The concept of infinite space and time has very interesting implications. I remember reading a book that discussed the composition of the universe given that space and time were infinite.

The basic premise was that only a certain amount of matter and energy in a given amount of space is stable. This means that there is a finite set of arrangements that the matter can exist in in that space. If the universe is infinite then there must necessarily follow that every single state of existence exists. In other words, the probability that matter and energy will exist in a certain state is 100% if space is infinite. So there exists an infinite amount of doppelgangers of you, me, and everyone else that has ever existed.

I don't know how accurate that is because it supposes an infinite amount of matter to fill the infinite universe and I don't know enough about physics to make any sort of judgement.