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See convince.

Persuade, induce imply influencing someone's thoughts or actions. They are used today mainly in the sense of winning over a person to a certain course of action: It was I who persuaded him to call a doctor. I induced him to do it. They differ in that persuade suggests appealing more to the reason and understanding: I persuaded him to go back to his wife (although it is often lightly used: Can't I persuade you to stay to supper? ); induce emphasizes only the idea of successful influence, whether achieved by argument or by promise of reward: What can I say that will induce you to stay at your job? Owing to this idea of compensation, induce may be used in reference to the influence of factors as well as of persons: The prospect of a raise in salary was what induced him to stay.