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Special case

In logic, especially as applied in mathematics, concept is a special case or specialization of concept precisely if every instance of is also an instance of but not vice versa, or equivalently, if is a generalization of . 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 has no solutions in positive integers with , is a special case of Beal's conjecture that has no primitive solutions in positive integers with , , and all greater than 2specifically, the case of .