this analogy illustrates the opposite of what I think you intend it to. if we could artificially iterate the sun rising infinite times, somewhere very high up, maybe after 10^10, it eventually would no longer rise
True, and that did occur to me as I was writing it.
The point was more that any length of time greater than a few thousand years is as good as infinite for a human, so (for, you know, everyday purposes) we might as well assume that the sun will keep on rising forever.
