Definition:Euler's Number/Base of Logarithm

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Definition

The number $e$ can be defined as the number satisfied by:

$\ln e = 1$.

where $\ln e$ denotes the natural logarithm of $e$.

That $e$ is unique follows from Logarithm is Strictly Increasing.


Decimal Expansion

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

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

This sequence is A001113 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).


Also see


Source of Name

This entry was named for Leonhard Paul Euler.


Sources