Earlier quoted context omitted.
> They care about how you approach it, how you think through it, what you do when challenged, etc. I was asked to sketch the proof for the irrationality of sqrt(2) in a quant programming interview. I kind of froze, and explained that though I had learned it, I could not recall. He prompted me with "Well, what does it mean to be irrational?", and with that little hint I did the rest. Though ultimately I did not end up…
Errr in the set of numbers that complete the rationals wrt to standard metric? I guess you have to show it’s not rational so you probably did a proof of upper/lower converging bounds always having nonzero difference for 1/n increments or something? I would definitely not get this in a pressure interview situation.
Assume sqrt(2) is rational and has the reduced form (x/y). Thus we are assuming that x and y are integers and that gcd(x,y) is 1. You square it and get x^2/y^2 which are somehow simultaneously coprime integers and also reducible to 2/1...