1. Singularity in tangent line
The undefined point that seems to be "approaching" to ∞ in real numbers is the singularity x= 0. The equation g(x) = |x| (see absolute value) also contains the singular point x= 0 (because it is non-differentiable at this point). Similarly, there is a singularity (0,0) at y=x, because this point contains a vertical tangent. An algebraic set in the (x, y) dimensional system is defined as y= 1/x, and the singularity is (0,0), because tangents are not allowed here. ?
2. Singularity in geometry
A "geometric singularity" is also an infinitesimal and nonexistent "point". You can imagine a one-dimensional space (such as a straight line), a two-dimensional space (such as a surface), or a three-dimensional space. When it is infinite, take the last "point" with a small limit, which does not exist, that is, the singularity.
3. Mathematical Graph Theory
In mathematical graph theory, in undirected graph G, the number of edges associated with vertex V is called the degree or degree of vertex V, and vertices with odd degrees are called singularities.