Continuous Function

A function $f$ from the real line to the real line is continuous if $f(x)\to f(a)$ as $x\to a$, for any value of $a$.

It is called right continuous if this is true when approaching from the right, i.e., $f(x)\to f(a)$ as $x\to a$ while ranging over values with $x>a$, and left continuous if this is true when approaching from the left.