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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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Examples
We found at least one identifiable discontinuity in all analyses and more than one discontinuity in some.
The sudden discontinuity was often poetically associated with the attaining of enlightenment.
The juxtaposition of this passage with the following pericope underscores this theme of discontinuity.
That is, it is necessary to understand both continuity and discontinuity between closely related species.
Yet they may have come across moments when they discovered a profound gap or discontinuity in their supposedly continuous self.
Overall, these studies have generally underscored the lack of discontinuity among human groups and the relative homogeneity of the human species.

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