cannot vs. can not

A discussion has just occurred with the group I’m currently teaching. The students say they were taught at school that there is no such word ‘cannot’ and that it has to be ‘can not’. As far as I can see, both versions exist and they have different meanings. The question is what exactly is the difference between ‘cannot’ and ‘can not’? I’ve read about this question on various forums but haven’t been able to really grasp it.

Could you please give me a hand?

Many thanks,

TOEIC listening, question-response: Would you rather have juice or a soft drink?[YSaerTTEW443543]

First, it is wrong to say that there is no such word as “cannot”. There is, and it is the usual way of writing “can not”. Except in certain special cases such as that mentioned below, I do not perceive any difference in meaning between “cannot” and “can not”. However, I normally prefer “cannot”, and “can not” can tend to look slightly clumsy or awkward to me, as if the writer did not realise it is usually written as one word.

I agree with the advice at … ot?view=uk , namely that “the two-word form is better only in a construction in which not is part of a set phrase, such as ‘not only … but (also)’”. In other words, in all* other cases the one-word form is better.

*unless some other exceptions pop up out of the woodwork!