Results 1 to 2 of 2

Math Help - Bijective matching between the points of a disk and the points in the plain

  1. #1
    Junior Member
    Joined
    Sep 2010
    Posts
    43

    Question Bijective matching between the points of a disk and the points in the plain

    There are two sets:
    - A set: is the points of a disk (of radius 1), so x^2+y^2<1
    - B set is: RxR

    We should prove that two sets have the same cardinality, so we should find a bijection from A to B.

    Thanks for helping me!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member HappyJoe's Avatar
    Joined
    Sep 2010
    From
    Denmark
    Posts
    234
    You can take the following function f\colon D^2\rightarrow \mathbb{R}^2, where D^2 is the open unit disc:

    f(x,y) = \frac{(x,y)}{1-|(x,y)|^2},

    where (x,y) is a point of D^2, and where |(x,y)| is the norm of the point, i.e.

    |(x,y)|^2 = x^2+y^2.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: August 24th 2011, 12:35 PM
  2. Replies: 1
    Last Post: February 9th 2011, 11:52 AM
  3. fixed points of sin in the complex unit disk
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: January 24th 2011, 10:22 AM
  4. Replies: 1
    Last Post: November 1st 2009, 03:35 PM
  5. Replies: 3
    Last Post: January 11th 2009, 12:49 PM

Search Tags


/mathhelpforum @mathhelpforum