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Math Help - Limit proof

  1. #1
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    Limit proof

    Assume f(x) >= g(x) for all x in some set A on which f and g are defined. Show that for any limit point c of A we must have \displaystyle \lim_{x \to c} f(x) >= \lim_{x \to c} g(x).

    I think I start with the \epsilon and \delta definition of a limit. So let \displaystyle \lim_{x \to c} f(x) = F. Let \epsilon > 0. 0 < |x - c| < \delta implies there exists \delta > 0 such that |f(x) - F| < \epsilon.

    Is that the right place to start? Because I am not sure where to go from here.

    Thanks in advance.
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  2. #2
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    Let  \displaystyle \lim_{x \to c} f(x) =F~\&~ \lim_{x \to c} g(x)=G.

    Suppose that that F<G. You can get a contradiction.

    Hint: consider \varepsilon  = \frac{{G - F}}{2}.
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  3. #3
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    Thank you so much. I believe I have it.
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