It is conjectured that pi is normal: http://en.wikipedia.org/wiki/Normal_number

If the conjecture is true then any finite sequence of numbers can be found in the digits of pi. As others have noted, infinite sequences are not guaranteed or even likely to appear. As zackattack points out, for example, the decimal expansion of 1/9 does not appear in the digits of pi.

I'm not a mathematician, but I read a lot of time ago that since pi is infinite but not periodic, you shold be able to find in it any sequence you want, given infinite time to search in it.

This is what I remember, but I could be wrong.

The statement (infinite && not periodic) ==> (any finite sequence is in it) is not true. \a number could have a decimal expansion that is not periodic but does not include certain digits. E.g: write Pi in binary and consider the same sequence of 0's and 1's as a number in decimal

You can't find 1/9 in pi. 1/9 precludes the possibility of any other sequence.

I think the parent was talking about sequences of digits, i.e. integers, not just "any rational number"

Related: http://www.angio.net/pi/whynotpi.html