^^ Well, I'm saying that existence must be infinite because there's no such thing as non-existence. There can be no "outside." The Big Bang doesn't represent finity, it either represents an event in a larger context or a process that we can't see beyond.
That's an interesting thought experiment, and very likely useful in higher mathematics, but it's an artifact of the calculation, not representative of an attribute of reality. A particular subset of infinity doesn't require a particular one-to-one correspondence to another subset to qualify as infinite.Pretty good. I think "some infinities are larger than others" is a cute way of putting it, but, of course, the great thing about infinities is that they are all the same size (which is bigger, the set of all integers or the set of all odd integers?).
That is not correct.
There are different sizes of infinities.
http://www.scientificamerican.com/article.cfm?id=strange-but-true-infinity-comes-in-different-sizes