Expert: Sherry Wallin - 9/12/2009

Question
Hello,

I am wanting to know if the definition of a limit below normally used is the best definition of a limit, the only definition of a limit or could there be a better definition of a limit not up to now thought of?

for each real ε > 0 there exists a real δ > 0 such that for all x with 0 < |x − c| < δ, we have |f(x) − L| < ε.

Kind Regards,

Scott

Answer
Hi Scott~
    |f(x) − L| < ε means  -ε < f(x) − L < ε which just means the the difference between f(x) and the limit is small (either positively small or negatively small). All versions of the limit amount to the same thing. Sorry I couldn't be of more help.  Math Prof