User:RSiferd

This is just for note taking for projects. Let f(x) = {x} denote the distance from x to the nearest integer for $x \in \mathbb{R}$. $f(x)=\sum_{n=1}^{\infty} 1/{10^n} \{10^nx\}$

e

First you have to define what log is, $log(x)=\int_{1}^{x} 1/t \cdot dt$. Now we have this function log, which is clearly 1-1 for $x>0\wedge x\in \mathbb{R}$, so there must be an inverse to it, so there you have e, $log^{-1}(x)=e^x\because e^{log(x)}=log(e^{x})=x$.