Definition of Limit

  • #1
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.
 

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  • #2
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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.
 
  • #3
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