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!
Best Answer
HINT: Can you find two uncountable sets which are disjoint? Now find a countable set and add it to both of them.