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Math Help - True/False questions about sequences

  1. #1
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    True/False questions about sequences

    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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  2. #2
    Senior Member TheAbstractionist's Avatar
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    Quote Originally Posted by qtpipi View Post
    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 <x_n> converges, then <x_n> is bounded.

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