Single Idea 13030

[catalogued under 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I]

Full Idea

Axiom of Extensionality: ∀x ∀y (∀z (z ∈ x ↔ z ∈ y) → x = y). That is, a set is determined by its members. If every z in one set is also in the other set, then the two sets are the same.

Gist of Idea

Extensionality: ∀x ∀y (∀z (z ∈ x ↔ z ∈ y) → x = y)

Source

Kenneth Kunen (Set Theory [1980], §1.5)

Book Reference

Kunen,Kenneth: 'Set Theory: Introduction to Independence Proofs' [North-Holland 1980], p.10