"In the first place, let me say that delta depends upon epsilon and not the other way round as you have stated. We select an arbitrary epsilon greater than zero and if we succeed in finding delta greater than zero satisfying the dfinition of the limit, then L is the limit. We have to express delta in terms of epsilon and taking the condition that epsilon is positive, prove that delta is positive for every positive epsilon. If, on the other hand, the relation between delta and epsilon so turns out that delta is not positiver for "every" positive epsilon, then we can conclude that L is not the limit. Remember that the definition has to be satisfied for every possible positive epsilon and not just one arbitrary positive epsilon."(adsbygoogle = window.adsbygoogle || []).push({});

reference:

http://answers.yahoo.com/question/i...MhyZTxIazKIX;_ylv=3?qid=20090429004411AAa2BJz

So, I`ve asked about how do we know (what is the proof) that Epsilon is a function of Delta?

and now I wanna ask the same question here..

but also, I have an additional question, why is the MR talking about "positive-negative"

I thought that the limit doesn`t exist when we can`t even make a relation between the two parts of the definition??

Thank you,

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# Concerning the definition of limit

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