Q. I am uncertain about the correct usage in the following sentence: “There is no solution, since the absolute value, by definition, can not be equal to a negative number.” I’ve looked through your book and it appears to me that it is a closed (or solid) compound word—cannot. The editor I work for insists that it is can not. Please advise.
A. The negative form of “can” is “cannot” or, contracted, “can’t.” The two-word phrase “can not” is rarely necessary : e.g., “I can eat this slice of pizza, or I can not eat it: the choice and its consequences are entirely mine.” In your example, certainly, “cannot” is correct.