Is Infinity Real?

Arguments for a "First Cause" presented by philosophers from Aristotle to Jaki are that infinite regression is not possible. Hilbert, the great 20th Century mathematician, produced the infinite hotel paradox to show that infinity is not real. I am enough of a mathematician to understand how limiting processes can use infinity in looking at convergent series, the calculus, and so forth, and I appreciate Cantor's arguments about the cardinality of infinity. What is of interest are arguments (pro and con) about whether infinity "really" exists and, therefore, whether the universe might be finite or infinite.Edited by anselm, : plurality didn't agree

If you're not sure which forum to put this topic in, I'd suggest "Cosmology and Big Bang". The point here is that if you want to posit cyclic universes, then you have to show that infinite regress is a valid philosophical concept. And insofar as cosmology and the Big Bang are relevant to EvC, then so is the suggested topic.
Thank you.
Anselm