- #1

- 44

- 0

## Homework Statement

Let S = {(x,y): x[itex]^{2}[/itex]+y[itex]^{2}[/itex]<1}. Prove that [itex]\overline{S}[/itex] is (that formula for the unit circle) [itex]\leq[/itex] 1 and the boundary to be x[itex]^{2}[/itex]+y[itex]^{2}[/itex]=1.

## Homework Equations

Boundary of S is denoted as the intersection of the closure of S and the closure of S complement.

p [itex]\epsilon[/itex] boundary of S iff for every r > 0, B(p;r)[itex]\cap[/itex]S is non-empty and B(p;r)[itex]\cap[/itex]S complement is non-empty.

## The Attempt at a Solution

I understand this conceptually and it's obvious that the boundary and closure are those equations respectively but I don't know how to translate that into a math proof. I wasn't exactly given any concrete examples and how to apply the theorems into a proof, was only presented with the theorems.