The universe is finite (idea)

I can think of at least three ways in which the universe could be infinite off the top of my head:

1. My closet is infinite because I can keep sticking things in it. (Is there infinite space between or around the mass in the universe?)
2. My set is infinite because I can find a one-to-one correspondance with the natural numbers. (Is there an infinite number of things that can be counted?)
3. My volume is infinite because given any subset of my volume, you can divide it. (Is the universe infinitely divisable?)

Each of those types of infinite could be satisfiable:

1. If you're counting particles, then look no further than your nearest vacuum.
2. If you're measuring space, then just wait long enough.
3. If you believe Gorgonzola, then you can fit infinity in the palm of your hand.

...Or maybe they're not:

1. If you +1 to your count for every particle and -1 for every antiparticle then your vacuum contains nothing (see the Law of Conservation of Mass).
2. Waiting an infinite amount of time before counting is cheating.
3. Our computers are virtual machines in the real machine that is the universe so I don't believe Gorgonzola. :)

Is the universe infinite? That's an ambiguous question.