I read over the guide stickied at the top of the forum, but I did not understand the section on solving proofs when given a particular epsilon value. Could someone walk me through it with the attached problem?

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- Sep 15th 2010, 03:29 PMpenguinpwnSolving Delta Epsilon Proof (Given Epsilon)
I read over the guide stickied at the top of the forum, but I did not understand the section on solving proofs when given a particular epsilon value. Could someone walk me through it with the attached problem?

- Sep 15th 2010, 03:42 PMyeKciM
perhaps it's better to show you what is that $\displaystyle \epsilon $ region ...

you will (if not yet) have sequence which $\displaystyle a_n = (-1)^n $ (which don't converge) . why is that. well if you assume different , that for some $\displaystyle a \in \mathbb{R} $ there is $\displaystyle \lim_{n \to \infty } x_n = a $ now you realize that all members of that sequence are going to either one or negative one, that means that in any $\displaystyle \epsilon$ region around point "a" there should be both members of that sequence. that can't be true because if you chose any $\displaystyle \epsilon < \frac {1}{2} $ there is no chance that both that numbers be in some region $\displaystyle (a-\epsilon , a+ \epsilon)$ which length is less than one :D