Talk:Set Theory/Zermelo-Fraenkel (ZF) Axioms

The two-way arrow symbol is never explained. The term 'disjoint' is never explained.

Axiom schema of separation
In the discussion of the axiom of separation, it seems awkward to me that the predicate is described as ranging over the members of A; a naiive reader might miss that, or think that it's some special kind of predicate. See for example the alternative explanation from Wikipedia's entry on the axiom:

> in words: > Given any set A, there is a set B such that, given any set x, x is a member of B if and only if x is a member of A and φ holds for x. > Note that there is one axiom for every such predicate φ; thus, this is an axiom schema. > To understand this axiom schema, note that the set B must be a subset of A. Thus, what the axiom schema is really saying is that, given a set A and a predicate P, we can find a subset B of A whose members are precisely the members of A that satisfy P. By the axiom of extensionality this set is unique.

This seems more lucid to me in that the subset relationship between A and B is clear.