User blog comment:MachineGunSuper/My problem with pi/@comment-30754445-20171217195220

When people say "pi doesn't repeat" they simply mean that the entire pattern never repeats. Partial repeats are fine, and - indeed as you said yourself - are inevitable.

You can be certain that in any 11 digits of pi, two of them will be the same. Similarly, if you take 101 pairs of digits from pi, two of them must match. This is not a "problem" at all, but simple common sense.

A far more interesting question is whether pi contains ALL the possible digit patterns. Does the entire decimal expansion of Graham's Number appear in pi? Nobody knows. Most mathematicians believe that the answer is yes, but no one has ever been able to prove it.

(it should be noted that the mere fact that pi goes on forever and never repeats does not tell us anything either way. The number 0.101001000100001... also goes on forever and never repeats, yet it only contains the digits 0 and 1)