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Math Help - Solving Delta Epsilon Proof (Given Epsilon)

  1. #1
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    Solving 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?
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  2. #2
    Senior Member yeKciM's Avatar
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    Quote Originally Posted by penguinpwn View Post
    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?
    perhaps it's better to show you what is that  \epsilon region ...

    you will (if not yet) have sequence which  a_n = (-1)^n (which don't converge) . why is that. well if you assume different , that for some  a \in \mathbb{R} there is  \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  \epsilon region around point "a" there should be both members of that sequence. that can't be true because if you chose any \epsilon < \frac {1}{2} there is no chance that both that numbers be in some region  (a-\epsilon , a+ \epsilon) which length is less than one
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