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You can’t do that sort of thing. (Random House Unabridged)
You can't leave until you finish washing the dishes. (Webster’s Learner’s)

When ‘can’ is used for prohibition, does it have to stuck with not, that is, do cannot or can’t have to be used; not permitting 'can not'? I thought that ‘you can not do that sort of thing’ has equal meaning of the dictionary's example, but I don’t find any examples of ‘can not’. Can’t we use ‘can not’, when we do not give permissions?

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Looking around for differences between can not and cannot, dailywritingtips has a nice list of sources that tell you to use cannot:

OED says:

[cannot is] the ordinary modern way of writing can not.

askoxford says:

Both cannot and can not are acceptable spellings, but the first is much more usual. You would use can not when the ‘not’ forms part of another construction such as ‘not only.’

Washington State University says on their site:

These two spellings [cannot/can not] are largely interchangeable, but by far the most common is “cannot” and you should probably use it except when you want to be emphatic: “No, you can not wash the dog in the Maytag.”

So it doesn't seem to have to do with the prohibitive use of cannot, but the preference seems quite universal.

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Orthographically speaking, cannot is the preferred form. In fact if I write can not, my computer automatically changes it to cannot. However, I feel there's a place for can not, namely when you want to emphasize the word not:

You can't talk to her like that. (=denying permission or statement of fact)

You cannot talk to her like that. (=same as above, somewhat more authoritative)

You can not talk to her like that! (=separated in order to emphasize not - categorical denial of permission)

Sometimes this emphasis is achieved by italicizing cannot. My personal recommendation is to stick with can't and cannot, however if you use can not for effect, use italics to make this clear.

This article might help.

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