C/D dupe of FAQ - immediate consequence of CRT solvability criterion. Was gold badge reopened by lone answerer (who has done the same recently).

Oops, above was not a gold badge reopening, but it should still be reclosed & deleted

We already have many tens (if not hundreds) of such straitghforward applications of CRT solvability. Nothing at all novel there.

please close this

It seems the reopeners did not read carefully, likely reading only the first dupe link, which gave the proof of the CRT solvability criterion. The 2nd dupe link gave a very detailed example which is exactly the same as in this question, ie. the moduli gcd = 2 so reducing the system mod 2 immediately yields a parity contradiction, viz. r = r+1 (mod 2), explained in a closing comment.

Such parity contradictions are the simplest manifestations of CRT nonsolvability and they occir in many prior posts here. Nothing is novel in that Q&A.

It's hard to imagine a better example of an abstract duplicate.

Please consider reopen this post math.stackexchange.com/q/4314909/462621. One voter argues that it is not clear enough and “can only be answered with certain interpretations”, but I believe this is not the case. That voter’s claim was built on the judgement that “for arbitrary polynomials, degree of that polynomial can vary in integers, whereas the sign of a determinant can only be 1 or -1”.

However, the OP has specifically stated that his function is linear. Thus, to answer this question require no interpretation with further unwarranted information at all. I think the votes did not look into the question very clearly.

Moreover, my claim is supported in comments: “ So I don‘t think That the statement is wrong if $f:\mathbb{R}ˆ2 \rightarrow \mathbb{R}ˆ2$ is a linear map with nonzero determinant. Then it should also work for the restriction right doesn‘t it?” from OP;

and “ @hardmath he clearly means the degree of a continuous map. This is standard terminology as defined by Brouwer. Linear maps are not polynomials so there is no ambiguity here.” from another user.

(FYI, I answered the question.)

*typo, should be: I think the votes did not look into the question very carefully.

@fantasie Are there deleted comments to that question? (Is the OP replying to someone who since deleted their comments?)

I do side with hardmath here though, at least morally: the question is essentially a Problem Statement Question. Hardmath's suggestion is basically to include more context that just "I need this step to complete a Proof".

If "the "proof" for which this step is needed to complete were described", or at least outlined, then hardmath would not have been confused, which is the point of context - it helps everyone to understand where the question comes from, what tools can be used, all assumptions are present and correct, etc. etc.

@user1729 Yes, there were comments deleted. One user question OP with almost exactly what hardmath says; I think that is because he/she did not look at the statement “for all linear f…”.

My interpretation of hardmath’s comment is that he/she thinks this question is not clear because the premises of the question cannot prove the conclusion(which is not the case), therefore it has to be closed unless the OP has rewritten so it can be answered.

I haven’t learned any incompatible definitions of degree other than the one used here, so IMO this closure is kind of confusing.

In my opinion, the closure of a post is undertaken to enforce some sort of regulations to help this QA site run healthy. I kind of get what you “do the side, at least in moral”, that is, askers should specify their questions whenever possible. But this question, in my mind, is already way better than some of these I saw in first question posts, and people around can get what OP want through question body and comments, what else?

Plus, hardmath overlook an important point in question body, which significantly undermines his/her argument.

(Sorry for the words, I am not a native speaker, telling things already, let alone speaking them in a more easy tone.)

@fantasie I understand what you are saying, but my point is: The question lacks context. It was closed as being "unclear", but it also could have been closed as lacking context. A secondary point is: Including the context hardmath suggested would have clarified the question, and meant hardmath would not have been confused. (Context isn't about clarity of a question, which seems to be what you're saying? It just so happens that it would have helped with clarity here.)

(Don't worry about language - I think I understood all your points, but if you think I didn't please just say :-) )

(also if you don't understand something I said, just tell me and I will explain myself better.)

Thanks for the explanation. To see if I get it right, the context should be added would be “I need step to complete a proof, where the proof is for some P we will get Q and R blabla….”, is that so?

@user1729 I mean, instead of explaining the Brouwer’s stuff about how to define the degree of a continuous map.

@fantasie Basically, yes. (Stating that "deg" means the degree of a continuous map would be helpful too, but I don't think it needs explained. Just stated.)

Then I see what’s going on here, although we might have a minor disagreement about if this situation is severe enough to get the question closed.

It is a pity that seems pointless to advise the OP to include more context, for he/she has already got what is intended. I think I will just leave it here.

@BillDubuque Closing as a dupe with the first link. I would urge someone to use the second link now.

Allow me to express one more dissatisfaction: the reason for the closure and comments of the voter did not address the real problem, and this makes MSE a platform unintuitive to interact. And it makes people around think “oh it’s these math cops again closing questions for whatever reason they like”, but this not true because most moderators are patient listeners. If it wasn’t that the reason was so bad, I wouldn’t have spent my time here.

D

D

@Feeds self-deleted. I wonder why so many posts about such proof-trials land here as Feeds.

CD

@Peter Open-conjecture-related posts were added to Feeds by @user21820.

Hello, @TheSimpliFire !

Hello @amWhy

How's it going? Given you've been moderating for some time, I imagine there weren't too many things to "learn", save for site-specific/mod-team-specific nuances.

Good, nothing too eventful, but MSE is a huge site so there were a few interesting things to pick up on

Today might be a slower day, given three mods are experiencing Thanksgiving and focused on stuffing themselves with turkey and trimmings. And some users may be taking the day off, or at least, part of the day off!

@TheSimpliFire Great! Next you can take on moderating on SO!!! ;D

@amWhy I have no idea how SO mods manage it, it's so much worse than here (despite having many more mods) :P

@TheSimpliFire Yikes!! That might make consensus among all the mods very difficult!

26 mods to be exact, until yesterday when two of them decided it was time (one of whom handled half a million flags)

@TheSimpliFire You want to say that it is no fun to moderate and in particular to moderate in SO ? I always thought it is a great feeling to be able to do that.

@TheSimpliFire I guess not by hand :)

@Peter I might be biased as I don't particularly enjoy programming, but IMO bigger doesn't always mean better

@TheSimpliFire OMG! I've heard SO enthusiasts downplay our concern when we get over 500, even 600 posts in the Close Review queue!

@TheSimpliFire I assume we can safely say that math.se is the second largest site? (Put meta.se is likely busy).

I think we're coping relatively well :P

@amWhy Yeah, apparently it goes SO, MSE, Russian SO and Ask Ubuntu

@TheSimpliFire Got it. Just want to mention, that users who frequent, meta.se, and on meta, and network wide, MSE is intended to be meta.se. For years I referred to math.se as MSE, until I mention MSE in reference to the math.se... Don't do that!!!

I think in the confines of this site, we pretty much assume MSE references means math, given it is typically referring to math.se. But in the last three years, I've come to automatically write "math.se" or "meta.se" to avoid ambiguity.

Indeed, on network sites I use math.se and on this site I refer to meta.se as the main meta

@TheSimpliFire Yay!!

speaking of abbreviations:

I just encountered it a few months ago. I love it!

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