# Continuous

Let $X$ be a subset of real numbers, let $f \colon \mathbb{R} \rightarrow \mathbb{R}$ be a function, and let $x \in A$. A function $f \colon \mathbb{R} \rightarrow \mathbb{R}$ is called continuous at $x$ if for every real number $\epsilon > 0$ there is a corresponding real number $\delta > 0$ with the property that $|f(x)-f(s)|<\epsilon$ for all $s$ with the property that $|s-x|<\delta$. If $f$ is continuous at all $x \in X$ we say that $f$ is a continuous function.