1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Open set

  1. Jan 31, 2017 #1


    User Avatar

    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

    2x1 -1 < x < 1

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


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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).
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted