We use “able” especially in the structure be able +infinitive. This often has the same meaning as can. The negative form is unable.
- Some people are able/can walk on their hands
- I am unable/can’t understand what she wants
Can is preferred in the sense of “know how to” and in expressions, like can see, can hear..etc
- Can you knit? / I can see a ship
Be able is used in cases where can is not grammatically possible (future/present perfect, conditional…)
One day scientists will be able to find a cure for cancer (NOT… will can find)
Many students ask me why the negative of “can” is “cannot ” but the negative of “could” is not “*
In British English, the single form “cannot” is used, while in American English, you can use both “cannot” and “can not”, though “cannot” is more common.
The contraction for both “cannot” and “can not” is “can’t”.
In summary, “cannot” is, by far, more usual and it’s the one I’d recommend you use. Having said that, there some cases when it’s necessary to use the form “can not”. When?
♥ When it’s used for emphasis.
No, you can not go out on New Year’s Eve. You’re only fourteen!
♥ When “not” is part of another construction as in, for example, the rather formal structure,” not only…. but (also)”
She can not only play the piano but also the violin
I hope to have answered your questions!