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Math Help - The Negation

  1. #1
    Newbie
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    Oct 2009
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    1

    The Negation

    The Question:
    Rewrite the definition in terms for logical symbols, then write the negation using the same symbols.

    The real number L is the limit of the function \rightarrow \mathbb{R} " alt="f \rightarrow \mathbb{R} " /> at the point c iff for each  \varepsilon > 0 there exists  \delta > 0 such that  |f(x) - L|< \varepsilon whenever  x \in D and  0 < |x - c| < \delta .

    My Answer
    The definition:
     \forall \varepsilon > 0, \exists \delta > 0, ( x \in D \cap 0 < |x - c| < \delta )\Rightarrow |f(x) - L| < \varepsilon

    The negation:
     \exists \varepsilon > 0, \forall \delta > 0, ( x \in D \cap 0 < |x - c| < \delta ) \cap |f(x) - L| \geq \varepsilon

    Can any1 tell me if im right or wrong?
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  2. #2
    Junior Member
    Joined
    Oct 2009
    Posts
    68
    I think you need another quantifier for the x:

    \forall\,\epsilon>0,\,\exists\,\delta>0,\,\forall\  ,x\in D,\,0<|x-c|<\delta\ \Rightarrow\ |f(x)-L|<\epsilon
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