grammar - What's the difference between a few, few, the few

What's the difference between a few, few, the few?
Which one is formal or informal?

Answer

The few is quite rare, and used only when designating a small number of things or people that have some special distinction

• the few rounds left in their magazines, the few guests who escaped the fire

There's a big difference between few and a few, however.
They're directed quantifiers, and they point in opposite directions.

• a few means 'a small, but still positive, number', while


• few is a negative quantifier, and means 'fewer than expected, predicted, or wished'

Few governs negative polarity items like ever, producing the following pair:

• Few people ever come here in the winter, but not ...


• *A few people ever come here in the winter.

because a few isn't negative and therefore can't trigger ever;
as well as the following pair, which produce opposite results:

• Thank heavens that few people were hurt!



• Thank heavens that a few people were hurt!

because you're thanking heavens for negative versus positive injuries.

Negatives are pretty tricky; much trickier than most people expect.