# Pathological Function

A Pathological Function is a Mathematical Function that is constructed to violate certain conditions of a function's applicability in order to test universally true mathematical statements.

**Example(s):****Counter-Example(s):****See:**Pathology, Pathological Sciences, Molecular Pathologic Epidemiology, Gait Analysis, Biological Function.

## References

### 2019a

- (Wikipedia, 2019) ⇒ https://en.wikipedia.org/wiki/Pathological_(mathematics) Retrieved:2019-5-23.
- In mathematics, a
**pathological**phenomenon is one whose properties are considered atypically bad or counterintuitive; the opposite is**well-behaved**.

- In mathematics, a

### 2019b

- (Ashraf, 2019) ⇒ T. Ashraf (2019). "Pathological Functions: The Continuous But Nowhere Differentiable" (PowerPoint Presentation) Retrieved:2019-5-23.
- QUOTE: The term "Pathological" is used in mathematics to refer to an example specifically formed to violate certain almost universally valid properties. Pathological problems often provide interesting examples of counterintuitive behavior, as well as serving as an excellent illustration of why very detailed conditions of applicability are required in order for many mathematical statements to be universally true.