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Math Help - Injective and Surjective

  1. #1
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    Injective and Surjective

    I need help! can someone help me with this?

    Prove or disprove the following statements:
    (a) There exists an injection from
    N to N^2.
    (b) There exists a surjection from
    N to N^2.
    (c) There exists an injection from
    N to N^3.

    (d) There exists a surjection from
    N to N^3.

    where N is the set of natural numbers.

    Thanks
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  2. #2
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    What exactly is your difficulty? Do you know what "injection" and "surjection" mean? It should be very easy to do part (a) or part (c). Parts (b) and (d) are a little harder. Can you use the fact that N, N^2, and N^3 are all "countable" sets?
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  3. #3
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    Quote Originally Posted by HallsofIvy View Post
    What exactly is your difficulty? Do you know what "injection" and "surjection" mean? It should be very easy to do part (a) or part (c). Parts (b) and (d) are a little harder. Can you use the fact that N, N^2, and N^3 are all "countable" sets?

    I know the definition of injectivity and surjectivity and I know the proof for N--->N. My problem is I don't know how to prove for N^2 and N^3. Thanks.
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  4. #4
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    Quote Originally Posted by ineedyourhelp View Post
    I know the definition of injectivity and surjectivity and I know the proof for N--->N. My problem is I don't know how to prove for N^2 and N^3. Thanks.
    You didn't anaswer HallsofIvy's last question.

    Have you seen this before?

    http://personal.maths.surrey.ac.uk/s...ntable.svg.png
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  5. #5
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    Quote Originally Posted by undefined View Post
    You didn't anaswer HallsofIvy's last question.

    Have you seen this before?

    http://personal.maths.surrey.ac.uk/s...ntable.svg.png
    Yes i made used of countability and also the picture. I solve for N^2 already. Is there a shortcut on N^3 such that we can make use of N^2? instead of using 3D space and come up with a general formula for the function? For example let F: N--> N^2 and G: N^2--->N3? so that f(x)=(x,y) and gf(x)=(x,y,z)?
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  6. #6
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    Quote Originally Posted by ineedyourhelp View Post
    Yes i made used of countability and also the picture. I solve for N^2 already. Is there a shortcut on N^3 such that we can make use of N^2? instead of using 3D space and come up with a general formula for the function? For example let F: N--> N^2 and G: N^2--->N3? so that f(x)=(x,y) and gf(x)=(x,y,z)?
    Well the image gives a bijection between N and N^2. You can repeat the exact same procedure, looking at N^3 as Nx(N^2). See how that works?
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  7. #7
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    Quote Originally Posted by undefined View Post
    Well the image gives a bijection between N and N^2. You can repeat the exact same procedure, looking at N^3 as Nx(N^2). See how that works?
    yes i am seeing it as N X N^2 but how to show it on paper? I need to submit it as a graded assignmentT.T
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  8. #8
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    Quote Originally Posted by ineedyourhelp View Post
    yes i am seeing it as N X N^2 but how to show it on paper? I need to submit it as a graded assignmentT
    If it is a graded assignment, then the rules of this forum do not allow us to do any more on this for you.

    Sorry.
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  9. #9
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    Quote Originally Posted by Plato View Post
    If it is a graded assignment, then the rules of this forum do not allow us to do any more on this for you.

    Sorry.
    OMG ok. the grade is basically as long as you write something you will get the marks but I dont know what to write. but I understand the rules. Thanks!
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  10. #10
    MHF Contributor undefined's Avatar
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    Quote Originally Posted by ineedyourhelp View Post
    OMG ok. the grade is basically as long as you write something you will get the marks but I dont know what to write. but I understand the rules. Thanks!
    Clearly this can't be the case, otherwise you could just write 1+1=3 and get full marks. Perhaps a mod should close this thread.
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  11. #11
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    Quote Originally Posted by undefined View Post
    Clearly this can't be the case, otherwise you could just write 1+1=3 and get full marks. Perhaps a mod should close this thread.
    Precisely my teacher marks for effort marks and he doesnt explain after that because he expects us to know it by learning from the internet ourselves and I'm here to learn from you guys=)
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  12. #12
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    Quote Originally Posted by ineedyourhelp View Post
    Precisely my teacher marks for effort marks and he doesnt explain after that because he expects us to know it by learning from the internet ourselves and I'm here to learn from you guys=)
    We are not here to give tutorials. It is also in the forum rules.
    Are you sure that you did read the rules?
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