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What is a discontinuity?

What is a discontinuity? Here are some definitions.

Noun
  1. A lack of continuity, regularity or sequence; a break or gap. [from 16th c.]
  2. (mathematics) A point in the range of a function at which it is undefined or discontinuous. [from 19th c.]
  3. (geology) a subterranean interface at which seismic velocities change
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That is, it is necessary to understand both continuity and discontinuity between closely related species.
As such, philosophy itself must orientate itself to the continuous discontinuity of the event.
This discontinuity opens the possibility of exploring the impossible, the little boy's prelinguistic consciousness.
Although I suppose the above changes are marked more by continuity than by discontinuity.
We found at least one identifiable discontinuity in all analyses and more than one discontinuity in some.
The sharp boundary between the crust and mantle is called the Mohorovicic discontinuity or Moho.

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