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Definition Of Infinite Limits

  1. May 24, 2012 #1
    I have attached this definition that my book provides. My question is does that part "for each M > 0 there exists δ > 0 such that f(x) > M, mean that whenever you M close to the limit, you can find a δ that will give M1 that is closer to the limit?
     

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    Last edited: May 24, 2012
  2. jcsd
  3. May 24, 2012 #2
    Is there more information that is needed? Because that is all the information contained in the book.
     
  4. May 24, 2012 #3

    HallsofIvy

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    No, just don't expect people to be sitting around waiting to answer your question! To get a response within 24 or 48 hours is pretty good.

    Not exactly. It means that no finite number, M, can be the limit because, for any [itex]\delta> 0[/itex] there exist x within [itex]|x- c|< \delta[/itex] such that f(x)> M.
     
  5. May 26, 2012 #4
    You are wrong in a couple of ways halls of ivy

    1. "no finite number is the limit." that is not correct. it is implied, but it is not the same

    2. "there is some x in the delta ball." that would just mean the function is not bounded near there. You are allowing f to jump back down as often as it wants.

    The definition needs to say that within these delta balls, all x values land above M. Choose M as large as you want, then there is such a delta ball. And all of us, even me, need to be careful about the order in which we say these things. What I said just now could easily be misinterpreted.

    So, to put it better, Pick any M value, large as you want, I dare you. Then I promise you a delta ball. You can pick any x in that delta ball, and I guarantee that x will land above M. That's why in the picture they shaded it blue, they're trying to suggest all x vaules inside will work.
     
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