# Definition The definition of continuity is an elementary definition of what it means for a function to be continuous at some point. A function is continuous at some point if the [[Limits|limit]] from the left and right of that point is finite and the function exists at the point, defined below. $ \begin{array}{c} \displaystyle \lim_{ x \to a^- } f(a) &= n \\ \displaystyle \lim_{ x \to a^+ } f(a) &= n \\ f(a) &= n \end{array} $