Find an example of non-locally finite collection I got stuck on this problem and can't find any hint to solve this. Hope some one can help me. I really appreciate.


Give an example of a collection of sets $A$ that is not locally finite, such that the collection $B = \{\bar{X} | X \in A\}$ is locally finite.


Note: Every element in $B$ must be unique, so maybe there exist 2 distinct sets $A_{1}, A_{2} \in A$, but have $\bar{A_{1}} = \bar{A_{2}}$. So that's why this problem would be right even though $A \subset \bar{A}$.
Thanks everybody.

Let Q be the rationals in R, and A be the collection of sets of the form {a+√p, a ∈ Q}, p ∈ N.
