Axiom:Axiom of Extension/Linguistic Note

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Linguistic Note on Axiom of Extension

The nature of the Axiom of Extension, or Axiom of Extensionality as it is frequently called, suggests that the Axiom of Extent, ought in fact to be the preferred name, 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.