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
\[ f(x) = c \]
then
\[ \lim_{\delta \to 0} f(x+\delta) = c \]
and
\[ \lim_{\delta \to 0} f(x-\delta) = c \]
or, equivalently, given infinitesimal \(\delta\)
\[ f(x+\delta) = f(x-\delta) = c \]