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I often encounter a problem with adding "the" or not. I had a proofreading teacher last year that gave us a concrete example as follows:

Cows eat grass = Cows, in general, eat grass

The Cows eat grass = Those specific cows eat grass

Yesterday I was writing an email and hesitated in adding "the" or not in this phrase:

"Although weeks 31 and 32 are not problematic anymore, we still need volunteers for weeks 34 and 35."

I finally decided to add "the" as I think it was a request for specific weeks...

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    "weeks 31 and 32" is very clearly talking about specific weeks. You don't need to add "the" and in fact you should not. – Max Williams Jul 27 '16 at 10:51
  • Hello Guilherme, and welcome to the site. I've edited your title because »“Weeks” or “the weeks”?« is not a very useful one—it doesn't tell the reader much about what your actual problem is. The thing you're wondering about here is not really related to the word week, but to whether a noun that is followed by a number in the sense “[noun] number X” should have a definite article or not. – Janus Bahs Jacquet Jul 27 '16 at 11:36
  • I feel 'the' is required for weeks 31 and 32- being the weeks deliberated enough during recent past.Although ''THE '' weeks 31 and 32 are not problematic anymore, we still need volunteers for weeks 34 and 35." That is my view please. – Abhilaaj Jul 27 '16 at 11:41
  • @Abhilaaj Why would you add the for weeks 31 and 32 but not for week 34 and 35? – oerkelens Jul 27 '16 at 14:40
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    In general, the number indicates that you talk about a specific week, so you don't need the article. In a hotel, you stay in room 243, not in the room 243. However, you could stay in the blue room. Blue does not have to specify a specific room, so you use the definite article to make clear that there is only one such room. – oerkelens Jul 27 '16 at 14:42
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There are two common ways to show that a noun is numbered, i.e., that it occupies a particular number in a list of things of the same type. Those two ways are:

  • using an ordinal number before the noun
  • adding the number right after the noun, optionally preceded by the word number

Ordinal numbers (first, second, third, etc.) function more or less like adjectives, and as such, they can be used as part of both definite and indefinite noun phrases—the difference being whether the noun phrase as a whole should be considered definite or not in the context it appears.

Since ordinal numbers are most commonly used to limit a range of things down to one specific one (the one that occupies the nth place in the list), which makes the noun phrase definite, the definite article is much more common than the indefinite article.

The other way to express a certain number in a list or range functions differently. The number (with or without the word “number” itself) added after the noun does not act as an adjective as such, though they are quite similar to; what exactly it is generally categorised as syntactically, I don't know offhand.

Crucially, though, this postpositive number inherently marks the noun phrase as definite. In that sense, it functions like Saxon and pronominal genitives.

Saxon genitives act like determiners (like articles) and mark the noun phrase as definite—but since you can't have multiple determiners and you can't mark a noun phrase for definiteness more than once, you cannot combine a Saxon genitive with an article: *my the house doesn't work.

Postpositive numerals are not, as far as I know, generally considered determiners, but they do have the effect of marking a noun phrase as definite and blocking at least articles: *a week 33 doesn't work, nor does *the week 33.

Oddly enough, they don't block other determiners like Saxon and pronominal genitives: My week 33 is looking terribly busy is a bit awkward and not how most people would phrase it, but it's grammatical. A more likely scenario would be a student in class who, upon being told to flip to page 20 in the class book, raises his hand and says, “But my page 20 has been torn out!” (meaning “page 20 in my book”).

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When a designation follows a common noun, that noun phrase does not allow the definite article.  It doesn't matter whether those designations are numbers, letters, proper names, or anything else. 

  • weeks 31 and 32
  • columns A and B
  • team members Alice and Bob
  • operations Charlie and Delta

These designations are restrictive appositives. As restrictive appositives, they are definitive determiners and preclude the addition of the definite article. 

However, using the same destinations as adjectives (or, more correctly, as attributives) does allow the definite article:

  • the 31st and 32nd weeks*
  • the A and B columns
  • the Alice and Bob team**
  • the Charlie and Delta operations

The one exception to this pattern that comes to mind involves placenames:

  • the cities Chicago and Boston

I'm tempted to think that the placenames don't stand as an appositive but rather as a genitive.  The phrases "the cities Chicago and Boston" and "the cities of Chicago and Boston" mean the same thing.  We can't say the same about pairings like "columns A and B" & "the columns of A and B", or "team members Alice and Bob" & "the team members of Alice and Bob". 

_______________ 

* The ordinal numbers are adjectives, but plain numbers don't act like attributives. Instead, they act like cardinals, which are adjectives in their own right.

** It may be grammatically correct to speak of "the Alice and Bob team members", but that phrasing is also unnaturally dehumanizing.

  • I think you're conflating two things here. There are restrictive appositives, which include team members Alice and Bob (and which do allow determiners such as the definite article, though it's not as common as null articles, I'd say); and then there are these pseudo-appositives that include the numbers and the “columns A and B”. In general, an appositive can replace the noun phrase it restricts without rendering the sentence unintelligible, which isn't true (except in certain circumstances) for the number ones here. – Janus Bahs Jacquet Jul 27 '16 at 16:22
  • I have to wonder what dialect finds "the team members Alice and Bob" acceptable, or what distinction you see that prevents only certain ill-defined designations from standing in literal apposition. It requires no special circumstances for alphanumeric designations to stand either in apposition or alone. – Gary Botnovcan Jul 28 '16 at 4:30

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