Thinking about infinity

[Ignorant]

But, of course, there are different levels of infinity as well.  For instance, you can famously prove that there are the "same" amount of natural numbers and rational numbers, but there are "more" real numbers than there are natural numbers.

I remember in Real Analysis 2 we discussed Omega (the "level" of infinity of the reals), which is greater than Aleph_0 (the level of infinity of the naturals), and then how you could make sets of things with different measures of infinity, like Omega^2 and such

Do you think that tells us anything about the logical possibility of an infinite set which has every member simultaneously existing in reality?