In English, double negatives theoretically cancel each other out — or, more accurately they’re considered bad grammar. Not so in Greek — they use double negatives for emphasis:
Truly I say to you, until heaven and earth pass away, one dot-of-an-I or cross-of-a-T will not not pass away from the law until all be fulfilled. (Matt 5:18)
All whom the Father gives to me come to me, and the one coming to me I will not not cast out. (John 6:37)
There are about a hundred double negatives in the New Testament. And occasionally, New Testament writers use a triple negative for super-duper emphasis. Marvelously, there is a verse in the New Testament that has two clauses, one with a double negative and the other with a triple negative — for a total of five negatives in one 9-word sentence! (Nine words in the Greek.) And that verse would be:
I will not not leave you, and I will not not not forsake you. (Heb. 13:5)
In more colloquial English we might say:
I will never never leave you, and I will never never never forsake you. (Heb. 13:5)
Get it? Get it? Get it? Get it? Get it? <wink!>
Further Reading:
Zerwick (1963), ¶444: a succinct article on “ου μη”.