1. The problem is to understand and describe the surface defined by the equation $x=0$ in $\mathbb{R}^3$. 2. The equation $x=0$ represents all points in three-dimensional space where the $x$-coordinate is zero. 3. This means the surface includes all points $(0, y, z)$ where $y$ and $z$ can be any real numbers. 4. Geometrically, this is the $yz$-plane, a flat, infinite plane perpendicular to the $x$-axis. 5. The formula for a plane parallel to the $yz$-plane is $x = c$, where $c$ is a constant. Here, $c=0$. 6. Important rule: A plane defined by $x = k$ is vertical and extends infinitely in the $y$ and $z$ directions. 7. Therefore, the surface $x=0$ is the $yz$-plane in $\mathbb{R}^3$. Final answer: The surface $x=0$ is the $yz$-plane, consisting of all points $(0, y, z)$ with $y, z \in \mathbb{R}$.