the "usual" proof can be found on Wikipedia using the argument of Joseph Fourier (of Fourier series fame) https://en.wikipedia.org/wiki/Proof_that_e_is_irration

the "usual" proof can be found on Wikipedia using the argument of Joseph Fourier (of Fourier series fame) https://en.wikipedia.org/wiki/Proof_that_e_is_irrational https://en.wikipedia.org/wiki/Proof_that_e_is_irrational The idea is the same, that all the truncated series 2 < 1 + 1/2! + 1/3! + ... < 3 lie between two integers can cannot be integer. This is a different outcome than the geometric series 1 + 1/2 + 1/4 + 1/8 + ... = 1 which converges to a whole number. http://math.stackexchange.com/questions/476939/proving-the-irrationality-of-en http://math.stackexchange.com/questions/476939/proving-the-i... http://math.stackexchange.com/questions/713467/prove-that-e-is-irrational http://math.stackexchange.com/questions/713467/prove-that-e-... http://math.stackexchange.com/questions/425963/is-there-a-simple-proof-that-e2-is-irrational-using-a-positional-numeral-syst http://math.stackexchange.com/questions/425963/is-there-a-si...