I introduced the concept of CoinSpace to make it clear that all the coinflips are independent of each other: if I were actually flipping a single coin I would assign it a nonzero (though very small) probability that it never lands "tails". Possibly I should have just said the independence assumption.

And yes, I agree that if we postulate a finite time condition, then P(X) = 0 means one can't ever update on X. However, in the context of this post, we don't have a finite time condition: God-TimFreeman explicitly needs to stop time in order to be able to flip the coin as many times as necessary. Once we have that, then we need to be able to assign probabilities of 0 to events that almost never happen.