# Continuous

A function is continuous if a small change in its argument yields a small change in its result.

In the language of limits this means that if

In the language of limits this means that if

\[
f(x) = c
\]

then
\[
\lim_{\delta \to 0} f(x+\delta) = c
\]

and
\[
\lim_{\delta \to 0} f(x-\delta) = c
\]

or, equivalently, given infinitesimal \(\delta\)
\[
f(x+\delta) = f(x-\delta) = c
\]