I think you summed it up pretty nicely there :)

Keith Barrow wrote:

The probability of a generator being created over a unit of space (and/or time) can change in such a way that even in an infinite universe an non-infinite number of generators exits.

if you're talking about a truly infinite universe then even considering varying probabilities of the existence of random number generators, you still end up with an infinite number of random number generators; it's just a smaller infinity than the size of the universe, but no less infinite.