Hmmm, can we claim that the universe is not infinite?
It's clearly not infinitely old (too many paradoxes with that one), but who's to say it's not infinite in matter?
What is infinity when discussing the Universe. Is our concept of infinity capped by the expansion of spacetime?
It's interesting because no matter how small of a segment we look at in the sky, we always find clusters of galaxies. And when we get a cluster of galaxies, if we look between those clusters, we see more clusters of galaxies, and so on.
Why couldn't the universe be infinite?