Definition:Singular Point

Definition

Real Analysis

Let $C$ be a locus.

A point $P \in C$ is called a singular point if and only if $P$ does not have a unique tangent to $C$ which is itself differentiable.

Complex Analysis

Let $U \subseteq \C$ be an open set.

Let $f : U \to \C$ be a complex function.

A singular point of $f$ is a point at which $f$ is not analytic.

Also known as

A singular point is also known as a singularity.

However, this has other similar yet different uses, so it is deprecated on $\mathsf{Pr} \infty \mathsf{fWiki}$.