Definition:Normal Number
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Definition
A real number $r$ is normal with respect to a number base $b$ if and only if 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 common to refer to a real number $r$ which is normal with respect to base $10$ merely as normal, without specifying the base.
Such usage can be confused with the concept of an absolutely normal number, so this usage is not to be used on $\mathsf{Pr} \infty \mathsf{fWiki}$
Also see
- Results about normal numbers can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Champernowne's number