1. ## Boundary Question

Hi,
I have this one other question and I think it requires a rigorous proof involving balls etc and I have no idea about how to go about it.

Prove: $\partial \{ x \in \mathbb{R}^n : |x| < 1 \} = \{ x \in \mathbb{R}^n : |x|=1 \}$

Thanks again

2. What do you know about the boundary?

For instance, do you know that Boundary(S) = Closure(S)\Interior(S)?

If you do, then

Boundary(open solid unit ball) = (the closed solid unit ball)\(the open solid unit ball) = the unit ball.

Edit: Ah, you wanted a points-and-balls proof. I'll let this be anyway.

3. yaa, I needed a point-ball proof for this. Any help?

Thanks a lot!

4. I see that you have over twenty postings.
By now you should understand that this is not a homework service
So you need to either post some of your work on this problem or explain what you do not understand about the question.