degeneracydɪˈdʒɛn ər ə si
degeneracy (n)
English Definitions:
degeneracy, degeneration, decadence, decadency (noun)
the state of being degenerate in mental or moral qualities
corruption, degeneracy, depravation, depravity, putrefaction (noun)
moral perversion; impairment of virtue and moral principles
"the luxury and corruption among the upper classes"; "moral degeneracy followed intellectual degeneration"; "its brothels, its opium parlors, its depravity"; "Rome had fallen into moral putrefaction"
degeneracy (Noun)
the state of being degenerate (in all senses)
Degeneracy
In mathematics, a degenerate case is a limiting case in which a class of object changes its nature so as to belong to another, usually simpler, class. A degenerate case thus has special features, which depart from the properties that are generic in the wider class, and which would be lost under an appropriate small perturbation. ⁕A point is a degenerate circle, namely one with radius 0. ⁕A circle is a degenerate form of an ellipse, namely one with eccentricity 0. ⁕The line is a degenerate form of a parabola if the parabola resides on a tangent plane. ⁕A segment is a degenerate form of a rectangle, if this has a side of length 0. ⁕A hyperbola can degenerate into two lines crossing at a point, through a family of hyperbolas having those lines as common asymptotes. ⁕A set containing a single point is a degenerate continuum. ⁕A random variable which can only take one value has a degenerate distribution. ⁕A sphere is a degenerate standard torus where the axis of revolution passes through the center of the generating circle, rather than outside it. ⁕A degenerate triangle has collinear vertices. ⁕See "general position" for other examples. Similarly, roots of a polynomial are said to be degenerate if they coincide, since generically the n roots of an nth degree polynomial are all distinct. This usage carries over to eigenproblems: a degenerate eigenvalue is one that has more than one linearly independent eigenvector.
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"degeneracy." Kamus.net. STANDS4 LLC, 2024. Web. 26 Apr. 2024. <https://www.kamus.net/english/degeneracy>.
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