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I have a question regarding the use of the article "the" in the following sentence. What is correct?

"[...]. The answer of each agent depends on the number of other agents answering the same."

or

"[...]. The answer of each agent depends on the number of the other agents answering the same."

I want to refer to the number of all the other agents answering the same.

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depends on the number of other agents indicates all the agents. It works like this, if I say 'the fingers on my hand' it means all the fingers my hand. Therefore, if we say 'the number of' also means 'all' - the whole number of 'other agents'.

depends on the number of the other agents rather suggests they all share a single telephone number, or similar, unless we have previously defined the group of 'other agents'. No text is an island, and 'the' links the same noun phrase for as long as wish it.

  • I don’t see where the telephone number bit comes from. The two sentences are completely equivalent to me, except that the latter presupposes knowledge that there are some other agents who give/gave/have given the same answer. – Janus Bahs Jacquet Jul 25 at 11:31
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The number of the other agents is correct.

Let's prove it:

Can a construction like "...depends on the number of the other agents..." be grammatical?

Yes. it can.

For example:

Sunnyvale has many local businesses. Most are restaurants, and several produce food. There are also some other types of business in town. The fate of each businesses depends on the number of the other businesses that succeed.

What does such a construction mean?

So, interestingly, your second sentence does put all the agents into a set, just as "...depends on the number of the other businesses..." puts all of the businesses of the example above into a set.

Your second sentence is correct, and it does express what you want.

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