Eventually means that something will happen after a period of time, often after delays or other events. It doesn’t say exactly when, only that it will happen in the end.
It is the adverb form of 'eventual', based on Latin 'eventus' (outcome). It shifted from meaning 'in the final result' to a looser sense of 'at some later time'.
When people say 'I’ll do it eventually', they’re hiding the ending of the story without giving you any dates. It’s a time word that promises an outcome but refuses to schedule it.
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