Definition:Unit Arithmetic Function

Definition

The unit arithmetic function $u: S \to \Z$ is defined by $u \left({n}\right) = 1$ for all $n$:

$\forall n \in S: u \left({n}\right) = 1$

where $S$ is (in theory) any set, but in this context is usually one of the standard number sets $\Z, \Q, \R, \C$.

Also see

This is a particular instance of a constant function:

$f_1: S \to \Z: \forall x \in S: f_1 \left({x}\right) = 1$