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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
His development of the pole and polar lines associated with conics led to the principle of duality.
But our poem's horizon expanded far beyond this confined duality to embrace the universal, the human, as well as the intimate and personal.
It is a duality that only the most mushyheaded of his admirers can blissfully ignore.
Just how Gilliam's duality came about is unclear, but he apparently mastered it early in life.
Despite her good deeds, this wizened enchantress's sinister duality surfaces when she senses the threat of a changeling among the Quinn clan.
I know it looks like the old positivist duality, but it does give some insight into the way that political romanticism poeticizes politics.

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