Definition:Non-Vanishing
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Definition
A function $f$ is said to be non-vanishing if and only if it has no zeroes in its domain.
That is, $f$ is non-vanishing if and only if:
- $\forall x \in \Dom f: \map f x \ne 0$
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.
Also known as
Some sources give this as nonvanishing.