Classification problem

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Further information: Class (philosophy), Class (set theory), and Russell's paradox

The Classification Problem, in terms of science or mathematics, is the problem of separating a large class of objects into smaller classes, and giving a criterion for determining whether a particular object is or is not in a particular class.

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.