Will you oppose to scientific conclusions if they'll lead to theology?

Will someone remind me why any finite string of digits are necessarily contained somewhere in the decimal expansion of pi? I mean, without looking up the first million digits of pi, can someone prove that somewhere in the decimal representation there is a 5 immediately followed by a 2?

Hi, jar.Maybe, but I specifically asked for a proof that didn't involve looking up the digits, heh.There seems to be an assertian on this thread that any finite sequence of numbers must appear in the decimal representation of pi. I have never seen a proof of this. I assume that people are saying this because they think that since pi is irrational it's decimal representation is not periodic, and then that means it must contain, somewhere, any finite sequence of digits you can think of. This is most assuredly false.On the other hand, maybe there is something about pi itself where this is true; however, I have not seen this written anywhere.

Are you assuming that the digits in pi form a truly random sequence?Here is a nice irrational number:5.05005000500005000005000000500000005000000005...I can specify lots of finite sequences that never appear in this decimal expansion. but then, this sequence is not very random.I know that sometimes people use the digits of pi to produce a sequence of random digits, but I don't think that it has been proven that pi behaves as a truly random sequence.By the way, I see that you are an admin now. Congratulations.

Hi, Jon.Yes, if the digits of pi do form a truly random sequence (whatever that means) then jar's explanation would be sound -- given any finite sequence we the probability that we would find that sequence would approach 1 as we look further and further out in the expansion.On the other hand, there may be other reasons to believe that pi contains all finite sequences even it were not truly random.

I actually dislike number theory. I wonder if they are going to make me teach it here?