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!
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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 $\displaystyle <x_n>$ converges, then $\displaystyle <x_n>$ is bounded. (b) Consider the sequence $\displaystyle \left<\frac{(-1)^n}n\right>.$
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