‘A number of people is’ or ‘a number of people are’?

Although the expression ‘a number’ is strictly singular, the phrase ‘a number of’' is used with plural nouns (as what grammarians call a determiner (or determiner)). The verb should therefore be plural:

A number of people are waiting for the bus.

This is not the case with ‘the number’, which is still singular:

The number of people here has increased since this morning.

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