We use 'none' to say there is no amount or no people of something. It means zero or not any. It is a common way to show nothing or no one.
None of the students are here.
I have none left in my bag.
'None' can be used as an adverb to show no change or no increase in something. It means 'not at all' or 'not in any way'. It is more formal and often used in writing.
I am none the wiser now.
She felt none the better after rest.
In less common use, 'none' can mean a person or thing that has no value or importance. It is a noun and often used in criticism or negative context.
He is a none in the company.
The idea was treated as a none.
'None' can sometimes be used like a determiner before nouns to show zero quantity. This usage is less common and more formal. Usually, 'no' is used instead in speaking.
None apples are fresh today.
I have none money left now.
In math and logic, 'none' refers to having no elements or members in a set or group. It means empty or zero items are there. This is a technical meaning.
The intersection is none in this case.
None of the numbers fit the rule.
'None' is used in fixed expressions and idioms meaning no degree or amount of something. These expressions show how someone feels or what something is like in a negative or neutral way.
He felt none too pleased about it.
She was none the worse after the fall.