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Is it possible to define an injective function with domain N×N and codomain N. Where N is the set of all Natural Numbers. Must such a function be sujective?

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    Think (for example) of prime numbers and unique factorisation.2012-11-05
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    Are you giving me an assignment? It just happens that I gave *my* students such function and requested they prove it is a bijection.2012-11-05
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    What exactly do you mean, I'm in a math class where I am in way over my head, hence the question. A more specific answer would be helpful.2012-11-05
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    A more pleasant phrasing of the question would be helpful. Some evidence that you have given it some thought, rather than just regurgitating it in an undigested form, would be helpful.2012-11-05
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    Anthony, I don't owe you anything and you are not my teacher. You don't have to give me any homework assignment, nor you have the right to complain when you just paste your homework assignment and expect people to post solutions. Students have to study. Study.2012-11-05
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    I wish that I could, I don't understand the question that was posted, I understand what an injective function is and I know what the set of all natural numbers are but I'm not sure how I would go about determining if it is possible, is there a way for me to come up with a specific number example to disprove it? Or am I way off?2012-11-05
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    Then you should *say* that in your question. I don't want to just post an answer to your question, I want to help you *understand*. In order for me to help you understand I first need to know what it is about the problem that you don't understand.2012-11-05
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    I'm sorry that I didn't I am new to the forum, my mistake, my main problem is that I don't understand what is meant by domain and codomain in the problem.2012-11-05
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    Would I be correct in saying that it is possible for it to be injective because the function with domain NxN would all have values matching in the codomain N since all NxN are also natural numbers?2012-11-05

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