expression
Used to express strong conviction that something is definitely the case; often appears at the end of a statement or as a standalone interjection. Similar to 間違いない, but 間違いなし is slightly more casual and emphatic.
あの店のラーメンは美味い。間違いなし！
That shop's ramen is delicious. No doubt about it!
この計画なら成功は間違いなしだ。
With this plan, success is certain.
間違いない is the standard adjectival phrase meaning 'certain' or 'sure' and can modify nouns (e.g., 間違いない事実). 間違いなし is a more emphatic, often sentence-final expression that functions like an interjection or standalone assertion.
間違いなく is the adverbial form meaning 'without fail' or 'undoubtedly', used to modify verbs or adjectives. 間違いなし is a predicative expression that asserts certainty about a situation.
Compound of 間違い (mistake, error) + なし (classical terminal form of ない, 'not exist'). Literally 'there is no mistake', used idiomatically to mean 'certain' or 'no doubt'.