Should the noun after "any" be singular or plural? [duplicate]

Before you can choose whether to use a singular or plural noun with any, you need to know which of the various functions and meanings it has in the context in which you are using it. In each of your affirmative sentences any is equivalent to every.

It can be found in any / every book.

This can be understood by anyone / everyone.

It can be said in any / every language.

For this reason, the following does not work:

? It can be found in any / every books.

In the interrogative sentences any does not mean every. In fact it does not really have a meaning at all and could be omitted:

Do you have books?

Is there a rule?

As to whether the singular or plural should be used with uncount nouns, the plural is more common:

Do you have any children? - ? Do you have any child?

Do you have any books? - ? Do you have any book?

But if you are expecting there to be only one of the thing in question, the singular may be used. In other words:

Is there any rule?

may be said in expectation that there will be only one rule.

Italian speakers are often confused by the different uses of "any" and its different meanings.

Any is usually defined as being an adjective, an adverb, a pronoun, a determiner and until today I was unaware of a further subclass: a numeral

Many words of different parts of speech indicate number or quantity. Quantifiers do not enumerate, or designate a specific number, but give another, often less specific, indication of amount. Examples are words such as every, most, least, some, etc.

Hence, "any" has a similar meaning to "a" and is normally used with uncountable and plural nouns.

1. (a) Do you have any books? (plural noun)
   (b) I haven't got any books.
2. (a) Do you have a book? (singular noun)
   (b) I haven't got a book
3. (a) Do you need any information? (uncountable noun)
   (b) I haven't got any information.
4. (a) *Do you need a information? NO
   (b) *I haven't got a information. NO

Examples and explanations taken (and adapted) from Practical English Usage by Michael Swan:
"Any" meanings and uses

1. It doesn't matter which

   • It's my treat. Choose any dress you like. [Choose a/one dress]
   • Take any card. [Take a/one card]
   • Any book on grammar will tell you how to use "any". [Any one book = every book on grammar]

2. In questions and negative sentences "any" can be used with comparatives, with "different" and in the expressions any/good, any/use, and any/point.

   • Is she any better?
   • I can't walk any further
   • You don't look any different now than ten years ago.
   • Is there any point in carrying on?
   • Was the film any good?

3. In sentences with negative adverbs such as never, hardly and rarely

   • He never has any spare time
   • She hardly eats anything
   • They rarely visit anyone

As a result the OP's phrases:

It can be found in any book
It can be said in any language
This can be understood by anyone (i.e. any person)

mean it doesn't matter which book/language/person, because every book/language/person has this quality or ability.