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I have written the phrase:

"The set of elements whose each pair is ...".  

Is the 'whose each' acceptable?

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I think whose is more appropriate in case of person, not necessarily, but in most of the cases. –  Mistu4u Feb 13 '13 at 3:07
I think we need a bit more of the sentence. It's not clear, at least to me, what is is you are really trying to convey here so I'm not sure if something like, "The set of element pairs such that each pair is ..." makes sense yet. I have a feeling you can get rid of the possessive altogether but until we have the whole sentence I can't be sure. –  Jim Feb 13 '13 at 3:55
I was trying to ask this question in Quora: quora.com/Languages/Which-multiple-false-friends-are-there and the phrase I would like to write is " I would like to know sets of at least 3 words, whose each pair of words are false friends" –  Alex Grilo Feb 14 '13 at 13:41
"The set whose each pair of elements...". –  Jon Hanna Feb 15 '13 at 13:11
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2 Answers

The short answer, I'm afraid, is 'no'. Whose each is not grammatically correct.

I assume the phrase is referring to a list of elements, for which each element in the list has a pair (element?), and you are interested in said pair elements that exhibit a certain characteristic?

The way I would word this would be:

The set of elements where each element's pair is ...

Slightly more verbose, but also fine is:

The set of elements for which each element's pair is ...

To alleviate any confusion, there is nothing grammatically incorrect about The set of elements whose pair is... There is an ambiguity however as to whether the elements have the pair or the set does, so you wouldn't use that particular wording in this instance.

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mcalex, how about "The set of elements 'for which' each element's pair is ..."? –  user114 Feb 13 '13 at 2:44
Per my own answer, clearly I disagree with this "not grammatically correct" line. –  FumbleFingers Feb 13 '13 at 17:46
The ambiguity is not in the perfectly standard "whose each", but in how it applies. Indeed, it seems they meant pairs of the elements, and so "The set whose each pair of elements..." is what they meant. –  Jon Hanna Feb 15 '13 at 13:13
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As indicated by answers to Can “whose” refer to an inanimate object? on ELU, some people wouldn't be happy with OP's use of it here. I'm not one of them, and given how awkward it would be to avoid the word in OP's construction, I'd just ignore those pedantic prescriptivist grammarians who say it's wrong.

Note specifically Peter Shor's answer on that ELU question, with several examples of Shakespeare using whose to indicate association with inanimate objects.

Here are many thousands of written instances of "equations whose solutions", which is perfectly normal English. By the same token, there's nothing wrong with OP's ...sets of elements whose pairs...

Having (I hope) dismissed criticism of whose, I'd say that most native speakers would use every rather than each in OP's particular sentence. I know I said in another answer that using every in this way is usually a bit stylised/dated. But here it's just "formal", which is appropriate in a "mathematical" context.

I can't exactly explain why "every" is better than "each" here, and I very much doubt it involves any "grammatical rule". But to support my contention that it is "better"...

whose each response (0 hits in Google Books)
whose every response (142 hits)

Also note that the corresponding figures for "whose each/every pair" are 3/116, and for ...solution they're 5/27, which may suggest that mathematicians are less attuned to such subtle distinctions.

There seems to be some disagreement over the distinction between "less common" and "ungrammatical" here, so I'd like to quote from New Scientist - 5 Aug 1989 - Page 55

Rather it elaborates a millionfold democracy whose each unit is a cell.

I've been reading New Scientist every week for decades, and I honestly can't recall ever seeing a grammatical error get through their admirable proofreading procedures. It's also reasonable to assume the authors of Encyclopedia of British Writers, 1800 to Present know their own language...

Golding is an author whose each successive work deals with a different subject in a different time...

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errr, OP does not say sets of elements whose pairs. The question is about whose each, which you then prove is not in general use (i.e. the type of English ell is all about) except by mathematicians. What gives? –  mcalex Feb 13 '13 at 18:11
@mcalex: The grammaticality or otherwise is totally unaffected by whether it's set or sets. OP appears to be asking about both words whose and each simultaneously, and your answer seems to focus on replacing whose with some variation using which or where, which I think is neither grammatically nor even stylistically necessary. However, I think there are stylistic (but not grammatical) grounds for preferring every over each, and I've supported (not "proved") that position using some crude statistics on related usages. What gives, indeed? –  FumbleFingers Feb 13 '13 at 18:20
I'm not focussing on replacing whose with some variation I'm giving alternatives for whose each because it's wrong. I didn't include 'whose' on it's own for the edited (ambiguous, not grammatical) reason, and I didn't think the stylised/dated nature of 'whose every' warranted a mention (though the mathematical context is a good point). I could add that but don't need to, now you have, but none of that changes whose each. –  mcalex Feb 13 '13 at 18:34
@mcalex: What can I say? I don't agree with your bald unsupported statement that OP's whose each is "wrong" in any meaningful sense - it's just not a common form compared to whose every, or indeed whose each and every –  FumbleFingers Feb 13 '13 at 18:37
Suppose it's about time I join ELL, and voting this answer up is reason enough to do so right now. –  Jon Hanna Feb 14 '13 at 1:34
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