when reading newspaper,listening to music (esp. in American English),I usually see sentence like:
I don't love you no more.
so is it correct to say so?as I was taught,that sentence should be :"I don't love you anymore"
As far as I know , two negations in an English sentence are not allowed, so the correct sentence should be : I don`t love you anymore.
"I don`t love you no more " might be either informal English or an emphasis on the message conveyed by the speaker -or both.
I'd caution you against using a double negative in this way. It may be quite common in speech as a result of the influence of American slang, but it is still not accepted as correct English. It is most definitely not accpetable in written English, and using it in speech will make you sound odd if you are not a native speaker.
The double negative is not correct in standard English; it is, however, widely used in many dialects. People who use the double negative are generally seen as poorly educated or unintelligent; however, it is generally well understood (although frowned upon), so that the Rolling Stones could write a song called I Can't Get No (Satifsaction).
The reason the double negative is considered wrong is on grounds of logic: two negatives cancel each other out and make a positive, so "I haven't got none" (or, as it's usually said in the dialects of south-east England, "I ain't got none") translates as "I have got some".
Very occasionally you will see respected authors using the double negative for reasons of clarity. For example, Jane Austen wrote: "There was none too poor or remote not to feel an interest." This is a difficult thing to do, and it works only because the negative in the main clause ("There was none...") is parallelled by a negative in the subordinate clause ("...not to feel..."). If you don't understand what I just wrote, you shouldn't try to do the same.
As a matter of interest, in the past double and even triple negatives were once acceptable in standard English -- but many centuries ago, not today. I did have an example of a triple negative written by Chaucer, but I can't find it at the moment. This explains why so many dialects use the double negative; they're just using old grammar rules which are no longer part of standard English.
Some modern languages today still use double negatives. French and Russian are examples where double negatives are common and part of formal grammar rules.
Yes, the whole double negative thing is even more complicated in dialect than in standard speech. "No-one doesn't understand" would, as Coffa says, mean that everyone understands, although it would be a little more natural to say "No-one fails to understand".
On the other hand, a sentence like "He doesn't understand nothing" would, in certain dialects, be understood to mean the same as "He doesn't understand anything", but in standard speech to be complete nonsense.
And the moral of the story is: Steer clear of the double negative.