# Definition:Champernowne Constant

## Definition

The Champernowne constant is the real number whose decimal expansion is formed by concatenating the positive integers in asccending order:

$C_{10} = 0 \cdotp 12345 \, 67891 \, 01112 \, 13141 \, 51617 \, 18192 \, 02122 \ldots$

## Also known as

The Champernowne constant is also known as Mahler's number for Kurt Mahler, who proved it transcendental in $1937$.

## Source of Name

This entry was named for David Gawen Champernowne.