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

No, a repeat would mean that the a finite number of digits repeat periodically. Yes given infinit digits you can find any finite number that shows up more than once in the digits of pi. But there are no numbers that periodically show up. Like the number 31. Yes it shows up occasionally but you can never predict when it will show up again. Yes numbers do repeat but the lack of a periodic cycle of digits is what makes pi irrational. (Well irrational numbers irrational in general.)

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