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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
    Commented Jan 29, 2013 at 12:56
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    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
    Commented Jan 29, 2013 at 23:04
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    I’m voting to close this question because I just think the question is intended to solicit votes in favour of using his suggested alternative conjunctions. – FumbleFingers
    – Greybeard
    Commented Oct 14, 2020 at 9:36

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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.

Somewhat less mathematical but maybe makes the point more clearly:

  • The tidal pools are filled whenever the local high-tide level is above 2.1 metres.
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  • Fancy that - a phantom downvoter after 7.5+ years. No stated reason, as is often the case. I wonder what their thought processes were and/or why they (could possibly have) thought that this answer did not meet the "this answer is useful" criterion.
    – Russell McMahon
    Commented Oct 13, 2020 at 9:22
  • Here’s a phantom upvote. Ok now it’s not phantom anymore
    – Jim
    Commented Feb 11, 2021 at 19:27
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    @Jim Thanks. +2 / -1, 8.1 years on :-). I find it sort of interesting that this question did not attract at least a few more answers, and that my answer was not either accepted or commented on.
    – Russell McMahon
    Commented Feb 11, 2021 at 23:19
  • Here, have another corporeal upvote ;-). Alas, math is overrated... get a job in something more lucrative like crypto currencies, NFTs, big data! Erm... wait...
    – petre
    Commented Jan 22, 2022 at 16:46
  • @petre thanks for the vote. I note that I have one downvote and 4 upvotes as of Jan 2022. Evidently at least one voter lives in the timeless now :-).
    – Russell McMahon
    Commented Jan 23, 2022 at 7:23

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