Learn English – How should I write “(the) number of unique items { is / are } few”

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.

Short answer

If people expect that there are a large number of animals there, and you know that there are some animals, although not very many, then you could say:

There are a very few animals there.

However, if you want to stress not the fact that the animals are there, but that there are not many, then you should say:

• There are very few animals there.

The phrase a very few is relatively rare, but it is perfectly fine, and very effective if you use it correctly.

Full answer

Few and a few are words that have a Determiner function in noun phrases. The Cambridge Grammar of the English Language, regards few as a determinative and a few as a lexical determinative (which I understand to mean an idiom which behaves like a determinative).

Few and a few look similar and they both give the impression that we are talking about a small number of items. However, they are very different, and getting them mixed up can cause serious problems. For example, using the wrong one can make your sentence false.

Few

Few is a negative word. It has a negative meaning, and it behaves like a negative word syntactically.

The word few means not many. This is its literal meaning. It also implies—gives us the idea—that we are talking about a number greater than two. However, this is just an idea that it gives us. It is not part of the literal meaning of the word. If I have a hundred criminals in a prison and I say:

• Few criminals will escape from here.

Then I am saying that not many criminals will escape. However, my sentence only implies that there will be a small number of escapees. There may be no escapees at all. So if no criminals escape, my sentence is true. If two criminals escape, my sentence is true and if five criminals escape, then my sentence is true (if we agree that five is not a large number). However, if ninety criminals escape, my sentence is false. It is not true that few criminals escaped because it is not true that not many criminals escaped.

Now I can modify this word few with an adverb like relatively or very. If I say:

• Very few criminals will escape.

Then I am lowering the upper limit on the number of escapees. Say we agree that eight or nine escapees is not a large number, but ten is (considering there are only a hundred criminals altogether). If I think nine criminals will escape, I can say few criminals .... But if I say very few, the listener will think that there are less than nine, maybe four, for example.

We can show that few is a negative word, because negative sentences always take positive question tags, and positive sentences usually take negative tags:

• Very few prisoners will escape, will they?
• *Very few prisoners will escape, won't they? (ungrammatical)

A few

A few is a positive word, with a positive meaning, and which has the syntax we expect from words in positive clauses. The word a few means more than two. It strongly implies—gives us the idea— that the number of things is not very large. But this is just an idea it gives us. It is not part of its literal meaning.

If I am inspecting a prison which has a hundred criminals, and I can see that there are some problems with the security, I might say:

• A few criminals are going to escape from here.

When I say this sentence I am guaranteeing more than two escapees. If nobody escapes then my sentence is false. If three escape, my sentence is true. Although I have only guaranteed a small number, if they all escape, my sentence is still true as well.

Now, I can modify the word few inside the phrase a few, using the words very, good or fair. If someone denies that any criminals will escape, then I could say:

• I bet you £10 a very few do manage to escape.

Now, here the word very is lowering our expectation of the upper end of the range of possible escapees. I am still guaranteeing more than two, but I am lowering the expected upper limit on the number of escapees. But notice that this is only an implication. It is not a guarantee. If the person who said that no one will escape takes my bet, then if everybody escapes, they will still have to pay me ten pounds. (They might still say You were wrong about it only being a very few though—as they give me my ten pounds!)

Notice when we use the words good or fair we are increasing our understanding of the lower limit, not the upper limit. Unlike when we used the word very, this does indeed affect the truth conditions of the sentence. If I say:

• I guarantee a good few criminals will escape.

Then if only three criminals escape, everyone will agree that I was wrong. My sentence turned out to be false.

We can show that a very few has a positive meaning, because it normally takes negative question tags. A positive tag will sound unusual and will have a special meaning:

• A very few criminals managed to escape, didn't they? (normal tag)
• A very few criminals managed to escape, did they? (marked - sounds confrontational)

Entailments

We can show that a very few does not mean the same thing as very few. The phrase very few means not many or perhaps not many at all. If I say:

• Not many people here eat animals.
• Very few people here eat animals.

These both mean the same thing. This sentence guarantees that if we substitute the word animal for a more specific type of animal, the sentence is guaranteed to be true:

• Very few people here eat monkeys.

So the more general statement guarantees (or "entails") the truth of the more specific statement. You cannot not eat animals without also not eating monkeys.

However, if I say:

• A very few people here eat animals.

This means I am guaranteeing a positive number more than two. I have lowered your expectation of the higher number in the possible range. But I have guaranteed something and not denied it. In this case, I cannot substitute a more specific word for the noun animals. My general statement does not entail a more specific one. Just because it is true that A very few people here eat animals it does not mean that:

• A very few people here eat monkeys.

People can eat animals without eating monkeys!

The Original Poster's question

If you want to stress that there are some animals there and people think there aren't any, you could say:

• There are a few animals there.

If you want to do this but you also want to show that you only commit to the fact that there is a very small number, you can say:

• There are a very few animals there.

However, if people are expecting that maybe there are quite a lot of animals, and you want to stress that there are not many, then you should probably say:

• There are few animals there.

And if you think the number of animals is much, much smaller than people expect, then you can say:

• There are very few animals there.

Conclusion

It can be very important not to confuse a very few with very few!

Grammar Note

Here is the entry from The Cambridge Grammar of the English Language by Huddleston & Pullum, 2002. Cambridge University Press: