\begin{definition}[Definition:Nonvanishing]
A function $f$ is said to be '''nonvanishing''' {{iff}} it has no zeroes in its domain.
That is, $f$ is '''nonvanishing''' {{iff}}:
:$\forall x \in \Dom f: \map f x \ne 0$
In this context, $f$ is (usually) either real-valued or complex-valued.
In any case, its codomain needs to contain a zero, so at the very least its codomain needs to be a ring.
Category:Definitions/Analysis
Category:Definitions/Complex Analysis
\end{definition}