# What does continuity mean?

In general, for a function $f$ to be continuous at a point where $x = a$ means that as values of $x$ get close to $a$, the values of $f \left(x\right)$ get close to $f \left(a\right)$.
${\lim}_{x \to a} f \left(x\right) = f \left(a\right)$