Results 1 to 9 of 9

Math Help - cardinals

  1. #1
    Junior Member
    Joined
    Dec 2007
    From
    University of California, Berkeley
    Posts
    48

    cardinals

    .




    .
    Last edited by yellow4321; March 6th 2008 at 05:05 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by yellow4321 View Post
    i just want to check im doing this right because it seems too easy
    the question asks for the cardinals of the sets A {5,6} and B {1,2,3}, i said 2 and 3 respectively. then i assumed |AxB|=2.3=6. just looking for some verification?
    you are correct
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,668
    Thanks
    298
    Awards
    1
    Quote Originally Posted by yellow4321 View Post
    i just want to check im doing this right because it seems too easy
    the question asks for the cardinals of the sets A {5,6} and B {1,2,3}, i said 2 and 3 respectively. then i assumed |AxB|=2.3=6. just looking for some verification?
    Cardinal values of finite sets are easy.

    The cardinality of infinite sets is not so easy.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  4. #4
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by topsquark View Post
    The cardinality of infinite sets is not so easy.

    -Dan
    don't i know it!

    working with infinite sets defies logic sometimes... or maybe our logic just isn't up to the standard
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Dec 2007
    From
    University of California, Berkeley
    Posts
    48
    .



    .
    Last edited by yellow4321; March 6th 2008 at 05:05 AM.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by yellow4321 View Post
    (sorry for posting in elementary math forum,i dont know how to move thread)
    you should create a new thread for new questions
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,393
    Thanks
    1476
    Awards
    1
    Quote Originally Posted by yellow4321 View Post
    clearly theres much passion for this topic,i now need help with an introductory question on schroder-berstein theorem. Let X,Y be finite sets with |X|=n and |Y|=m show n is 'less than or equal to m' then there is a injection X->Y.
    First, donít be concerned about the statements on cardinality.
    Once you have the basic idea down, all the rest is easy.

    Secondly, the above is not the Schroeder-Bernstein. But nonetheless it is easy to prove anything about finite sets.
    The basic idea of a finite set is: Any finite set can be listed using positive integers as subscripts.

    Thus if n = \left| X \right| \le \left| Y \right| = m then we can write X = \left\{ {x_1 ,x_2 ,x_3 , \cdots ,x_n } \right\}\,\& \,Y = \left\{ {y_1 ,y_2 ,y_3 , \cdots y_m } \right\}.

    If we define f:X \mapsto Y by f\left( {x_j } \right) = y_j the result follows easily.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Junior Member
    Joined
    Dec 2007
    From
    University of California, Berkeley
    Posts
    48
    .. for all x,y in X f(x)=f(y) then x=y ?
    the less than/equal to sign is confusing me.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,393
    Thanks
    1476
    Awards
    1
    Quote Originally Posted by yellow4321 View Post
    .. for all x,y in X f(x)=f(y) then x=y ?
    the less than/equal to sign is confusing me.
    It is easy. The m terms of Y are all distinct.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Cardinals and order problems
    Posted in the Discrete Math Forum
    Replies: 9
    Last Post: April 12th 2010, 08:13 AM
  2. How to prove distributivity of cardinals?
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: March 31st 2010, 04:50 AM
  3. Help With Cardinals
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: February 21st 2010, 10:27 AM
  4. Cardinals - Exponents
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: August 24th 2009, 11:56 AM
  5. Discrete Math - Cardinals
    Posted in the Discrete Math Forum
    Replies: 8
    Last Post: August 23rd 2009, 12:14 PM

Search Tags


/mathhelpforum @mathhelpforum