> Sort of like if you have an infinite number of coin flips then at some place and time you'll land on heads a million times in a row, no matter how unlikely.
If random event result is any real (i.e. not limited integers and fractions) number from interval 0-1, then no number will appear twice even after infinite number of throws.
Open question surely follows: Time and space, are they integer or real?
That's kind of like asking if spacetime is quantized or not. We have bits of evidence in both directions. For example, the entropy of a 2D (conventional) Event Horizon, is identical to the number of planc-length (square) units of area on the EH sphere, and so that's a definitely quantity/number, for any given Black Hole mass. You could interpret that as saying the EH is broken up into "pixels" sort of, which a kind of quantized view of spacetime if our universe is indeed a big Event Horizon.
If random event result is any real (i.e. not limited integers and fractions) number from interval 0-1, then no number will appear twice even after infinite number of throws.
Open question surely follows: Time and space, are they integer or real?