Axiom:Axiom of Extension/Linguistic Note

Linguistic Note on Axiom of Extension
The nature of the axiom of extension, or axiom of extensionality as it is frequently called, suggests that it might better have been named the axiom of extent, as it gives a precise definition of the extent of a collection.

However, the word extensionality is a term in logic which determines equality of objects by its external features, as opposed to intensionality, which is more concerned with internal structure.