dis·con·ti·nu·i·ty

[dis-kon-tn-oo-i-tee, -yoo-]
noun, plural dis·con·ti·nu·i·ties.
1.
lack of continuity; irregularity: The plot of the book was marred by discontinuity.
2.
a break or gap: The surface of the moon is characterized by major discontinuities.
3.
Mathematics. a point at which a function is not continuous.
4.
Geology. a zone deep within the earth where the velocity of earthquake waves changes radically.
Origin:
1560–70; < Medieval Latin discontinuitās. See discontinuous, -ity

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Based on the Random House Dictionary, © Random House, Inc. 2013.
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Discontinuity is always a great word to know.
So is integer. Does it mean:
a function having the dependent variable expressed directly in terms of the independent variables, such as y = 3x + 4
one of the positive or negative numbers 1, 2, 3, or zero
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Collins
World English Dictionary
discontinuity (dɪsˌkɒntɪˈnjuːɪtɪ) [Click for IPA pronunciation guide]
 
—n , pl -ties
1.  lack of rational connection or cohesion
2.  a break or interruption
3.  maths
 a.  the property of being discontinuous
 b.  the point or the value of the variable at which a curve or function becomes discontinuous
4.  geology
 a.  See also Mohorovičić discontinuity a zone within the earth where a sudden change in physical properties, such as the velocity of earthquake waves, occurs. Such a zone marks the boundary between the different layers of the earth, as between the core and mantle
 b.  a surface separating rocks that are not continuous with each other

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
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American Heritage
Science Dictionary
discontinuity   (dĭs-kŏn'tə-n'ĭ-tē)  Pronunciation Key 

  1. A usually uneven surface between two layers of rock or sediment that represents either an interruption in the deposition of the layers, as in an unconformity, or a displacement of one or both layers relative to each other, as in a fault.

  2. A surface within the Earth across which the velocities of seismic waves change. The discontinuities are located at the boundaries between the Earth's various layers and correspond to changes in the elastic properties of the Earth's materials.


The American Heritage® Science Dictionary
Copyright © 2002. Published by Houghton Mifflin. All rights reserved.
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Example sentences
Emergence arises from a discontinuity of aggregation.
There was a significant discontinuity, however, as halftime scores moved closer
  to a tie.
Other disciplines recognise that when a model is operating close to a
  discontinuity, the model must be modified appropriately.
The meteorological discontinuity sensor is sited to detect operationally
  significant discontinuities in visibility.
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