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Definition of Limit

  1. Nov 15, 2011 #1

    doubleaxel195

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    This isn't really a homework problem, but I was wondering why in the precise definition of a limit do we choose to make [tex] |f(x)-L| < ε [/tex] and not less than or equal to ε? I was just wondering. I asked my professor, he said he'd think about it, but he never got back to me.
     
    doubleaxel195, Nov 15, 2011
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  3. Jun 28, 2012 #2

    math man

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    Technically you could define it as ≤ ε, but it would be less natural. With the delta-epsilon definition, you define a range of values for x within a certain window (δ). For the given function, this defines a window around a range of y values (ε). If you change it to ≤ ε, you include the window as part of the range. It is more intuitive if the range of values is within a given window or < ε.
     
    math man, Jun 28, 2012
  4. Jun 29, 2012 #3

    micromass

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    This thread is from last year. Please be careful to check the date when posting.
     
    micromass, Jun 29, 2012
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