7.5 ZF and ZFC
Set theory becomes a foundation for mathematics only after its basic principles are stated as axioms. Informal set language is useful, but it can lead to contradictions if every definable collection is allowed to be a set. The Zermelo Fraenkel axioms provide a controlled formal framework in which sets may be built, compared, and used without allowing unrestricted comprehension. Motivation A naive view says that every collection described by a...