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Open set

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  1. Jan 31, 2017 #1

    Cyn

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    1. The problem statement, all variables and given/known data
    I have a set I = {x from R3 : x1<1 v x1>3 v x2<0 x x3>-1}

    2. Relevant equations
    Open disc
    B (x,r)
    (sqrt (x-x0)^2 + (y-y0)^2) < r

    3. The attempt at a solution
    I have done, for example by x1<1, that let r = 1-x1
    Then sqrt ((x-x1)^2 + (y-y1)^2) < sqrt (x-x1)^2) < r = 1-x1
    So |x-x1| < 1-x1

    x1-1<x-x1<1-x1
    2x1 -1 < x < 1

    So x<1 satisfy the inequality, so it is open. Is this correct?
     
  2. jcsd
  3. Jan 31, 2017 #2

    andrewkirk

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    You seem to have the right general idea, which is to show that the set S={(x1,x2,x3) : x1<1} is open because, any point (x1,x2,x3) in S is contained in the open ball centred on that point with radius (1-x1).

    But you have not shown that. All you've done is write a few equations, with no explanations of their relevance, or how they relate to one another, and most of the terms undefined. A proof must tell a story, with a beginning, a middle and an end. And just like how in a novel, the characters must be introduced to the reader, the symbols you use must be explained (defined).
     
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