Special case

Summary

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. If $B$ is true, one can immediately deduce that $A$ is true as well, and if $B$ is false, $A$ can also be immediately deduced to be false. A degenerate case is a special case which is in some way qualitatively different from almost all of the cases allowed.