Definition:Discontinuity of the First Kind/Definition 2

Definition

Let $X$ be an open subset of $\R$.

Let $f: X \to Y$ be a real function.

Let $f$ be discontinuous at some point $c \in X$.

$c$ is known as a discontinuity of the first kind of $f$ if and only if either:

$c$ is a jump discontinuity

or:

$c$ is a removable discontinuity.

Also known as

A discontinuity of the first kind is also known as a simple discontinuity.

Some authors define a discontinuity of the first kind and a jump discontinuity to be the same thing.

Some other authors allow removable discontinuities to be a subset of jump discontinuities.

Also see

• Equivalence of Definitions of Discontinuity of the First Kind

• Results about discontinuities of the first kind can be found here.

Sources

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