User:RSiferd

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

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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, $$log^{-1}(x)=e^x\because e^{log(x)}=log(e^{x})=x$$.