Interesting observation! Yes, I think reduced to its essence, it boils down to: the expected value of "a finite number" is infinity. Which is strange in itself.
So you end up with a sequence that converges to 100%, but that convergence never starts, but it certainly happens eventually.
I guess a similar, less verbose thing would be "pick a random rational in (0, 1)". In decimal representation it'll repeat after "a finite number" of random digits, but "a finite number" again is expected to be infinity. So is a random rational really rational? Someone more educated on set theory will have to comment.
So you end up with a sequence that converges to 100%, but that convergence never starts, but it certainly happens eventually.
I guess a similar, less verbose thing would be "pick a random rational in (0, 1)". In decimal representation it'll repeat after "a finite number" of random digits, but "a finite number" again is expected to be infinity. So is a random rational really rational? Someone more educated on set theory will have to comment.