**Definition** A [[Function|function]] $f:E \to \mathbb{R}$ is *discontinuous* at $c \in E$ if we can find $(x_{n}) \in E$ such that $x_{n} \to c$ as but $f(x_{n}) \not \to f(c)$ as $n \to \infty$. Note that we can either use this definition to prove that a function is discontinuous at a point or we can use this definition: [[Discontinuous Function (Epsilon-Delta Definition)]]. See [[Examples of Discontinuous Functions]].