Definition:Discontinuity (Real Analysis)/Non-Removable

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

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

Let $f$ be discontinuous at $a\in A$.

The point $a$ is a non-removable discontinuity of $f$ it is not a removable discontinuity.

Also known as
Some sources do not hyphenate: nonremovable discontinuity.