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What is a duality?

What is a duality? Here are some definitions.

Noun
  1. A classification into two subclasses or opposed parts.
  2. (projective geometry) The interchangeability of points and planes.
  3. (mathematics) The mathematical equivalence of two seemingly different theoretical descriptions of a physical system.
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Examples
Despite her good deeds, this wizened enchantress's sinister duality surfaces when she senses the threat of a changeling among the Quinn clan.
His development of the pole and polar lines associated with conics led to the principle of duality.
Presumably it's meant to further illustrate the themes of duality and inner struggle, but the only effect is that of an irritating side-show.
Wine and life-giving waters were on equal footing in Egyptian culture, and they also shared a duality in both myth and in fact.
But our poem's horizon expanded far beyond this confined duality to embrace the universal, the human, as well as the intimate and personal.
And this presents on screen the kind of duality of which Brecht was so fond on the stage.

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