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. For example, a triangle is an object of dimension two, and a degenerate triangle is contained in a line, which makes its dimension one. In geometry, a degenerate conic is a conic section that fails to be an irreducible curve.
In general, the term "degenerate" refers to something that has declined or become less specialized from an ancestral or former state. It can be used as an adjective, verb, or noun, and is often associated with negative connotations. For example, a person who exhibits degenerate behavior is often considered immoral or corrupt.
In physics, "degenerate" can refer to modes of vibration of a system that have the same frequency or quantum states of a system that have equal energy.
Overall, the meaning of "degenerate" depends on the context in which it is used.
