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⭐ Core Definition: Degenerate case

In mathematics, a degenerate case is a limiting case of a class of objects which appears to be qualitatively different from (and usually simpler than) the rest of the class; "degeneracy" is the condition of being a degenerate case.

The definitions of many classes of composite or structured objects often implicitly include inequalities. For example, the angles and the side lengths of a triangle are supposed to be positive. The limiting cases, where one or several of these inequalities become equalities, are degeneracies. In the case of triangles, one has a degenerate triangle if at least one side length or angle is zero. Equivalently, it becomes a line segment.

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👉 Degenerate case in the context of 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. 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.

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Degenerate case in the context of "Special case"

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⭐ Core Definition: Degenerate case

👉 Degenerate case in the context of Special case