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From time to time, in Math textbook, I encounter the statement using whenever, e.g. on page 12 of Horst Herrlich's Axiom of Choice "A has an upper bound in X whenever each pair of elements of A has an upper bound in A."

In my mind, the assignment of truth value of a particular mathematical proposition is either a prior belief at the metalevel of reasoning, or a logical consequence of some other more “basic” axioms, both of which are irrelevant to time, which could be specified or not.

Why not replace "whenever" by "if" and its timeless synonyms, say, "provided"?

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You are free to replace synonyms with one another as you see fit. That's why they are synonyms. Not sure what the question here is. Had Herrlich used provided, someone would ask the opposite question, why he hadn't used whenever. He has to use some word. The sentence is perfectly grammatical and the meaning is perfectly clear. – RegDwigнt Jan 29 '13 at 12:56
I'm closevoting as Not Constructive. But in this case that doesn't mean there is no single unambiguously correct answer, since RegDwight's comment sums it up perfectly. I just think the question is intended to solicit votes in favour of using his suggested alternative conjunctions. – FumbleFingers Jan 29 '13 at 23:04

In your specific example "if" is a reasonably reasonable synonym for "whenever".
But, in mathematics, this is not always the case.

eg "Whenever the value of X changes from negative to positive."
Whenever A decreasing exponentially = B increasing linearly ... "
"Whenever the rotating field vector is at 90 degrees to ..."

In these cases one or both of the compared variables are dynamic and the term "whenever" not only signifies coincidence, but also the fact that one or both variables are changing, and that the equality occurred at a dynamic point in time. Using "if" here also conveys coincidence but loses the time variable nuance.

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