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

You don’t see the a second version of the number 3 until the 10th digit of pi, you don’t see a repeat of 31 until you get to 140 digits, and you don’t get to 314 until the 2,122nd digit. So sure you start to see larger repeating portions of pi showing up, but they are showing up at a way slower speed than the total sequence is expanding. So by the time you get to that patter you’ve got 1000’s more digits you need to match to fully repeat. There is no reason to believe that you will always repeat in an infinite series like this.

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