Skip to main content

New answers tagged

1 vote

How can you prove that the square root of two is irrational?

Here is a "Calculus" proof that doesn't use number theory whatsoever. (1) $|\sqrt{2}-1|<1 \therefore \lim_{n\to\infty}(\sqrt{2}-1)^n=0$, (2) $(\sqrt{2}-1)^n$ is of the form $k\sqrt{2}+\...
Antony Theo.'s user avatar
  • 1,272

Top 50 recent answers are included