# Two uncountable sets A and B are countably infinite

I'm having trouble finding the solution to the following problem...

Give an example of an uncountable set $A$ and an uncountable set $B$ such that $A$ intersect $B$ is countable infinite.

Answer - I know that $(-\infty, 1]$ and $[1, \infty)$ has an intersection of $\{1\}$. $\{1\}$ is countable but $\{1\}$ is also finite. I need to find two sets that have a result of countably infinite. Thanks guys!

-
please use latex :) –  Albanian_EAGLE Dec 17 '13 at 3:16

@user2933041: Now that you’ve worked it out, here’s a moderately natural example: $A=\Bbb R\times\Bbb Q$ and $B=\Bbb Q\times\Bbb R$. –  Brian M. Scott Dec 17 '13 at 5:48
@DonLarynx: I’m not sure what your $A$ is. –  Brian M. Scott Dec 17 '13 at 20:20