You are here
Homepathological
Primary tabs
pathological
In mathematics, a pathological object is mathematical object that has a highly unexpected property.
Pathological objects are typically percieved to, in some sense, be badly behaving. On the other hand, they are perfectly properly defined mathematical objects. Therefore this “bad behaviour” can simply be seen as a contradiction with our intuitive picture of how a certain object should behave.
Examples

A very famous pathological function is the Weierstrass function, which is a continuous function that is nowhere differentiable.

The Cantor set. This is subset of the interval $[0,1]$ has the pathological property that it is uncountable yet its measure is zero.

The Dirichlet’s function from $\mathbbmss{R}$ to $\mathbbmss{R}$ is continuous at every irrational point and discontinuous at every rational point.
See also [1].
References
 1 Wikipedia entry on pathological, mathematics.
Mathematics Subject Classification
00A20 no label found Forums
 Planetary Bugs
 HS/Secondary
 University/Tertiary
 Graduate/Advanced
 Industry/Practice
 Research Topics
 LaTeX help
 Math Comptetitions
 Math History
 Math Humor
 PlanetMath Comments
 PlanetMath System Updates and News
 PlanetMath help
 PlanetMath.ORG
 Strategic Communications Development
 The Math Pub
 Testing messages (ignore)
 Other useful stuff
Recent Activity
new question: numerical method (implicit) for nonlinear pde by roozbe
new question: Harshad Number by pspss
Sep 14
new problem: Geometry by parag
Aug 24
new question: Scheduling Algorithm by ncovella
new question: Scheduling Algorithm by ncovella