can't/cannot/can not 区别

What we should use when we mean “are unable to” or “are not permitted to” is one word: cannot. This is the word that we contract when we write “can’t.” It is a common error to separate “can” and “not.” The American Heritage Dictionary is quite clear on this point: cannot is the negative form of the word can.

Here’s one example I use:
If I say “I cannot smoke,” I mean that I am unable to or not permitted to smoke. If I say, “I can not smoke,” not modifies smoke. My meaning is: “I am able to not smoke,” i.e., I have the ability to avoid smoking, to prevent myself from smoking, or to stop smoking.

Another example:
If I am unable to go or am not permitted to go, I should write, “I cannot go.” If I have a choice between going and not going, I may write, “I can go, or I can not go – it is my choice.”

To all my fellow nitpickers out there: I am fully aware that the two-word construction “can not” is often used where the opposite of “can” is intended. Despite the ubiquity of this usage, it is still an error.