# Sets and intervals

1. Dec 7, 2014

### bonildo

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,
l∈A.

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. Dec 7, 2014

### haruspex

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?