## Countable Sets

If anyone helps me with these questions, I will be thankful.

Q1) Let {A_n : n=1,2,3,...} be a collection of (finite or infinite) countable sets.

Show that A=U A_n is countable.

Hint: Since each A_n is countable, we can find onto maps f_n : N→A_n. Use these maps to construct an onto map F : N×N→A

Q2) Let A be a subset of R={x∈R : x > 0}. For each positive integer n let A_n= { x∈A : x ≥ 1/n }.

Show that A=U A_n.

You need to use some property of the real numbers, what is it?