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Math Help - sequence 2

  1. #1
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    sequence 2

    Suppose that  x_n is a sequence of real numbers and M \in R
    with  x_n \leq M , \forall n \in N
    if  x_n \to x for some  x \in R
    prove that  x \leq M
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  2. #2
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    Quote Originally Posted by flower3 View Post
    Suppose that  x_n is a sequence of real numbers and M \in R
    with  x_n \leq M , \forall n \in N
    if  x_n \to x for some  x \in R
    prove that  x \leq M
    Suppose that x>M.
    So in the definition of converence use \varepsilon  = {x - M} > 0.
    That leads directly to a contradiction.
    Last edited by Plato; October 30th 2009 at 02:38 PM.
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  3. #3
    MHF Contributor Bruno J.'s Avatar
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    Quote Originally Posted by flower3 View Post
    Suppose that  x_n is a sequence of real numbers and M \in R
    with  x_n \leq M , \forall n \in N
    if  x_n \to x for some  x \in R
    prove that  x \leq M
    You're welcome for the help in your other thread, by the way.
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