Real Analysis - 1- if A1,A2,A3,...,Am are each countable sets, then the union A1 U A2 U A3...U Am is countable
2- if An is a countable set for each n belong to N,then Un=1(to infinity) An is countable
Union of countable set - Prove that union of countable sets is countable. See attached file for full problem description.
Proof Set is Countable : Bolzano-Weierstrass Theorem - Given S is a subset of R
Suppose S' (set of all accumulation points in S) = emptyset
Prove S is countable.
I think I am supposed to use the Bolzano-Weierstrass Theorem but I can't figure out how ...