Classification problem

In science or mathematics, a classification problem for objects in a particular domain is the problem of separating these objects into smaller classes, and giving criteria for determining whether a particular object in the domain is in a particular class or not.

One of the most famous attempts at classification in biology is Carolus Linnaeus's famous classification of living things by class, order, genus, and species. An example in physics is the classification of the physical world into matter and energy, and the classification of matter according to its atomic number and energy according to its wavelength. In mathematics, one successful solution to a classification problem is the classification of vector spaces by their dimension. Two vector spaces are isomorphic if and only if they have the same dimension. Another example is the classification of two dimensional manifolds: every two dimensional manifold is a connected sum of spheres, tori, and projective planes.

See also