Exclusive AMA with Adam 'coffeeyay' Sobolewski

Btw, the definition of e as the limit of (1+1/n)^n is very recreational and inconvenient. A faster way to develop the theory of e basing on integral and differential calculus (of functions of one real variable) was shown to me at high school:

Ironically, a relevant video has suddenly showed up on my Youtube feed. It uses the definition of exp(z) that I don't like (as I said above): as the limit of (1+z/n)^n (in the complex domain!) as n->infty.

That proof is quite elegant [well, it's a proof for laymen but it can be easily made rigorous by noting that 1 + pi*i/n = (cos(pi/n) + i*sin(pi/n)) * (1 + O(1/n^2))] but I know that Euler used the power series for exp, sin and cos to give a nonrigorous proof of the formula (convergence wasn't studied strictly enough until the 19th century), whereas the geometric (plane) representation of complex number multiplication was discovered only after his death, independently by Wessel (1799), Argand (1806) and Gauss (1831).

What have I done 8-o8-o

whats your general 3b strat at 40/30/20bbs? its fairly easy to come up with reasonable value ranges at those stack depths, however i struggle a bit with finding "good" bluffing hands. do you even have balanced ranges in those spots or are you just relying on not having a huge sample against most people anyway and 3b a super value heavy range in general?

thx a lot for doing this!

Originally posted by KTU
What have I done 8-o8-o

Haha you don't even know, and yet not everything is answered !!! I can't resist to give my two cents there

Originally posted by KTU
Do you use the axiom of choice personally?

I don't "like" to use it personally as I clearly prefer Bishop constructivist type theory (axiomatisation Martin-Lof) to the standard model, but you should note that albeit it is often discussed, the axiom of choice isn't really the core of the standard model weirdness, far from it actually, the key point lays in the principle of the excluded middle, which is a far more "problematic" axiom than the one of choice.

Therefore people supporting ZF have an easy case to defend that ZFC isn't really worse and that anyway once you're in ZF, whitout C or something at least equally problematic (like game axiom etc) you won't even be able to fall back on your feet in some areas as sounds and basics as the Bolzano-Weierstrass theorem. (Not to talk about trying to build some kind of a measure theory and such xD). Duh, ZF sucks to the core, it's not between ZF and ZFC, it's not about falling back to NBG either, if you don't like "limited omniscience principle" then just work in TCT !

But in the end it's just fairly theoretical questions anyway and in a wittgenstein (best genius ever) perspective it doesn't change our mathematical practice at all, it only changes eventually what we are tempted to say about that practice, and that's there that lays the nonsensical blur, in the "prose" part that we are sometimes misleaded to take for as granted, clear and true as the "computation" part. (For exemple the Russell and Burali-Forti paradoxes haven't been solved by a computation or a new syntax but by an analysis of the semantic we were using mistakenly.)

Originally posted by KTU
Do you like our definition of cardinality or does it still feel somehow wrong to you.

If "our" is the Cantor one, I don't like it at all as a constructivist. Not to mention, Heyting, Poincaré or Brouwer clever attacks, let's just say Wittgenstein compared it to Freudian psychoanalysis, the same kind of greet intellectual achievement that was bound to stand more as a mythology in the background than as an actual concrete scientific stuff.
But I'd not qualify it as "wrong" either. From what criteria of truth to begin with ?
Once again what matters isn't that you're using it when you compute or not, the computation will stand for itself, it's that you stop saying weird metaphysical things like "there isn't only one infinite but an infinite hierarchy of ones who differ in nature and degree" which sounds like a religious claim and is everything but a scientifically proven (and sound) statement.

Sorry for the geek rot and the bad english ♦
Next time maybe a question about the notion of "relative truth" in model theory and how Woodin's work doesn't change at all the status of the continuum hypothesis ?