Verified answer

ない can indeed be used as a word on its own, because it's the plain negative form of the verb ある(which means "to be" for animate objects.) The formal negative is ありません(arimasen)

In case you haven't already, you should study verb conjugations. This is where the "nai" plays a big part. To form a negative form:

For -ru verbs, drop the る and attach ない

Example: 食べる(to eat) becomes 食べない(do not eat)

For -u verbs that end in u, replace the u with わ and add ない

Example: 買う(to buy) becomes 買わない( do not buy)

For all other -u verbs: Replace the u-vowel sound with the a-vowel equivalent and attach ない

Example: 話す( to talk) becomes 話さない(do not talk)

These are all plain forms though, so I suggest you look into the conjugations further especially so you can see how to conjugate to polite form.

違う is also a verb meaning to differ or to be wrong just like you said. it can be conjugated to 違わない as the plain negative form.

Hope this helps

ない alone is the negative exception of the verb ある (to exist) and it means "to not exist" (for not-living things like money, rocks etc...) .

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But also, [ない] is actually a suffix for negative verbs.

For example (for RU verb):

食べる (taberu) > 食べない (tabenai)

(not eat)

There is also a suffix for Adjectives: [くない] (kunai)

example (for I adjectives): 高い (takai) > 高くない (takakunai)

(not tall)

And for nouns: [じゃない] (janai)

example: 人 (hito) > 人じゃない (hitojanai)

(not person)