(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let X = R2 with the Euclidean metric and let S = {(x1, x2) : x1^2+x2^2 <1}.Prove that Closure of S ={(x1,x2):x1^2+x2^2<= 1} and that the Boundary of S= { (x1, x2) : x1^2 +x2 ^2=1 } .

2. Relevant equations

3. The attempt at a solution

I was able to prove all my theorems but I don't know how to prove this concrete example. All my theorems just talked about one point in the closure or boundary. I can clearly see from a picture that these are the answers but how do I prove it without a picture?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# How do I prove the closure and the boundary of a concrete example?

**Physics Forums | Science Articles, Homework Help, Discussion**