Today I came across the following sentence:
We asked for help and were given none.
It feels and sounds right to me. However, after decomposing none into not one, it becomes apparent that you can't have one help in this context. So is none the right word to use originally?
If so, what does that say for the none = not one equivalence? If not, then what is a better way to phrase it?
Using none in the example sentence is correct.
When none is used with countable nouns, it means not one. However, none can also be used with uncountable nouns, in which case it means not any.
"We asked for help and were given none."
This is correct. We asked and we were given. If "none" was the subject of "given," it would be written "We asked for help and none was given." "None were given" would sound odd because in this case "none" is not plural (nor is "help").
About using a plural or a singular verb with none, the NOAD reports:
It is sometimes held that none can take only a singular verb, never a plural verb: none of them is coming tonight, rather than none of them are coming tonight. There is little justification, historical or grammatical, for this view.
None is descended from Old English nān, meaning not one, and has been used for around a thousand years with both a singular and a plural verb, depending on the context and the emphasis needed.
I would rather write the sentence you reported as
We asked for help and none was given us.
As for the equivalence between none and not one, the meaning of none is not any, no person, or no one when used as pronoun, and by no amount, not at all when used as adverb and it is followed by the definite article.
Don't use any more water, or there'll be none left for me.
None could match her looks.
It is made none the easier by the differences in approach.
Replace none with not one in the first sentence, and you get a sentence that is not correct.
(*) Don't use any more water, or there'll be not one left for me.
