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Epsilon delta definition of limit

  1. Feb 13, 2010 #1
    Can someone please explain Epsilon delta definition of limit in detail?
     
  2. jcsd
  3. Feb 13, 2010 #2

    HallsofIvy

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    I'll give it a shot. You don't say whether you are talking about the limit of a function or the limit of a sequence so I will assume the limit of a function: [itex]\lim_{x\to a} f(x)= L[/itex] if and only if, given any [itex]\epsilon> 0[/itex] there exist [itex]\delta> 0[/itex] such that if [itex]|x- a|< \delta[/itex], then [itex]|f(x)- L|< \epsilon[/itex].

    |a- b| essentially measures the distance between a and b. Saying that [itex]|f(x)- L|< \epsilon[/itex] just says that f(x) is closer to L than distance [math]\epsilon[/math]. And since [math]\epsilon[/math] can be any positive number, that means that we can make f(x) as close to L as we wish, just by making x "close enough" to a.
     
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