\begin{definition}[Definition:Normal Real Number]
A real number $r$ is '''normal''' with respect to a number base $b$ {{iff}} 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 $r$.
\end{definition}