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A limit definition problem.

  1. Sep 29, 2004 #1
    show by example that the stament
    for all d>0 there exists e>0 such that o<|x-a|<d ->
    |f(x)-L|<e is Not the definition of limit.

    would somebody give me a hint?
     
  2. jcsd
  3. Sep 30, 2004 #2

    matt grime

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    Why not let e be 2?
     
  4. Sep 30, 2004 #3
    I don't understand..

    I think it's "there exists e"
     
  5. Sep 30, 2004 #4

    matt grime

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    I take it that means you didn't understand the hint?

    Ok, the function f(x)=2 for all x in R is obvioulsy continuous. Take your known incorrect definition, take my hint and think....
     
  6. Sep 30, 2004 #5

    Hurkyl

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    If you can do it by setting e = 2, then this clause is certainly satisfied.
     
  7. Sep 30, 2004 #6

    mathwonk

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    how can you answer this without a definition of limit? a more meaningful question would be to also give the definition of limit and then ask for a function and number that satisfies one definition and not the other.
     
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