This sounds like the claim that Pi is "normal" in a particular base. It's not actually known whether Pi is normal in any particular base, I don't think, but in some sense most real numbers are. It doesn't say that every other number is contained somewhere in pi, just that any finite string of digits is. So no irrational or repeating numbers required, if I have it right.
@lxo
This addresses inter alia the claim that every (finite?) string of numbers appears somewhere in Pi. https://en.m.wikipedia.org/wiki/Normal_number
@futurebird