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.
当我们想要表达“没有能力做”或是“不被允许做”的意思时，我们都用到了一个词是“cannot”。也就是我们经常缩写成为“can't”。很多人喜欢把can 与 not 分开写，但其实这是一个普遍的错误。《美国传统词典》中对于这一点的解释相当明确：cannot这个单词，是can的否定形式。
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.
可以举这样一个例子：
如果我说I cannot smoke，我的意思是，我不会抽烟，或者，这里不让抽烟。
如果我说I can not smoke，这时，not就是修饰smoke的，那么这句话的意思其实是：我可以不抽烟。就好比，我有能力让自己克制吸烟，或者我可以戒烟。
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.”
另外一例：
如果我去不了某处，我会写：I cannot go；
而当我可以去，可以不去的时候，我才可能会写：I can go, or I can not go——这是我的选择自由。
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.
致我的所有喜欢“吹毛求疵”的朋友们：
我非常清楚这一点：
在很多时候本来应该使用单词[can]的否定式[cannot]的时候，往往人们却使用了两个单词构成的词组[can not]。
即使这样的用法遍天都是，但是事实仍然是：它是错误的。