Results 1 to 6 of 6

Math Help - Mappings problem

  1. #1
    Junior Member
    Joined
    Nov 2008
    Posts
    45

    Mappings problem

    Hi,
    Can anyone offer advice on this problem below please - the text book I'm working with doesn't have any problems like this and I need a solution asap. Thanks in advance.

    Construct a mapping B:N → N (natural numbers) such that the equation
    B(n)=3nē has exactly three solutions.
    For which elements n E N is the solution solved? (solutions must be in N)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by jackiemoon View Post
    Hi,
    Can anyone offer advice on this problem below please - the text book I'm working with doesn't have any problems like this and I need a solution asap. Thanks in advance.

    Construct a mapping B:N → N (natural numbers) such that the equation
    B(n)=3nē has exactly three solutions.
    For which elements n E N is the solution solved? (solutions must be in N)
    Define B(n) = (n-1)(n-2)(n-3) + 3n^2
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Nov 2008
    Posts
    45
    Hey man thanks for the reply. Could you explain a little how you got the answer. Sorry to be a pain!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by jackiemoon View Post
    Hey man thanks for the reply. Could you explain a little how you got the answer. Sorry to be a pain!
    There are many answers to this question. I realized that (n-1)(n-2)(n-3)=0 has exactly three solutions. Thus, I added 3n^2 to it so that in the equation (n-1)(n-2)(n-3)+3n^2 = 3n^2 it cancels and we are left with (n-1)(n-2)(n-3)=0.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Nov 2008
    Posts
    45
    Thanks again. Kinda makes sense now.

    I'm stuck on one final question if anyone can help.

    "A set P is said to be smaller than a set Q if there exists a mapping from P to Q, but there does not exist a mapping from Q to P. The notation P < Q is used to denote that P is smaller than Q according to this definition. Prove that, given sets P, Q, and R, if P<Q and Q<R, then P<R."

    Any tips on how to solve this?

    Muchos gracias amigos.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,657
    Thanks
    1606
    Awards
    1
    Quote Originally Posted by jackiemoon View Post
    "A set P is said to be smaller than a set Q if there exists a mapping from P to Q, but there does not exist a mapping from Q to P. The notation P < Q is used to denote that P is smaller than Q according to this definition. Prove that, given sets P, Q, and R, if P<Q and Q<R, then P<R."
    First of all what is in red above is false.
    It should read: "A set P is said to be smaller than a set Q if there exists an injective mapping from P to Q, but there does not exist an injective mapping mapping from Q to P.
    There is always a mapping from Q to P but cannot be injective if Q is more numerous than P.
    The proof of the question just involves composition of mappings.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. automorphism mappings
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: May 9th 2011, 12:16 PM
  2. Complex Mappings
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: November 18th 2010, 09:52 PM
  3. Abstract problem - mappings and ops
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: November 30th 2008, 02:38 PM
  4. Mappings by 1/z
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 16th 2008, 11:22 AM
  5. mappings
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: August 2nd 2008, 10:20 AM

Search Tags


/mathhelpforum @mathhelpforum