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