Special case

From Infogalactic: the planetary knowledge core
Jump to: navigation, search

Lua error in package.lua at line 80: module 'strict' not found.

In logic, especially as applied in mathematics, concept A is a special case or specialization of concept B precisely if every instance of A is also an instance of B but not vice versa, or equivalently, if B is a generalization of A. A limiting case is a type of special case which is arrived at by taking some aspect of the concept to the extreme of what is permitted in the general case. A degenerate case is a special case which is in some way qualitatively different from almost all of the cases allowed.

Special case examples include the following:

  • All squares are rectangles (but not all rectangles are squares); therefore the square is a special case of the rectangle.
  • Fermat's Last Theorem, that an + bn = cn has no solutions in positive integers with n > 2, is a special case of Beal's conjecture that ax + by = cz has no primitive solutions in positive integers with x, y, and z all greater than 2—​​specifically, the case of x = y = z.

See also