[wool_gather]

This is the concept of [a "normal" number][0] (which is a strange choice of word, I think). Apparently pi is not proven to be normal. But the implication as I understand is that, yes, any given sequence that you'd care to look for is there somewhere.

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

[stephencanon]

Almost all numbers are normal, so it seems like a perfectly reasonable choice of terminology =)

[On the other hand, almost none of the numbers someone on the street might name are normal, so ...]

[pmiller2]

Offhand, I would guess that “normal” is the most overloaded word in mathematics. We should probably use it less.

[wool_gather]

Ah, I didn't realize that, thanks! That makes sense now that you say it.

[stephencanon]

Almost all real numbers are a lot of things, though:

   - uncomputable
   - irrational
   - transcendental
   - ...

So it's not really that good of a justification. =)