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Math Help - confused about definitions

  1. #1
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    confused about definitions

    i was reading my notes and it stated this def for continuity:

    f is continuous if for all ε>0 there exist δ>0 such that 0< l x-c l <δ, then lf(x) -f(c) l < ε.

    i thought that by saying 0< l x-c l <δ, we are considering the cases where x cant be c. which is that the limit is not f(c)..

    but from this lf(x) -f(c) l < ε, my professor is already assuming that the limit is f(c) right?

    and so its sufficient in the definition to just say l x-c l <δ... isit true?
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  2. #2
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    In the definition of continuity is suffices to say |x-c|<\delta.
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