I know that it should be "a number of people are", "the number of people is". We get this:
There are a number of people at the bus stop.
There is the number of people at the bus stop.
What does ARE correspond with? If you say it corresponds with "people" rather than with "a number" then I will ask you why does "is" correspond with "the number"? If it corresponds with "the/a number" it should be "is" in both cases, if it corresponds with "people" it should be "are" in both cases. But it's not the case. Why?