Definition:Discontinuity (Real Analysis)

Definition
A discontinuity is an element $D$ in the domain of a real function $f$ at which $f$ is discontinuous.

Discontinuity of the First Kind
Let $X$ be an open subset of $\R$.

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

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

Simple Discontinuity
This is the same thing as a discontinuity of the first kind.