@quid: To continue the tangent about divergent series, in my personal opinion it is the same fundamental problem; the singular failure to teach students that you cannot state anything as true unless you have proven it, and cannot define anything based on some desired property unless you have proven that such a thing exists, and cannot write down any expression unless it has a well-defined meaning.
Today one common fad is about divergent series, especially 1+2+3+... A decade later, it may well be something completely different.
Hence I actually think it is more meaningful to close all such questions as duplicates, even if they may at first layman glance be different questions. After all, what I just described covers almost all known 'paradoxes', including the liar paradox, Curry's paradox, Quine's paradox, Berry's paradox, silly things like "1/0+1/0 = 1/0" and "1+1+1+...", and to some extent even Russell's paradox and the Burali-Forti paradox.
I make an exception only if the asker shows a genuine effort to figure out what is wrong, especially if citing an earlier question and pinpointing what he/she does not get. What I especially dislike is when they just post a question of this sort.
