Zermelo-Fraenkel Set Theory

Naive set theory and the axiom of unrestricted comprehension have a massive flaw, which is that they allow Russell’s paradox; a serious logical inconsistency. Zermelo-Fraenkel set theory is a fresh definition of set theory that makes sure to not allow Russell’s paradox within it. This video covers 6 out of the 9 ZF axioms (axiom of extensiionality, power set axiom, pairing axiom, union axiom, axiom of infinity and the axiom of subsets/restricted comprehension). The further 3 axioms are far more complex and are not covered and instead are left for subsequent videos.The video also briefly discusses the axiom of choice (the 10th axiom in ZFC) and compares and contrasts it to the axiom of restricted comprehension.