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Math Help - Pitching Theorem Proof

  1. #1
    Junior Member
    Joined
    Mar 2010
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    45

    Pitching Theorem Proof

    I got this proof off this site: Squeeze Theorem - ProofWiki

    I've got a question about the step where it says Let N= max{N1,N2}. Why is it needed? and what is it saying? because I've got the same proof in a book which says in the last step that
    L-e < f(x) =< g(x) =< h(x) < L+e whenever x> max{N1,N2}




    This is the proof I'm referring to from the website:
    Note from the corollary to Negative of Absolute Value, we have .
    Let .
    We need to prove that .
    As we know that .
    As we know that .
    Let .
    Then if , and .
    So:

    • ;
    • .

    But .
    So
    and so .
    So .
    Hence the result.
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  2. #2
    Senior Member
    Joined
    Feb 2010
    Posts
    422
    Because you need N to be large enough that both y_n and z_n are within epsilon of their limits. You can chuse any N\ge both N_1 and N_2, the max is just the smallest one that will work.
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