Definition:Discontinuity (Real Analysis)/Infinite

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

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

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

$f$ is an infinite discontinuity on $f$ $\size {\map f x}$ becomes arbitrarily large as $\size {x - c}$ becomes arbitrarily small.

Also known as
An infinite discontinuity is also known as a singularity.

However, this has other similar yet different uses, so it is deprecated on.

Also see

 * Definition:Finite Discontinuity