Its easy to find two sets with these proerties if you can use 1 and 0. But, if you are limited to whole numbers greater than (but NOT equal to) 1, then it becomes near impossible. I don't think there is an easy way to prove, or disporve the idea.
Symmetry -- I need some more concrete ideas for episode 3. My idea is that you're an emerging consciousness in a Flat Earth experiment trying to escape the cruel grip of science.