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-35Stuck on an island with all the same sex...everyone would eventually turn gay, **eventually****amirite?**

I can see why it might seem that way given that it is infinite.

We can say that any sequence of digits will occur infinitely many times within the digits of Pi.

What we can't say for certain though, is that there is an initial number of decimal digits such that 3.{n}{n} occurs.

We can also say that there will definitely be no regular recurrence of digits in Pi, as that would make it predictable which is not compatible with it being a proven irrational number.

That really cannot be said with absolute certainty

Pi is infinite, goes on forever and ever and ever and ever and ever and ever and ever. In comprehensive amount of digits.

Think of it like this, there could be a point way down in pi after which the digit 9 never appears. We have no idea if this is true.

Yes, but that does not necessarily prove that it shall begin to repeat itself. Logically, an infinite series will eventually play all the combinations but on a theoretical level, one can never be absolutely certain as even logic bends backwards to give leeway towards practicality

Is this not the Infinite monkey theorem? An infinite number of continuing numbers is bound to repeat segments of itself at some point?

Not necessarily. First off it is impossible to prove. Second, given that it is infinite, some parts of it could possibly repeat, but not the number itself. Just certain digits or groups of digits. And that's hardly repetition.

True.