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Homework Help: Sets and intervals

  1. Dec 7, 2014 #1
    1. The problem statement, all variables and given/known data
    Hello, I'm not sure if it's the right place to post this exercise, but I'm learning it in a calculus course.

    I need to prove that:

    a) The complement of an open set is a closed.
    b) An open interval is a open set, a closed interval is a closed set.

    2. Relevant equations
    I have the following definitions:

    1) An subset A⊂R is open if for all sequence {an}n∈N that converges for l∈A,
    ∃n0 such that ∀n>n0 ,an∈A.

    2) An subset A⊂R is closed if for all sequence {an}n∈N that converges for l∈R,

    3. The attempt at a solution

    Sincerely, I don't have any ideia how to do it , I never worked on this kind of exercise before
  2. jcsd
  3. Dec 7, 2014 #2


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    Science Advisor
    Homework Helper
    Gold Member

    That's not quite right. You need the constraint that the an are elements of A.
    Start with an open set A and consider its complement B = R-A. Let bn be a sequence in B converging to l in R. Consider the consequences of l not being in B. If it's not in B, where is it?
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