Definition:Discontinuity of the First Kind/Definition 2

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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


$c$ 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

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