Let <x> be a sequence of real numbers
a) if <x> is unbounded, then <x> has no limit
b) if <x> is not monotone, then <x> has no limit

Proof if true, counterexample if false. I hate this class! It's almost over!

2. Originally Posted by qtpipi
Let <x> be a sequence of real numbers
a) if <x> is unbounded, then <x> has no limit
b) if <x> is not monotone, then <x> has no limit

Proof if true, counterexample if false. I hate this class! It's almost over!
Hi qtpipi.

(a) True. It is more usual to prove the contrapositive statement: If $$ converges, then $$ is bounded.

(b) Consider the sequence $\left<\frac{(-1)^n}n\right>.$