The Oxford Dictionaries online http://oxforddictionaries.com/definition/cannot explains that “both the one-word form cannot and the two-word form can not are acceptable, but cannot is more common”.
There are, however, occasions where the word ‘can’ needs to be separated from ‘not’. This is where the word ‘not’ belongs to another part of the sentence.
Consider the following three examples:
- I can not only read French, but I can speak it as well
- I cannot believe the price of petrol these days
- I can not believe the price of petrol these days
In example 1, it is correct to have ‘not’ as a separate word because it’s part of the phrase ‘not only’, where as in example 2 ‘cannot’ is correctly shown as one word. Example 3 is also correct, but not as common as saying ‘cannot’ (as explained in the introduction).
My thoughts: I would say that it’s up to the individual whether they use example 2 or 3, but personally I would use 2, as it reads better.
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The Oxford Dictionaries online http://oxforddictionaries.com/definition/cannot