Definition:Singular Point
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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 $\mathsf{Pr} \infty \mathsf{fWiki}$.