Those intrepid adventurers Alice and Bob, in their respective space craft, are the only occupants of an infinite void. Suppose that Alice and Bob are an infinite distance apart; if each moves, say, a billion light years towards the other, are they still an infinite distance apart? Intuitively, it might feel as though they should be two billion light years closer to each other, but that would mean that the distance between them was less than infinite. If the distance between them is less than infinite, it must be finite. This means that something that was infinite has become finite. Reverse their journey and something finite suddenly becomes infinite. This is impossible.

Any thoughts?

There never was nothing.