Singularities

Definition

Singularities are points in mathematics where certain functions become undefined or behave unexpectedly. They often occur when dividing by zero or taking square roots of negative numbers.

Analogy

Picture yourself driving along a road until suddenly you encounter a pothole that makes your car shake uncontrollably. This unexpected disturbance can be compared to singularities in math, where functions encounter unexpected behavior or become undefined.

Related terms

Asymptote: An asymptote is a line that a graph approaches but never touches. It can be related to singularities as they both involve the behavior of functions at certain points.

Discontinuity: A discontinuity occurs when there is a break or jump in the graph of a function. Some types of discontinuities are caused by singularities.

Removable Singularity: A removable singularity is a type of singularity that can be 'filled' or removed by redefining the function at that point.