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I'm proofreading this in a friend's paper:

There is the same number of elements in the set of odd numbers as there are in the even numbers.

The same number is singular and it's the thing being compared, so it does seem like is is the right word to use, but then it bothers me that it switches to are in the second half of the sentence. Shouldn't it parallel the first half, as in "There is the same number of elements in the set of odd numbers as there is in the even numbers."? But that sounds wrong.

Note: This is not a duplicate of 'Does “the same number of people” behave as singular or plural?' That question refers to a verb clause modifying "people", and not "the number". Also, I am primarily concerned with the switch to plural in the second half of the sentence, which is not covered in that other question.

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Do not post the same question twice. If your question is closed, take steps to fix it (see the FAQ) and the request a reopening. I am voting to close. If it isn't a dupe of "Does 'the same number of people' behave as singular or plural?", then it certainly is a duplicate of your first question. –  Mahnax Apr 26 '12 at 22:02
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Sorry to have done the wrong thing, I'm new to this site. But I think my question was closed incorrectly and didn't see (and still don't see) any way of asking that it be reopened (is there any way to contact a moderator?). The FAQ suggests taking steps to improve it; I've tried to be more specific in this repost. Editing the original question doesn't seem fruitful though, since it's unlikely to be viewed when it's closed. –  ario Apr 26 '12 at 22:11
    
OK, fair enough. I'm sorry that I assumed that you were doing this for the wrong reasons, but I cannot reverse my close vote. For future reference, as I stated rather harshly above, posting the same (or an updated) question twice is not generally considered good practice. –  Mahnax Apr 26 '12 at 22:17
    
Well you have just answered your own question. If in "the same number of people" the verb refers to "people", then in "the same number of elements" the verb refers to "elements". –  RegDwigнt Apr 26 '12 at 22:19
    
I disagree. The comparison is between the count of the elements, not the elements. –  Hack Saw Apr 26 '12 at 22:25
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4 Answers

up vote 4 down vote accepted

Either you are comparing one thing with another single thing, in which case they should both be 'is', or you are comparing one set of things with another set of things, in which case they should both be 'are'; you shouldn't mix and match.

Whether you consider 'the number of elements in a set' to be a single unit (a Number, which describes a characteristic of the set of odd numbers) or a multiple unit (all the odd numbers, and we are counting them) is more a matter of personal preference.

However, the set should be described the same way in both halves of the sentence:

There is the same number of elements in the set of even numbers as there is in the set of odd numbers.

or

There are the same number of elements in the set of even numbers as there are in the set of odd numbers.

Or, you could suggest a rewrite along the lines of

The set of even numbers has the same number of elements as the set of odd numbers.

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For the least intrusive rewrite, simply replace "the same number of" with "just as many". All problems solved immediately. "There are just as many elements in the set of even numbers as there are in the set of odd numbers". –  RegDwigнt Apr 26 '12 at 22:47
    
If it's a math paper, "just as many" is awkward wording. Even though it's a reasonable way to say it, the emphasis wants to be on precision. –  Hack Saw Apr 26 '12 at 22:51
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In a math paper, you should not refer to the number of elements in an infinite set this way. Better to refer to the size or cardinality of the sets being equal. –  Old Pro Apr 27 '12 at 6:34
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If we rewrite the sentence to:

"There is the same count of elements in the set of odd numbers as there is in the even numbers."

... it sounds less awkward, and also gives us a clue. In this sentence, the verbs ought to match, and probably ought to be "is". However, it'd also be better to rewrite the sentence to be less awkward.

Perhaps: "The set of even numbers has the same number of elements as the set of odd numbers."

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+1 Although @Hellion is technically more correct, and his first rephrase would probably suit a formal mathematics paper best, I like this rewrite for its simplicity. You could also say "as in that of the even numbers". –  JeffSahol Apr 27 '12 at 1:53
    
"There is the same count of elements" sounds horribly awkward to me. If I were your editor I'd make you rewrite that. Besides, it is wrong, as neither the set of odd numbers nor the set of even numbers are countable. :-) –  Old Pro Apr 27 '12 at 6:25
    
The example doesn't define the set. –  Hack Saw May 4 '12 at 16:31
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Firstly, I'll dismissive OP's example as completely indefensible because "There is the same number" is inconsistent with "as there are in the even numbers". Use either singular or plural, but not both.

As regards which is best, here are some usage figures from Google Books:

"there are the same number of" - 176,000 results ... "there is the same number of" - 223,000 results.

Superficially it seems there's not much to choose between them in the popularity stakes. But "is" slightly wins out (and it really grates on me!), so because I know GB can be a bit flakey with broad-based queries involving many common words, I dug a little deeper (by century)...

C21 are:1760 is:765 ... C20 are:5310 is:1890 ... C19 are:1420 is:847

Those numbers suit me better, and I've no doubt they're far more accurate. The fact of the matter is that associating the verb form with singular "number" is just misguided pedantry. Semantically, the "subject" is [some number of] elements, which is plural. If I wanted my sentence to focus on the specific singular number that is the same, I'd normally recast it as...

The number of elements in set A is the same as the number of elements in set B.

...but I certainly wouldn't use that form replacing set A/B with the set of odd/even numbers, because that confuses two different usages of the word "number". So in OP's case I'd say...

There are as many elements in the set of odd numbers as in the set of even numbers.

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"There are as many" has the advantage of being mathematically correct in the OPs case of uncountable sets. –  Old Pro Apr 27 '12 at 6:30
    
@Old Pro: Yes, although as you say in a comment elsewhere, equal "size" (or "cardinality", being more technical), would be a better way of putting it. I just think that at the level of everyday English it's a really bad idea to use the word "number" for "sum, count, total" in the same sentence where it's also being used to mean "integer, value". –  FumbleFingers Apr 27 '12 at 16:07
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Either:

  • the author definitely wanted the singular in the first case in order to place some particular emphasis;

or:

  • it was just a slip, and it would not change the author's intended meaning to put both verbs in the plural.

So, if you genuinely think it sounds jarring, why not ask them if they intended any special meaning with the singular? If not, change it; if so, leave it.

On the other hand, if you don't actually think it sounds jarring and you're just looking for problems where none exist, then why not just leave it as it is.

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Does that mean it would be grammatically correct to put both verbs in the plural, even though they are referring to "the number"? –  ario Apr 26 '12 at 22:14
    
Yes. And given that the verb can be in the plural, why do you conclude that it refers specifically to "number"? (Or why do you presume it matters in any case?) –  Neil Coffey Apr 27 '12 at 13:45
    
The human race put a man on the moon, folks. We can grasp this...! –  Neil Coffey Apr 27 '12 at 13:47
    
Trained by the SATs –  ario May 10 '12 at 5:39
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