You can take the following function , where is the open unit disc:
where is a point of , and where is the norm of the point, i.e.
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!