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 Reference
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]