continuous function

A continuous function is a function of a continuous variable.

Formally,
a function $f:X\to Y$ is continuous at point $c\in X$ if the limit of $f$ at $c$ equals the value of $f(c)$:

i.e.,
for any real $\epsilon >0$, there exists a $\delta >0$ such that for any $x$ with $0<|x-c|<\delta$, then $|f(x)-f(c)|<\epsilon$