# Math Help - Cardinality Question

1. ## 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.

2. Prove the the mapping $n\mapsto 2n+1$ is a bijection (one-to-one and onto).

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

--Flea.