# Special case

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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.

## Examples

- 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
*n*>2, is a special case of Beal's conjecture that has no solutions in positive integers with*x*,*y*, and*z*all greater than 2—specifically, the case of*x*=*y*=*z*.