You're right, Yor_on. I think my original post was imprecise.

What I was trying to say is that you can't get an infinite set of things by a process that adds one object to the set at a time, when each step takes finite time and the universe is only 14 billion years old... This is a physical limitation, not a mathematical one. In this case, each bounce generates one more image, but each bounce takes finite time, so you can't generate infinite images in finite time.

You can certainly form an infinite set of things from discrete elements. For example, there are infinitely many natural numbers (i.e. 1,2,3,4,5,...), but these are clearly discrete elements. The trick is that I just constructed this set theoretically--in other words, I didn't physically list each number. If I tried to write out, or have a computer compute, each natural number, it would never finish since that would take infinite time.