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It is widely thought that $\pi$ contains every possible finite digit sequence. But what if the sequence is infinite? When the first digit of the sequence appears somewhere in $\pi$ it should never end since both $\pi$ and the sequence are infinite. Does that mean that the sequence itself contains every possible sequence since it's essentially $\pi$ minus the digits from the first digit of pi to the digit where the sequence's first digit appears?

What about pi itself? Of course, I'm not talking about the first digit starting from first digit of $\pi$. That's kind of obvious. If I were to find $\pi$ in $\pi$ digits would that mean that $\pi$ actually is repeating? I guess that's impossible because that would mean $\pi$ is actually a rational number which it isn't. Am I thinking correctly here?

So what about infinite sequences in $\pi$? Any thoughts?

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closed as unclear what you're asking by Jack D'Aurizio, Adam Hughes, The Chaz 2.0, Crostul, suomynonA Oct 6 '16 at 1:07

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    $\begingroup$ Convince yourself that if this were so, $\pi$ would have a repeating decimal expansion (and hence be rational). $\endgroup$ – Adam Hughes Oct 5 '16 at 23:22
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    $\begingroup$ Think about whether this actually makes any sense. Consider two different infinite sequences. Where are they going to fit inside the digits of pi? $\endgroup$ – fleablood Oct 5 '16 at 23:27
  • $\begingroup$ How could it be shown whether pi has every finite sequence? No matter how many of its digits are counted, that will still represent but an infinitesimal part of the whole. $\endgroup$ – Ham Sandwich Oct 5 '16 at 23:28
  • $\begingroup$ It is widely thought that pi contains every possible FINITE sequence (although no one knows if it does). Nobody thinks it contains any infinite sequence except the ones that are pi itself with the front cut off. To contain an infinite sequence in the middle of pi and for pi to continue on after the infinite (nonending) sequence somehow ends is .... meaningless. $\endgroup$ – fleablood Oct 5 '16 at 23:32
  • $\begingroup$ A few comments are pointing out what I pointed out myself in my question. Anyway, I'm just thinking way too much about pi lately. $\endgroup$ – Cathier Oct 5 '16 at 23:39