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Full Idea
Calling a function a 'total' function 'over D' means that the function must have a well-defined output (which is a member of D) whenever it is given as inputs any n members of D.
Gist of Idea
A 'total' function must always produce an output for a given domain
Source
Theodore Sider (Logic for Philosophy [2010], 5.2)
Book Ref
Sider,Theodore: 'Logic for Philosophy' [OUP 2010], p.112
Related Ideas
Idea 10074 A 'total function' maps every element to one element in another set [Smith,P]
Idea 13811 A 'total' function ranges over the whole domain, a 'partial' function over appropriate inputs [Bostock]
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] |