Some where I read the two following notions: "Identically non-vanishing function of complex variable" & "non vanishing function of complex variable". Are they the same? What I know is tha a non-vanishing function is such that $f(x)\neq 0~~ \forall x\in R$. Is it the same in complex set?
What is the deference between identically non-vanishing function and non vanishing function
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complex-analysis
functional-analysis
1 Answers
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These two notions are the same. The use of the word identically is usually meant to emphasize uniformity across the domain, or something like that.
E.g. $f:\mathbb{R}\to \mathbb{R}$ given by $f(x)=0$ is identically $0$ on its domain.