- #1
Berrius
- 19
- 0
I have to prove that the cardinality of the set of infinite sequences of real numbers is equal to the cardinality of the set of real numbers. So:
[tex]A := |\mathbb{R}^\mathbb{N}|=|\mathbb{R}| =: B[/tex]
My plan was to define 2 injective maps, 1 from A to B, and 1 from B to A.
B <= A is trivial, just map a real number x on the sequence (xxxxxxxxx...). But I can't find a injective map from A to B. Can someone help?
[tex]A := |\mathbb{R}^\mathbb{N}|=|\mathbb{R}| =: B[/tex]
My plan was to define 2 injective maps, 1 from A to B, and 1 from B to A.
B <= A is trivial, just map a real number x on the sequence (xxxxxxxxx...). But I can't find a injective map from A to B. Can someone help?