# Definition:Liouville's Constant

## Definition

Liouville's constant is the real number defined as:

 $\ds \sum_{n \mathop \ge 1} \dfrac 1 {10^{n!} }$ $=$ $\ds \frac 1 {10^1} + \frac 1 {10^2} + \frac 1 {10^6} + \frac 1 {10^{24} } + \cdots$ $\ds$ $=$ $\ds 0 \cdotp 11000 \, 10000 \, 00000 \, 00000 \, 00010 \, 00 \ldots$

## Also known as

Some sources refer to this as Liouville's number.

## Source of Name

This entry was named for Joseph Liouville.

## Historical Note

Liouville's Constant was created by Joseph Liouville in $1844$ as an example of a real number which is provably transcendental.

He constructed several such numbers, of which this is the simplest.