If the digits of Pi really go on infinitely without repeating…

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… then don’t they inevitably repeat after all?

For example, the digit ‘3’ repeats a lot, of course.

The digits ’31’ also repeat.

Then the digits ‘314’ do as well.

And so on… 3141, 31415, 314159, etc etc.

According to [the Pi-Search page](https://www.angio.net/pi/):
>The string 31415926 occurs at position 50366472. This string occurs 3 times in the first 200M digits of Pi.
counting from the first digit after the decimal point. The 3. is not counted.

So, if it truly does continue forever, isn’t it likely that every set of digits must repeat at some point, no matter how long the string may be?

If not, please explain why.

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10 Answers

Anonymous 0 Comments

If Pi is, as is believed, a normal number then yes, any finite sequence of digits will appear, and indeed reappear infinitely many times.

But it would not fall into a repeating pattern. Those repeats would occur at different intervals, in a way indistinguishable from randomness.

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