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Convergent sequence?

  1. Nov 19, 2005 #1
    I found this in another threat
    however i do not know wat he means by convergent sequences. Is something like when u trying to take the limit at an ASYMPTOTE of a fuction? i know that the limit doesnt not exist( or goes to infinitive i cannot recall) is that wat he means by convergent sequence?

    Let f:I->R and let c in I. I want to negate the statements: "f has limit L at c" and "f is continuous at c". Are these correct?

    f does not have limit L at c if there exists e>0 such that for some sequence {x_n} converging to c, |f(x_n)-L|>e for every n.

    f is not continuous at c if there exists e>0 such that for some sequence {x_n} converging to c, |f(x_n)-f(c)|>e for every n.

    edit: also, what is the negation of "f has a limit at c"?
     
  2. jcsd
  3. Nov 20, 2005 #2
    the negation of "f has a limit at c" is "f does not have a limit at c". (meaning there is no L such that blah blah)

    for the one about the sequence f is not continuous at c if for some x in I, [tex]\lim_{x\rightarrow c}f(x) \neq f(c)[/tex]. that is.... well you know the definiton of limit, & if not it's in your book. of course if there's one x where f isn't continuous then if isn't continuous on the domain.
     
    Last edited: Nov 20, 2005
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