What is "extensionality"

n. 1 (context philosophy English) The principle that objects are equal if and only if their observed properties are the same, regardless of internal processes that lead to those properties. 2 (context mathematics functional analysis English) The principle that functions are equal if and only if they operate on the same domain and for any given element of the domain the result of each of the functions is the same. 3 (context mathematics set theory English) The principle, codified in the axiom of extensionality, that sets are equal if and only if they contain the same elements.

In logic, extensionality, or extensional equality, refers to principles that judge objects to be equal if they have the same external properties. It stands in contrast to the concept of intensionality, which is concerned with whether the internal definitions of objects are the same.