Definition:Singular Point/Real/Definition 1

Definition

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.

Also see

• Equivalence of Definitions of Singular Point

• Results about singular points can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): singular point (singularity): 2.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): singular point (singularity): 2.
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): singular point (singularity)