Single Idea 10097

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

Full Idea

The Axiom of Extensionality says that for all sets x and y, if x and y have the same elements then x = y.

Gist of Idea

Axiom of Extensionality: for all sets x and y, if x and y have the same elements then x = y

Source

A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3)

Book Reference

George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.50


A Reaction

This seems fine in pure set theory, but hits the problem of renates and cordates in the real world. The elements coincide, but the axiom can't tell you why they coincide.