Theorem classification

I claim (as an experiment) that there are three kinds of theorems "If A then B". Let \(|A|\) be the number of arrangements of objects that fit the description, i.e. interpret \(A\) as a set of tuples.

1. \(|A| = \aleph_0\) – these give exact answers
2. \(|A| = c\) – these give approximate results, usually to arbitrary precision
3. \(|A| > \aleph_0\text{ but }|A|\not=c\) – these are even deeper set-theoretical fantasies

If \(|A|\in\mathbb{N}\text{ or }|A| = 0\) then the theorem doesn't deserve to be called a theorem because the use of the implication can be avoided by enumerating all statements \((a_i\in A,b_i\in B)_{i=1}^n\).

A subtle issue is that my use of sets is not justified. For example, according to present set theory, there is no set of all sets, so my classification cannot handle statements like "All sets have a power set". I count all such theorems into category 3 because they are set-theoretic.