The phrase "can not" may mean "cannot" or "can't," but it also may mean "able not to," which is much different than "not able to" as it conveys the ability to not do something rather than the inability to do it.
The title of my question is a Russian proverb, for which I cannot think of an analog. All the examples I have seen on this website refer to actions rather than specifically speech. Can anyone give ...
Stick with cannot. Can't tends to be informal, and can not is usually considered a typo.
If I am writing a formal letter, should I use "can't," "cannot," or ...
Generally, people use can't in speech and informal writing, and cannot or can not in formal writing or very formal speech. Also (as @Kris points out in a comment), cannot might be used when you need to carefully distinguish it from can't in speech.
differences - When to use "cannot" versus "can't"? - English Language ...
Why is “cannot” spelled as one word whereas other similar constructions such as “do not,” “will not,” “shall not,” “may not” and “must not” are spelled as two words (unless they are contracted as “...
Why is “cannot” spelled as one word? - English Language & Usage ...
The irony of the idiom is that one would expect to be able to eat the cake that he or she owned. In that case, possession of the cake would logically come before usage of the cake: You cannot have your cake and eat it, too. Some other interesting observations: Paul Brians, Professor of English at Washington State University, points out that perhaps a more logical or easier to understand ...