I'm close to the end of my first year and I still haven't seen an irrationality proof. Come to think of it, I haven't heard the word irrational at all!mathwonk said:proving e is irrational

However:

While learning linear approximation, I linked that up with the physics equation, and saw that:

f(x+a) = f(x) + f'(x)*(a-x) + f''(x)*(a-x)^2/2! + ...

Then when we did taylor series, and we were told that e = (...) I wondered if it was related. Lo and behold:

e^(0+n) => 1 + n + n^2/2! ... = sum(e*x^n/n!)

I assume that equation itself is proof that e isn't rational, since if it is rational, the integer being divided needs to have an infinite amount of digits.

(n->inf)! = inf