Results 1 to 3 of 3

Math Help - Bijection

  1. #1
    Junior Member
    Joined
    Sep 2008
    Posts
    53

    Bijection

    Ive been trying to find a bijection formula for the below but no luck. Any help would be appreciated.

    |(a,b)| = |(1,infinity)| for any real numbers a and b and a<b.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,616
    Thanks
    1579
    Awards
    1
    Quote Originally Posted by TitaniumX View Post
    Ive been trying to find a bijection formula for the below but no luck. Any help would be appreciated.

    |(a,b)| = |(1,infinity)| for any real numbers a and b and a<b.
    Does this work?
    x\mapsto \frac{b-a}{b-x}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by TitaniumX View Post
    Ive been trying to find a bijection formula for the below but no luck. Any help would be appreciated.

    |(a,b)| = |(1,infinity)| for any real numbers a and b and a<b.


    (1,\infty) \rightarrow (a,b)\,,\, x\mapsto \frac{abx}{ax+b-a} , and we can assume 0<a<b . Check this map is 1-1 and onto.

    Tonio
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Bijection
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: May 6th 2010, 12:58 AM
  2. bijection of e^x * ln x
    Posted in the Calculus Forum
    Replies: 8
    Last Post: January 20th 2010, 12:46 PM
  3. Bijection
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: January 7th 2010, 06:24 AM
  4. bijection help
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: March 12th 2009, 07:59 PM
  5. Bijection
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: February 22nd 2006, 02:42 PM

Search Tags


/mathhelpforum @mathhelpforum