> Except equality never meant...
... opening to your comment which immediately makes you look like you're being antagonistic.
("except", and "never" probably being the key words. Especially opening with "except"...)
I doubt it. The parent is confused and hence the question obviously. But I get the impression that the parent would benefit from reading an elementary textbook on discrete math as the post is gibberish (as are a few other posts in this thread). I know it sounds rude, but I don't know how else to put it. It's not only the fact that the parent doesn't have a conceptual idea about equivalence relations and in particular equality, isomorphism, let alone homotopy, but is also very confused about what it means for a series to converge which is also very elementary. Before discussing the merits of Dostoevsky in Russian, one must learn and know the Russian alphabet at the very least or something.
I didn't get that impression at all. Rather, you came across as needlessly insulting. Why add that sentence, even if you thought so?! "Be kind."
> I'm not sure how far you could take math if you treat equality as meaning "exactly the same"; it seems even middle-school math requires understanding that that's not the case.
I honestly didn't mean that in a rude way, more like a "hey dude, be careful how you're coming across here, as there may be things you don't understand." I read the above phrase as describing a mathematician's work as something a middle schooler should already know. But I take back what I said. I'm all good, everyone's good, I think there was just a misunderstanding here.
In the same vein, I don't see how you could read my message as needlessly insulting, as I thought it was pretty softly worded. But I guess that's the nature of written communication. I think you should have given me the benefit of the doubt, just as I should have done for the original poster.
I thought the article was cool. From this comment, you are coming across as someone who is trivializing a potentially important piece of work. I didn’t really understand it, but I take mathematicians at IAS seriously.