I stumbled over this: Infinite Set is Disjoint Union of Two Infinite Sets
but from my current knowledge, this is far over my hat.
At university, we have learned that $\aleph_0$ and $\aleph_1$ are different by Cantor's proof, and that there are more cardinalities based on this, especially the power sets of a set with cardinality $\aleph_i$ has cardinality $\aleph_{i+1}$ but the link above opens a tar pit of confusion with other possible cardinalities.
Where should I start reading?
Please note the tag [soft-question], I know this is not a "good" questions based on the standards here, but as of now, I can't do any better.
