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 $a$ if and only if $f$ is not continuous at $a$.

Also see

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

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): discontinuous function
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): discontinuous function