# Math Help - Intersection of two countably infinite sets

1. ## Intersection of two countably infinite sets

If A and B are countably infinite, is $A \bigcap B$ countably infinite?

I'm working on this problem with my friend and we know that with countably infinite sets there is a bijection of each of the sets however we are not sure where to go from there.

2. Originally Posted by andirc5192
If A and B are countably infinite, is $A \bigcap B$ countably infinite?

I'm working on this problem with my friend and we know that with countably infinite sets there is a bijection of each of the sets however we are not sure where to go from there.
It does not have to be for

let $A=\{1,3,5,7,\cdots\}$ the odd integers and
$B=\{2,4,6,8,\cdots\}$ the even integers

both of these are countably infinite what does this say?