Definition:Normal Number

Definition
A real number $r$ is normal with respect to a number base $b$ its basis expansion in number base $b$ is such that:


 * no finite sequence of digits of $r$ of length $n$ occurs more frequently than any other such finite sequence of length $n$.

In particular, for number base $b$, all digits of $r$ have the same natural density in the basis expansion of $r$.

Also known as
It is usual to assume that the number being described as normal is real, so to refer merely to a normal number.

Also defined as
Some sources do not distinguish between a normal number and an absolutely normal number.

Such sources refer to an absolutely normal number merely as a normal number.

Also see

 * Definition:Absolutely Normal Real Number