# Definition:Euler's Number/Base of Exponential

## Definition

There is a number $x \in \R$ such that:

$\ds \lim_{h \mathop \to 0} \frac {x^h - 1} h = 1$

This number is called Euler's Number and is denoted $e$.

### Decimal Expansion

The decimal expansion of Euler's number $e$ starts:

$2 \cdotp 71828 \, 18284 \, 59045 \, 23536 \, 02874 \, 71352 \, 66249 \, 77572 \, 47093 \, 69995 \ldots$

## Source of Name

This entry was named for Leonhard Paul Euler.