Using an uncountable noun and 'none'

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?

Solution 1:

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.