Either can be used in different parts of speech such as: a conjunction, an adjective, a pronoun or an adverb. As a pronoun conjunction or an adjective 'either' means one or the other.
As an adverb 'either' means 'likewise'.
Neither can also be used as four distinct parts of speech: adjective, pronoun, conjunction, and adverb. As a pronoun conjunction or an adjective 'neither' means 'not one or the other'.
As an adverb 'neither' means 'similarly not; also not.
Either means one, neither means none, and not either equals neither. 'Or' goes with either and 'nor' goes with neither.
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