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I need some exercises about functions in general to make sure that I understand it, in a book or a material book. Concepts like function in general (the definition of function), concepts like one-to-one, onto and closure.

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    I don't think this qualifies neither as a question nor as something we do here. Why not to use google?2012-09-22
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    @DonAntonio: We have had this kind of question before, be sure that I know enough about Google and the fact that I can use it.2012-09-22
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    @WillHunting: I think everybody knows that. If you could name some of them, it'd be more helpful.2012-09-22

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See the section on functions in the first chapter of Fundamentals of Abstract Algebra by Malik, Mordeson and Sen for numerous exercises.