Normal number

Summary

A real number is normal in a base $b$ when every block of $k$ digits appears in its base-$b$ expansion with limiting frequency $b^{-k}$. A number is absolutely normal when it is normal in every base $b \ge 2$. Borel showed that almost every real number, in the sense of Lebesgue measure, is absolutely normal. Yet for familiar constants such as $\sqrt{2}$, $\pi$ and $e$, normality is not known in any base.