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Largest and smallest D intersect E can be

  1. Nov 15, 2008 #1
    1. The problem statement, all variables and given/known data
    Ok so I have D[tex]\cap[/tex][[tex]x_{0}-\epsilon,x_{0}+\epsilon[/tex]]=E[tex]\cap[/tex][[tex]x_{0}-\epsilon,x_{0}+\epsilon[/tex]].
    I wnat to find the largest and smallest that D[tex]\cap[/tex]E can be.



    2. Relevant equations



    3. The attempt at a solution
    For largest I got [tex][x_{0}-\epsilon,x_{0}+\epsilon][/tex]. I feel good about that, but I'm not so sure about smallest. I was thinking x0.
     
  2. jcsd
  3. Nov 15, 2008 #2
    Ok, I just realized the smallest = [tex]\oslash[/tex], right?
     
  4. Nov 15, 2008 #3

    Mark44

    Staff: Mentor

    Right, if [tex][x_0 - \epsilon, x_0 + \epsilon][/tex] is not a subset of D.
     
  5. Nov 16, 2008 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Yes, which raises the question, "What was the problem, really?"
     
  6. Nov 16, 2008 #5
    It was a problem about accumulation points and proving there was a limit. I figured out the rest of the problem already. It was just that part.
     
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