- Can’t is a contraction of cannot, and it’s best suited for informal writing.
- In formal writing and where contractions are frowned upon, use cannot.
- It is possible to write can not, but you generally find it only as part of some other construction, such as “not only . . . but also.”
Can Not vs. Cannot vs. Can’t—Which Is Correct?
Can’t is a contraction of cannot, and as such it’s sometimes unsuitable for formal writing. In everyday writing and in speaking, it’s ubiquitous:
Cannot is better for formal writing:
Don’t use can not when you mean cannot. The only time you’re likely to see can not written as separate words is when the word “can” happens to precede some other phrase that happens to start with “not”:
from Grammarly Blog https://www.grammarly.com/blog/cannot-or-can-not/