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. The terms cannot and can not are identical in meaning and are typically considered to be alternate forms of one. The ordinary modern way of writing can not both cannot and can not are acceptable spellings.
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Why is cannot spelled as one word whereas other similar constructions such as do not, will not, shall not, may not and must. Generally, people use can't in speech and informal writing, and cannot or can not in formal writing or very formal speech.
