Let $f \in \mathbb{R}[x,y]$ be such that there exists a non-empty open set $U \subseteq \mathbb{R}^{2}$ such that $f(x,y) = 0$ for every $(x,y) \in U$. Show that $f = 0$.
Let $f \in \mathbb{R}[x,y]$ be such that there exists a non-empty open set $U \subseteq \mathbb{R}^{2}$ such that $f(x,y) = 0$ for every $(x,y) \in U$. Show that $f = 0$.