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Math Help - limit proof

  1. #1
    Junior Member mremwo's Avatar
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    limit proof

    I am really have trouble with these proofs involving limits, and would really appreciate some help. Here is an example of a problem I am having trouble with:
    <br />
\mbox{Prove that if lim}(x_n)=x\ \mbox{and if}\ x>0\ \mbox{then there exists a natural number}\ \mbox{M such that}\ x_n>0\ \mbox{for all}\ n \geq M

    thank you!!
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  2. #2
    MHF Contributor

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    In the definition of sequence convergence use \varepsilon  = \dfrac{x}{2}>0

    Then get -\dfrac{x}{2}<x_n-x<\dfrac{x}{2}.

    Carry on.
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