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I once heard of that the article "the" can be omitted after "of".

So which sentence should I choose,

"in terms of the number of something" or "in terms of number of something"?

At the same time, I know that it's incorrect to say

"an expression for number of something".

It have to be

"an expression for the number of something".

For example,

"We derive an expression for the number of the mean value".

What's the difference between "the" after "of" and after "for"? Why?

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    Here's the Ngram for terms of the number of, in terms of number of. Concerning "expression for (the) number", it would be better to provide an example sentence. – CowperKettle Jan 24 '16 at 2:58
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    The article usage is determined by the noun ("number" in these examples), not the preposition. Because in your examples the "number" is specific, it is the number. Your question relates to article usage, but what you heard is wrong. – user3169 Jan 24 '16 at 3:48
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In that statement it says:

"We derive an expression for the number of the mean value".

This means that the expression is to give reason for the number(the purpose of the expression is the number), and the number is part of the mean value (we could also say that the mean value is a descriptor of the number).

So, the "for the" is to say that it is for the thing, and "of the" is to say that something is part of the whole.

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