Math Help - boundary

1. boundary

W is the region outside of a sphere with r=5
what is the boundary ?
sorry this might be a silly question. i'm just debating between nothing or the sphere

2. It would be useful to remember that (at least in $\mathbb{R}^n$) $\partial \Omega = \overline{ \Omega } \cap \overline{ \mathbb{R} ^n \setminus \Omega }$ ie. the boundary of a set is the same as that of it's complement.

3. i'm sorry what do you mean it's compliment?

4. Originally Posted by calc626
i'm sorry what do you mean it's compliment?
If the set is $\Omega$ it's complemet is $\mathbb{R} ^n \setminus \Omega$

5. so the boundary is the sphere?

6. Yes