# Definition:Discontinuity (Real Analysis)/Non-Removable

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## 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 $f$ if and only if it is not a **removable discontinuity**.

## Also known as

Some sources do not hyphenate: **nonremovable discontinuity**.

## Also see

- Results about
**non-removable discontinuities**can be found**here**.