I have taken a look at the following topics:
But still can't quite find/understand the answer.
1) What is the easiest way to prove (if possible, without using ordinals etc. as my current math understanding of set theory counts only cardinals, and countable & uncountable sets) that the number of cardinalities that exists is not countable (that is, can't be put into bijection with N)?
2) What exactly does it mean that the set of all cardinals is so big that it's not even a set, but a class? Where does contradiction that does not allow it to be a set arise? I have read Pete's notes at http://math.uga.edu/~pete/settheorypart1.pdf, but am not quite sure how #20 leads up to that conclusion.
Thanks a lot!