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no, none and not a/any

no: emphatic

No can be used instead of not a or not any when we want to emphasise a negative idea.

  • Would you believe it? There’s no mirror in the bathroom! (More emphatic than … There isn’t a mirror …)
  • Sorry I can’t stop. I’ve got no time. (More emphatic than … I haven’t got any time.)
  • There were no messages for you this morning, I’m afraid. (More emphatic than There weren’t any messages …)

none of

Before a determiner (e.g. the, my, this) or a pronoun, we use none of.

  • She’s done none of the work. (not … no of the work.)
  • We understood none of his arguments.
  • I’ve been to none of those places.
  • None of us speaks Greek.

When we use none of with a plural noun or pronoun, the verb can be singular (a little more formal) or plural (a little more informal).

  • None of my friends is interested. (more formal)
  • None of my friends are interested. (more informal)

We can use none alone if the meaning is clear.

  • ‘How many of the books have you read?’ ‘None.’

not a/any

We prefer not a/any in objects and complements when the sense is not emphatic. Compare:

  • He’s no fool. (= He’s not a fool at all. – emphatic negative)
  • A whale is not a fish. (not A whale is no fish – the sense is not emphatic.)

Subjects

Not any cannot normally be used in subjects. No and none of are used instead.

  • No brand of cigarette is completely harmless. (not Not any brand …)
  • No tourists ever came to our village. (not Not any tourists …)
  • None of my friends lives near me. (not Not any of my friends …)

Not used to talk about two

We use neither, not no or none, to talk about two people or things (see here).

  • Neither of my parents could be there. (not None of my parents …)

nobody, etc

Nobody, nothing, no one and nowhere are used in similar ways to no.

  • I saw nobody. (More emphatic than I didn’t see anybody.)
  • Nobody spoke. (not Not anybody spoke.)
note

For no and not, (see here).

For more about any, (see here).

For none and no one, (see here).

For no as a modifying adverb (e.g. no better), (see here).