The Axiom of Extensionality (Axiomatic Set Theory)

A description of the Axiom of Extensionality, showing that sets with the same members are identical.

This series covers the basics of set theory and higher order logic. In this month we are looking at the properties of sets and classes, including transitive sets, swelled sets, supercomplete sets, ordinary sets, proper subsets, null sets, empty sets, universal sets, and void sets. We are also looking at the first four axioms of a basic universe, following Neumann Berneays Gödel (NBG) set theory. In the next month we will look at relationships between sets.

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Information for this video gathered from The Stanford Encyclopedia of Philosophy, The Internet Encyclopedia of Philosophy, The Cambridge Dictionary of Philosophy, The Oxford Dictionary of Philosophy, Set Theory and the Continuum Problem by Smullyan and Fitting, Set Theory The Structure of Arithmetic by Hamilton and Landin, and more! (#SetTheory)

[stapleman]

3:29 there is a mising / extra parenthesis in the formal definition. Not sure how to fix.

[giovannaliviana]

"The number of classes in a given class is the class of all classes of the given set."
~ Frege

[조이량-cc]

Axiom of Extensionality is not an axiom but a definition of set equality. I don't know why they are all keep it after the begining fool. Is that a tradition?