Prove that the map f : C → R 2 , x + iy 7→ (x, y) is a bijection, i.e., a cardinal equivalence C ≈ R
The Answer to the Question
is below this banner.
Can't find a solution anywhere?
NEED A FAST ANSWER TO ANY QUESTION OR ASSIGNMENT?
Get the Answers Now!You will get a detailed answer to your question or assignment in the shortest time possible.
Here's the Solution to this Question
Let us prove that the map is a bijection.
Let Then and hence and We conclude that and thus the map is injective.
Let be arbitrary. Then for we get that and consequently, is surjective.
We conclude that is a bijection.