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I have the following sentence in my math work:

We were able to show when g(a,b)=1 for the case b|a because the distribution of rational numbers in the p-adic places is predictable.

I was told that usage of "when" is not really correct in this context because "when" is reserved strictly to time phrases. I know I can rewrite it as the following:

We were able to show for which a,b such that b|a we have that g(a,b)=1, because the distribution of rational numbers in the p-adic places is predictable.

However, the sentence appears to me to be much less clear than the original one, moreover it is longer, and I would have to change this way several sentences.

So the question: Is the original sentence incorrect? If so, can I make a small change to correct it?

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    By whom were you told this? By someone who is a native speaker AND a sophisticated mathematician? – StoneyB Jul 8 '14 at 18:26
  • @StoneyB Not a native speaker, my English teacher at the university. So you do think that it's ok? I get your comment with "in what cases", but then the sentence sounds ... ugly to me, I dunno why. – yo' Jul 8 '14 at 18:39
  • It doesn't fall so smoothly on the ear as your original; but in writing you have to consider that readers do not have your intonation and phrasing to guide them through a complex sentence--they have to supply intonation and phrasing from their imaginations, and they may get it wrong. – StoneyB Jul 8 '14 at 18:55
  • I have edited my answer somewhat. – StoneyB Jul 8 '14 at 19:03
  • And I'm still not sure whether the because clause explains why you were able to show &tc or is, on the contrary, a restriction on the cases involved. – StoneyB Jul 8 '14 at 19:06
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When is not “reserved strictly to time phrases” in ordinary English, any more than where is “reserved strictly to location phrases”. There are silly, literal-minded people who put forward propositions like this; but the propositions have no linguistic merit. In fact, I direct your attention to Introduction to mathematical arguments (background handout for courses requiring proofs), from the Berkeley math department, which is full of just such uses of when as yours.

Nonetheless, it is true that you should be very careful in your use of pronouns and pro-adverbs in very complex formal writing. It is easy to write sentences which lead the reader "down the garden path": the construction suggests that a subordinate clause plays one sort of syntactical role when in fact it plays quite a different role.

In this particular instance I do think it advisable to recast your sentence. I am not a mathematician, so I cannot be sure of my reading; but if I understand you correctly, this might be better:

Because the distribution of rational numbers in the p-adic places is predictable, we were able to determine under what circumstances g(a,b)=1 for the case b|a.

Your own rewrite has ambiguous phrase boundaries and wonky idiom in the middle. I would write it:

We were able to show for which a,b such that b|a it is true that g(a,b)=1, because the distribution of rational numbers in the p-adic places is predictable.

OR

We were able to show which a,b such that b|a yield g(a,b)=1, because the distribution of rational numbers in the p-adic places is predictable.

OR even better, as Damkerng T suggests,

We were able to show which a,b such that b|a satisfy the condition g(a,b)=1, because the distribution of rational numbers in the p-adic places is predictable.

But I would really be happier if there were some acceptable means of bracketing that [a,b such that b|a] as a unit. That may require intervention by a practised and widely published mathematician!

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I don't think it's entirely clear from either sentence what your intended meaning is. The first sentence doesn't make sense because there's an incomplete phrase. Here's the basic grammar structure of your sentence:

We were able to show X because Y.

X is a phrase that should resemble a sentence when removed from your larger sentence -- but in this case, removing it from the sentence:

"when g(a,b)=1 for the case b|a" -- this is an incomplete sentence of the form "When A, [then] B. The "[then] B" section is missing.

But I'm not sure what your intended meaning is -- Here's a grammatically correct sentence that may have a different meaning than you intend:

"We were able to show when g(a,b)=1 it is the case that b|a because the distribution of rational numbers in the p-adic places is predictable."

  • I don't see how it is incomplete. Is the following sentence incomplete? We were able to show when steganosaurus lived on the northern hemisphere because the carbon radionuclide method works. – yo' Jul 8 '14 at 18:20
  • Though that sentence's grammar does looks the same, its grammar structure is definitely interpreted differently from the way I was interpreting your first sentence (which admittedly, I could have interpreted incorrectly, but I find it hard to know because I'm not sure of the intended meaning). – Kai Jul 8 '14 at 18:25
  • I'm lost now completely. Wiktionary lists the usage of "when" as a noun only in a very special case, completely diffrent from my case. So either wiktionary is wrong or "being a noun" is not the same as "being a noun"... – yo' Jul 8 '14 at 18:27
  • @tohecz I may have messed up the grammar parsing -- I'm going to think on it some more, but I believe it's still true that these are slightly different grammar structures. – Kai Jul 8 '14 at 18:29
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    I believe the when clause here is a free relative construction. We were able to show "in what cases g(a,b)=1 for the case b|a" – StoneyB Jul 8 '14 at 18:32

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