>>12159216For a "type of infinity" well defined there needs to be a set of that size.
The set of natural numbers is an example of a set with the smallest type of infinity.
For every set, its power set is bigger, so there is not a finite list of all infinities.
However, you cannot form a set of all infinities. That's impossible because the set would be too big and cause paradoxes in set theory.
For every ordinal x, there is a set of with the size aleph_x. This is proven by induction.
If there were a set of all cardinals, then it would contain all ordinals. But that's impossible, since the class of all ordinals is too large to be a set.
