Syntactic T-Rex: Irregularized

Jun 20 2016, 20:39

One of my huge pet peeves is with people who think that writing \(1+2+3+\ldots=-\frac1{12}\) is a reasonable thing without context. Convention dictates that when no context is set, we interpret infinite summation as the usual convergence of a series, namely the limit of the partial sums, if it exists (and of course that \(1+2+3+\ldots\) does not converge to any real number). However, a lot of people who are [probably] not mathematicians per se, insist that just because you can set up a context in which the above equality holds, e.g., Ramanujan summation or zeta regularization, then it is automatically perfectly fine to write this out of nowhere without context and being treated as wrong.

But those people forget that \(0=1\) is also very true in the ring with a single element; or you know, just in any structure for a language including the two constant symbols \(0\) and \(1\), where both constants are interpreted to be the same object. And hey, who even said that \(0\) and \(1\) have to denote constants? Why not ternary relations, or some other thing?

Banach-Tarski Banach-T-Rex

Oct 21 2015, 01:10

I had already written about anti-anti-Banach-Tarski arguments. But now the Mathematical T-Rex has something to say too.

Mathematical T-Rex

Aug 28 2015, 22:53

Ever explained to a "working mathematician" about the undecidability of the continuum hypothesis? I bet you too had felt like this T-Rex.