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Subsets - analysis

  1. Feb 6, 2010 #1
    1. The problem statement, all variables and given/known data

    I need to find out whether the subset Re(real no's) of complex no's is open, closed or neither.

    2. Relevant equations



    3. The attempt at a solution

    Im not really sure how to begin this...any help please?
     
  2. jcsd
  3. Feb 6, 2010 #2

    HallsofIvy

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    Let x be any real number and consider a neighborhood of it in the complex numbers: [itex]\{z | |z- x|< \delta\}[/itex]. Does that contain any non-real numbers?
     
  4. Feb 7, 2010 #3
    yes i think it does contain non real numbers, so this would imply that it is an open subset?
    how would i go about sketching it?
     
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