Exercises
[03F] Prerequisites:[01P].(Proposed on 2022-12) Show that cardinalities are always comparable: given two sets \(A,B\) either \(| A|\le | B|\) or \(| B|\le | A|\) holds. (Use Zorn’s lemma and the construction explained in the exercise [01P]).
Solution 1[ (Present as theorem 1.19 in the notes) ]
This statement is equivalent to the Axiom of Choice, see [ 15 ] .