[grantpitt]

Right, like in math, not all infinite sequences contain every finite subsequence. For example, a non-repeating sequence of 2's and 7's contains no sequence "4". The further condition is that the number be normal[1].

Also, TIL we don't know whether π is normal thus the popular claim that "every string of numbers eventually occurs in π" is not known to be true

[1] https://en.wikipedia.org/wiki/Normal_number