Let $f$ be a function that is defined everywhere in an open interval containing $c$, except possibly at $c$. The number $c$ is called a removable discontinuity of $f$ if the function is discontinuous at $c$ but $\lim _{x \rightarrow c} f(x)$ exists. The discontinuity is removed by defining (or redefining) the value of $f$ at $c$ to be $\lim _{x \rightarrow c} f(x)$.