a bad question into a good question, so have not voted to delete. Does anyone else have an opinion?
@XanderHenderson: I don't really think "are there other solutions" is a form of context, or even really a question, unless there is a strong reason to expect there are other solutions, in which case the question could explain that reason.
I mean, I could post anything I already know and then type "Are there any other solutiions" below it. So that's not really context for what I typed.
Hi again. Could one of the people here please check if this answer is correct or not? I think it's incorrect but I'm not good at complex analysis. If it's incorrect, then it should be deleted I think.
First it would have to be downvoted. If there's an error, one nice thing is for someone to write a different answer that is correct and explains the error in the other answer
@CarlMummert Yes, I left a comment under the answerer's post. But I'm not sure whether the answerer is wrong or it's me that is wrong. That's why I asked for another person's opinion about it.
I think the answer is wrong because the answer depends on the way $|z|=1$ is parametrized. Also, Robert Z gives no justification for why |dz| have to be equal to dt.
But I'm not good at complex analysis. So, I'm looking for a second opinion.
@XanderHenderson Well, I'm more worried about the answer because it can teach something wrong to people who see the question. So, it is actually harmful.
@CarlMummert Do you agree that the answer is wrong? Should I downvote it and flag it?
If you flag it, I am sorry to say, the flag will probably be declined, because "this is wrong" is not a valid flag reason ("this is not an answer" means something else). You can definitely downvote it even if you don't know it's wrong.
@stressedout It doesn't look obviously wrong to me---if you change the parameterization, $|\mathrm{d}z|$ will change, but so will the limits of integration. The answer simply picks an easy parameterization to deal with. However, the question is quite lacking; for example, it mentions a line integral but doesn't actually show what is being integrated.
Anyway, also being rusty at that area, it seems to me that the issue in the answerer has conflated dt (change in time) with ds (change in arc length) because in the parameterization z = exp(it) the speed ds/dt is 1.
@XanderHenderson: i think the confusion is how you compute |dz| = -idz/z, because in the other parameterization if you follow the answer step by step you get |dz| = -idz/(2z)
Maybe the OP deleted it very quickly, the answer was written 2 minutes after the question but the OP has 5 minutes grace period with no edit history visible to non-moderators
stressed out - after writing it down, I can answer your main concern. The problem is to compute |dz| which is the change in z with respect to arc length, which is to say dz/ds. Now if we take z = exp(kit) for some k > 0 then we have dz/dt = ki z. But we want dz/ds, so we need to divide by ds/dt. Fortunately this is just the speed, which is || dz/dt|| = k. So we get dz/ds = (kiz)/(k) = i*z independent of k, as we should.
@CarlMummert I'll happily accept your explanation as an answer to my question if you care to post it. It's exactly the kind of explanation that I needed.
I am worried about checking all the details and definitions to write a clear answer - someone who is more familiar with the area can probably write something that is much more clear.
Fortunately, the OP on that answer is online and very responsive and updated the answer to use arc length instead of time. I suspect it is very natural for people who work with these things all day - I suspect they don't write down formalisms like 'ds' very much in practice, but just do the correct substitutions. Every field has its conventions
apparently a duplicate of math.stackexchange.com/q/3135617/29335, although that question looks like it's going up in flames as well. If a duplicate is to be found, I hope there is a better one...
