Prove the transcendence of the number $e$ How to prove that the number $e=2.718281...$ is a transcendental number? The truth is I have no idea how to do it. If I can recommend a book or reference on this topic thank you. There are many tests on the transcendence of $ e $? I'd read several shows on the transcendence of $ e $

Try Michael Spivak's _Calculus_. I find it amusing that he would prove the transcendence of $ e $ in a calculus textbook.