Some number doesn't contain $"7"$ in its decimal expansion.
For example Liouville's constant
$$L=\sum_{n=1}^\infty\frac{1}{10^{n!}}=0.11000100....$$
contains only $0$ and $1$.
It is well-known that if number is "normal" it contain infinite number of $\lbrace0,1,2...9\rbrace$. In other words, if $\pi$ is 10-normal, then the limiting frequency of "7" (or any other single digit) in its decimal expansion is $\frac{1}{10}.$
It is not known that $\pi$ is normal, but can we say that $\pi$ (or $\sqrt{2}$) has infinitely many 0 or any other single digit in its decimal expansion? If "no", how many zeros contains $pi$?
Also it is easy to prove that Champernowne number $0.1234567891011...$ contain infinite many "zeros" without know that it is 10-normal.