Decimal form of irrational numbers In the decimal form of an irrational number like:
$$\pi=3.141592653589\ldots$$
Do we have all the numbers from $0$ to $9$. I verified $\pi$ and all the numbers are there. Is this true in general for irrational numbers ?
In other words, for an irrational number
$$x=\sum_{n\in \mathbb{Z}} a_n 10^n$$
Does $a_n$ takes all the numbers between $0$ and $9$ ?

It is true that there are "irrational numbers" which their decimal expansion does not include all digits but some of them
There is also Benford's Law which is studied in Number Theory
i think there is a theorem that on average the probability of each digit in the set of irrational numbers is equiprobable with probability one (ie almost everywhere)
And this is related to equidistribution theorems
(Answer by Asaf Karagila provides a short proof of the above statement)
Please correct if i am mistaken here
