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!

- Sep 26th 2010, 06:36 AMdougBijective 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! - Sep 26th 2010, 07:49 AMHappyJoe
You can take the following function $\displaystyle f\colon D^2\rightarrow \mathbb{R}^2$, where $\displaystyle D^2$ is the open unit disc:

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

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

$\displaystyle |(x,y)|^2 = x^2+y^2.$