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I wrote:

In this formula, the number of the nodes is multiplied by (H + P) because for each node, it is checked against the list of the handles, and if a match is found, a pattern is retrieved from the list of the patterns.

In this sentence, patterns, nodes, and handles are specific to the reader then I used "the" before them, I just want to double sure that the sentence above required the second "the" in of-phrases and it's not equivalent to:

In this formula, the number of nodes is multiplied by (H + P) because for each node, it is checked against the list of handles, and if a match is found, a pattern is retrieved from the list of patterns.

Are they equal in the context I described?

What about the following sentences:

the time complexity is O(N * (H + P)) where N is the number of the DOM-tree nodes, H is the number of handles and P is the number of the patterns. ...

These operations depend on the size of the handles, H, and the size of the patterns, P.

Is the second "the" extra in this sentence too? because I feel I need to emphasize the items, so I need "the".

  • No, you can forego the there. the number of nodes is .... the list of handles... the list of patterns – Tᴚoɯɐuo Dec 25 '16 at 17:06
  • @TRomano thank you! Is there any rule for that? I mean in which phrases is it possible? – Ahmad Dec 25 '16 at 17:34
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    There's no need to use the article when the of-phrase qualifies the preceding noun like an attributive form (the nodes list...the handles list...the patterns list -> the list of nodes...the list of handles...the list of patterns). But it isn't ungrammatical to use the. Consider: The White House is throwing a gala. Here is the list of dignitaries. That form is pretty much equivalent to the adjectival "Here is the dignitaries list...". If you use the article (the list of the dignitaries) you're referring to the dignitaries who appear on the list rather than to the type of list. – Tᴚoɯɐuo Dec 25 '16 at 18:11
  • @TRomano thank you, I think your comment could be the answer. – Ahmad Dec 25 '16 at 19:00
  • @TRomano I added another sentence in which I used the size of the handles, I feel it's not an attributive form and needs "the" after "of", right? – Ahmad Dec 26 '16 at 6:30
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You do not need to use the second "the" in your example.

The determiner "the" is used to signify a particular object, which in your case is either "number" or "list"

the number
the list

If you had a case of nodes in a set A and nodes in a set B and only wanted to reference either A or B, you might write

the number of the A nodes
the number of the nodes in A
the number of nodes in A

In your second part

the time complexity is O(N * (H + P)) where N is the number of the DOM-tree nodes, H is the number of handles and P is the number of the patterns...

These operations depend on the size of the handles (H) and the size of the patterns (P).

Since you are using the "the +plural" pattern it is equivalent to "each +singular"

These operations depend on the size of each handle (H) and the size of each pattern (P).

unless it is the name of a group

My friend has two daughters and we call his wife and daughters: The Ladies.

which refers to all three (note capitalization), however

The Ladies in the band are all trained musicians.

refers to each woman assuming they are three other women.

| improve this answer | |
  • Thank you, I added another related sentence to my question, could you please consider that too? – Ahmad Dec 26 '16 at 6:25
  • By "the size of the handles" I mean the number of handles or the size of the handles set. I thought the size and number are equivalent in my sentence. Should I again use "the size of handles" or simply "the number of handles"? – Ahmad Dec 26 '16 at 12:14

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