Full Idea
A 'total function' is one which maps every element of a domain to exactly one corresponding value in another set.
Gist of Idea
A 'total function' maps every element to one element in another set
Source
Peter Smith (Intro to Gödel's Theorems [2007], 02.1)
Book Reference
Smith,Peter: 'An Introduction to Gödel's Theorems' [CUP 2007], p.8
Related Ideas
Idea 13700 A 'total' function must always produce an output for a given domain [Sider]
Idea 13811 A 'total' function ranges over the whole domain, a 'partial' function over appropriate inputs [Bostock]