Definition:Discontinuous Mapping/Real Function/Point

Definition
Let $A \subseteq \R$ be a subset of the real numbers.

Let $f : A \to \R$ be a real function.

Let $a\in A$.

Then $f$ is discontinuous at $a$ $f$ is not continuous at $a$.

Also see

 * Definition:Removable Discontinuity of Real Function
 * Definition:Jump Discontinuity