May and Can

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Both can and may can be used to talk about possibility. But there is some difference between them. Can is used to talk about theoretical possibility; may is used to talk about factual possibility.

Compare:

When we talk about possibility, could often means the same as may or might.

May not and Cannot

May not suggests improbability. Cannot suggests impossibility.

Compare:

Sections in this article

Modal Auxiliary Verbs
Can
May and Can: differences
Could
May
Might
Will
Would
Shall
Should
Should: other uses
Must
Must: uses
Must and have to: The Difference
Ought to
Need
Had better
Should, Ought and Must: The difference