Question

(a) Is the converse of Bolzano-Weierstrass Theorem true? If yes prove it. If false provide a counterexample.
(b) Since Q is countably infinite, it can be written as a sequence {xn}. Can {xn} be monotone? Briefly
explain. Hint. Assume it’s monotone, what would be the consequences?
(c) Use the , N definition to prove that if {xn} and {yn} are Cauchy then {xn + yn} is Cauchy too.

Answer 1