Web Reference: Apr 20, 2021 · The phrase "can not" may mean "cannot" or "can't," but it also may mean "able not to," which is much different than "not able to" as it conveys the ability to not do something rather than the inability to do it. Aug 20, 2012 · Generally, people use can't in speech and informal writing, and cannot or can not in formal writing or very formal speech. Also (as @Kris points out in a comment), cannot might be used when you need to carefully distinguish it from can't in speech. Sep 19, 2023 · So here it’s about minimizing ambiguity: can not permits two interpretations, while cannot permits only one. Such care is critical in the language of mathematics. As another example, West would tell you that in mathematical discourse, both “x is a minimum” and “x is a minimal” are valid utterances, but they mean different things.
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