noun, plural singularities for 2–4.
the state, fact, or quality of being singular.
a singular, unusual, or unique quality; peculiarity.
Mathematics, singular point.
Astronomy. (in general relativity) the mathematical representation of a black hole.

1300–50; Middle English singularite < Late Latin singulāritās. See singular, -ity

nonsingularity, noun, plural nonsingularities. Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
singularity (ˌsɪŋɡjʊˈlærɪtɪ)
n , pl -ties
1.  the state, fact, or quality of being singular
2.  something distinguishing a person or thing from others
3.  something remarkable or unusual
4.  maths
 a.  See also pole a point at which a function is not differentiable although it is differentiable in a neighbourhood of that point
 b.  another word for discontinuity
5.  astronomy a hypothetical point in space-time at which matter is infinitely compressed to infinitesimal volume

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009
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American Heritage
Science Dictionary
singularity   (sĭng'gyə-lār'ĭ-tē)  Pronunciation Key 
  1. A point of infinite density and infinitesimal volume, at which space and time become infinitely distorted according to the theory of General Relativity. According to the big bang theory, a gravitational singularity existed at the beginning of the universe. Singularities are also believed to exist at the center of black holes.

  2. Mathematics A point at which the derivative does not exist for a given function but every neighborhood of which contains points for which the derivative exists.

The American Heritage® Science Dictionary
Copyright © 2002. Published by Houghton Mifflin. All rights reserved.
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Example sentences
For example, the big bang theory says the universe started as a singularity.
He has an extraordinary singularity of focus, as stubborn and direct as the
  wall itself.
Education singularity is the moment in human history where all learning is free
  and accessible to all.
Admiration for his accomplishments, his singularity, and the longevity and
  diversity of his career intervene.
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