
Cardinality Question
Hi all,
I have a question that i would love some help with.
Q: Prove that the set of all integers and the set of all odd integers have the same cardinality.
So far i really haven't been able to come up with anything. I know that the cardinality of a set is the number of elements in the set. I assume :
all integers will = n
and all odd integers will = n+1.
Obviously both of these sets are infinite, i am just seeming to have trouble formulating a good start to a proof for this.
Any help would be appreciated.
Thanks,
Flea.

Prove the the mapping $\displaystyle n\mapsto 2n+1$ is a bijection (onetoone and onto).

I will start there. Thank you very much.
Flea.