See these similar threads, which I found by putting can not/cannot in the Google Custom Search box at the top of the page.
Student or Learner
What is the difference between "cannot" and "can't"? I think "cannot" is more emphasizing than "can't" as it is more loosened.
ex)I can dance very well, but she cannot(can't) dance very well.
You wouldn't use can't in a formal text.
I didn't mean cannot/can not, which are about "inability vs refraining", but cannot/can't, and as you said "can't" is informal while "cannot" is formal, but the two mean the same thing of "inability". If I am wrong, please let me know.
Can't is simply the contracted form of cannot. They both mean exactly the same thing. As Tdol said, you would not use can't in a formal text.
Last edited by Tdol; 13-Aug-2012 at 14:11. Reason: Mistake