auxiliary adjective, suffix
Attaches to the negative stem of verbs (未然形) to negate them. With rising intonation, it can form a question or invitation.
It will not rain today.
一緒に映画を見に行かない？
Won't you go see a movie with me?
ません is the polite negative ending used in formal speech, while ない is the plain, casual negative form.
無い is the independent い-adjective meaning 'to not exist/have,' whereas this ない is a grammatical suffix attached to a verb's negative stem to negate it.
Kana-only auxiliary adjective/suffix; no kanji form exists.
Derived from the classical negative auxiliary ず, with the 未然形 of verbs + ない becoming the standard modern negative form.