zero = not any
With countable nouns, zero is always followed by plural nouns. With uncountable nouns, the singular form is used. Compare the following:
no = not a / not any
Zero degrees centigrade is the same as 32 degrees fahrenheit.
We are likely to see zero growth on the stock market this year.
We are not likely to see any growth on the stock market this year.
With countable nouns, no is normally followed by plural forms. It sounds more natural and makes better sense to say:
It was early December and there were no leaves on the trees.
No dogs, unless they are on a lead, are allowed in the flower garden.
No road accidents were reported in Chelsea throughout August.
Sometimes, no may be followed by singular or plural nouns, depending on whether one is thinking of one or more than one:
It was early December and there was no leaf on the trees.
No dog, unless it is on a lead, is allowed in the flower garden.
No road accident was reported in Chelsea throughout August.
Sometimes, it is more natural to combine singular and plural use:
It was 9 a.m., yet there was no policeman on duty outside the embassy.
It was 9 a.m., yet there were no policemen on duty outside the embassy.
In the Premiership last Saturday, no players were sent off.
In the Premiership last Saturday, no player was sent off.
In the Premiership last Saturday, not a single player was sent off.
(A man normally has one wife, but often has more than one child!)
He must lead a lonely life in that village: he has no wife and no children.
no = emphatic use
Note that we tend to use no, rather than not a or not any when we want to emphasise a negative idea. In the lonely man example above, no is more effective than not a / not any. Compare:
With subject nouns, when no is used emphatically, not a / not any are not possible:
He must lead a lonely life: he doesn't have a wife and he doesn't have any children.
Note that singular use sounds more natural in these examples.
No politician tells the truth all the time.
No writer has won the Booker prize more than once.
There are a number of common nouns that normally combine with no, rather than not a or not any. Most of them are uncountable and include no amount, no time, no idea, no doubt, no reason, no need, no evidence, no problem, no way, no point, no use. Study these examples of use:
No amount of washing could remove the stain from the garment.
There's no time to lose. We must leave immediately.
I have no idea how you solve this problem. It's quite beyond me.
There was no doubt she had lied. All the evidence pointed to her guilt.
I've no reason to think he won't return. He needs me as much as I need him.
There's no need to cry. We can sort this out together.
She complained of chest pains but the doctors found no evidence of infection.
Can you help me with the ironing? ~ No problem. I'm not busy this evening.
Can you help me with the cleaning? ~ No way. I have to be out by seven.
There's no point in shouting. He's deaf and can't hear you.
It's no use complaining. They won't bother to answer your letter.