Continuous Function

Topics: Calculus - Function

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(definition)

Let $f:\mathbb{R}\to \mathbb{R}$. We say that $f$ is continuous at $x_0$ if $\forall \epsilon >0$, $\exists \delta >0$ such that:

$$|f(x)-f(x_0)|<\epsilon$$

…if $|x-x_0|<\delta$.

Vectorial functions can also be continuous.