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.