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.
Prove the the mapping is a bijection (one-to-one and onto).
I will start there. Thank you very much.