Euler's number

Euler's number $e$ , after Leonhard Euler, is a transcendental number, roughly 2.71828.

$e$ has many equivalent definitions:
As a limit:

e = lim_{n \to \infty} {(1 + \frac{1}{n})}^{n}

e = \sum_{n = 0}^{\infty} \frac{1}{n!}

e = \exp (1)

such that $\exp (t)$ is the unique function such that $\frac{d}{d t} \exp (t) = \exp (t)$ and $\exp (0) = 1$ .

\int_{1}^{e} \frac{1}{x} d x = 1