Editing Extensionality (section)

==Example==

Consider the two [[function (mathematics)|functions]] ''f'' and ''g'' mapping from and to [[natural number]]s, defined as follows:
* To find ''f''(''n''), first add 5 to ''n'', then multiply by 2.
* To find ''g''(''n''), first multiply ''n'' by  2, then add 10. 

These functions are extensionally equal; given the same input, both functions always produce the same value. But the definitions of the functions are not equal, and in that intensional sense the functions are not the same. 

Similarly, in natural language there are many predicates (relations) that are intensionally different but are extensionally identical. For example, suppose that a village has just one person named Joe, who is also the oldest person in the village. Then, the two predicates "being called Joe", and "being the oldest person" are intensionally distinct, but extensionally equal for the (current) population of this village.