> [!Definition] Definition > A *level set* of a [[Real-Valued Function on Real n-Space (Multivariable Function)|multivariate real valued function]] $f:U\subseteq \mathbb{R}^{n}\to \mathbb{R}$ is the set of points: $\{ \underline{x} \in \mathbb{R} \mid f(\underline{x}) = k\}$for a constant $k$ in the range of $f$. > [!info] Language > - When $n=2$, a level set is a [[Parametrized Curve|curve]] called a **contour** or **contour line**. > - When $n=3$, a level set is a [[Algebraic Surface|surface]] called an **isosurfaces**. # Examples Use [[matplotlib.pyplot]].