ABSTRACT
7.1 It seems to be a nontrivial step on the conceptual level to view subsets of a set as elements of a new set, as it is done in the definition of quotient set via classes with respect to an equivalence relation (see Definition 7.9). The use of partitions allows to obtain the equivalence between Zorn's Lemma and the Axiom of Choice (7.21), as well as Zermelo's Theorem (7.21); see Theorem 7.22. In the sequel some structure defined on a set often has to be transferred to the quotient set, so notions in this section are important later when defining quotients of groups, modules, etc ..
