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Full Idea
We count two functions as being the same if they have the same extension, i.e. if they pair up arguments with values in the same way.
Gist of Idea
Two functions are the same if they have the same extension
Source
Peter Smith (Intro to Gödel's Theorems [2007], 11.3)
Book Ref
Smith,Peter: 'An Introduction to Gödel's Theorems' [CUP 2007], p.87
A Reaction
So there's only one way to skin a cat in mathematical logic.
| 8490 | First-level functions have objects as arguments; second-level functions take functions as arguments [Frege] |
| 21566 | 'Propositional functions' are ambiguous until the variable is given a value [Russell] |
| 18961 | We can identify functions with certain sets - or identify sets with certain functions [Putnam] |
| 13812 | A 'zero-place' function just has a single value, so it is a name [Bostock] |
| 13811 | A 'total' function ranges over the whole domain, a 'partial' function over appropriate inputs [Bostock] |
| 10074 | A 'total function' maps every element to one element in another set [Smith,P] |
| 10076 | The 'range' of a function is the set of elements in the output set created by the function [Smith,P] |
| 10075 | A 'partial function' maps only some elements to another set [Smith,P] |
| 10605 | Two functions are the same if they have the same extension [Smith,P] |
| 10612 | An argument is a 'fixed point' for a function if it is mapped back to itself [Smith,P] |
| 10209 | A function is just an arbitrary correspondence between collections [Shapiro] |
| 13700 | A 'total' function must always produce an output for a given domain [Sider] |
| 15105 | F(x) walked into a bar. The barman said.. [Sommers,W] |