What's the point of Euler's number in exponents?

Question

I want to know why we use $(1+e^{\text{something}})^{-1}$ for artificial intelligence. I know $e$ is just $2.7$.

So what? Why $2.7$ and not $3$?

Does it have a special property?

Answer 1

You can see $e$ as the unique real number such that $$ \ln (e)=1 $$ giving $$ e=2.71828182845904523536028747135266249775724709370\ldots. $$ One may prove that $$ \ln(e^x)=x, \quad x \in \mathbb{R}, $$$$ e^{\ln (x)}=x, \quad x \in (0,\infty), $$$$ \frac{d}{dx}e^x =e^x \quad x \in \mathbb{R}, $$ $$ e^x =\sum_{n=0}^\infty\frac{x^n}{n!}\quad x \in \mathbb{R}. $$

Answer 2

The number $e^{\text{something}}$ can always be written as $3^{\text{something else}}$, where “something” and “something else” only differ by a constant factor ($\ln(3)$, to be precise). So it doesn't really matter what base you use for your exponentials. It's just that $e^x$ is much more convenient when computing derivatives, for example. And almost all programming languages already have a function for computing $e^x$, typically called exp(x), so don't write your own implementation!