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editing someone else's non-community-wiki answer should be limited to obvious typos, math fixes, and similar "invisible" fixes

Agreed, this should probably be added to the FAQ

This edit seems exactly like the sort of remark that should be in a comment.

Yes - infact it IS a comment. It is even signed.

Otherwise we will run into all sorts of "disagreements" over whether some proof is "correct".

That's a good point - acting this way can only cause friction.

I would not appreciate someone editing one of my posts in this way

No I don't think it is correct to add a signed comment onto someone's actual post - Here is an example of an edit which I thought was necessary.

It is easy to see (e.g. here) that Bill Dubuque appreciates a very high standard of rigour and that is one reason why his answers to other questions are so illuminating to read but I don't think it is necessary to get frustrated at non-rigorous, partial or false arguments - these can also be very useful and lead to insight too.

Of course it is important to be able to recognize these and differentiate them from formal arguments and this is probably a difficult thing for a beginner but I don't see it as a real problem because for any mathematical argument one reads - they should put enough thought into it to understand it and thus notice mistakes.. without doing so what would be the point of reading it at all?