I can not to see very well.
I cannot see very well.
They can be annoying for me but cannot be for you.
They may be annoying for me but may not necessarily be for you.
She said she was rather busy, so she said she cannot come to the party, but let’s hope she does.
She said she was rather busy, so she may not come to the party, but let’s hope she does.
It can be that I don’t have enough money to pay the bill.
I may not have enough money to pay the bill.
I may not come to the party - I am afraid I will be away that weekend.
I cannot come to the party - I am afraid I will be away that weekend.
I cannot come to the lesson tomorrow because I am on holiday. = It is impossible for me to come.
I may not come to the lesson – I will let you know later today if I can or not. = Perhaps I will not come.
She cannot be at home yet, she doesn’t stop work until after 6 pm.
I would try ringing her later because she may not be at home yet.
cannot is generally written as one word, or in the contracted form: can’t. Example: She can’t / cannot speak English very well.
Use cannot to express 100% impossibility and may not for speculations. Example: She cannot come to the meeting. (It is impossible for her to come). I may not be able to come. (Perhaps I will not come)