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## Homework Statement

Show that the set of [tex]\mathbb{R}^2[/tex] given by [tex]S = \{(x, y) \in \mathbb{R}^2 : x > y\}[/tex] is open.

## Homework Equations

## The Attempt at a Solution

Why is S the half plane that has boundary given by the line [tex]y = -x?[/tex]