Special case

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 $x = y = z$ .

See also