Pathological (mathematics)

The Weierstrass function is continuous everywhere but differentiable nowhere.

In mathematics, when a mathematical phenomenon runs counter to some intuition, then the phenomenon is sometimes called pathological. On the other hand, if a phenomenon does not run counter to intuition, it is sometimes called well-behaved or nice. These terms are sometimes useful in mathematical research and teaching, but there is no strict mathematical definition of pathological or well-behaved.[1]

  1. ^ Weisstein, Eric W. "Pathological". mathworld.wolfram.com. Retrieved 2019-11-29.