# Special case

## Specific, usually well-known application of a mathematical rule or law / From Wikipedia, the free encyclopedia

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 a
^{n}+ b^{n}= c^{n}has no solutions in positive integers with n > 2, is a special case of Beal's conjecture, that a^{x}+ b^{y}= c^{z}has no primitive solutions in positive integers with x, y, and z all greater than 2, specifically, the case of x = y = z.