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What is a continuum?

What is a continuum? Here are some definitions.

Noun
  1. A continuous series or whole, no part of which is noticeably different from its adjacent parts, although the ends or extremes of it are very different from each other.
  2. A continuous extent.
  3. (mathematics) The set of all real numbers and, more generally, a compact connected metric space.
  4. (music) A touch-sensitive strip, similar to an electronic standard musical keyboard, except that the note steps are 1⁄100 of a semitone, and so are not separately marked.
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Examples
The Kelso sand dune habitat is composed of a continuum of inclines, that vary from flat to steep.
Alluvial fans and related phenomena are depositional landforms which form a continuum.
The lymphatic system is a physiological continuum, yet the inguinal lymph nodes are traditionally divided into two anatomical groups.
At the other end of the age continuum, Luke Ladell had much his best game to date.
The only crack we see in the idea of the continuum comes from quantum theory.
Japanese Gothic plots typically place humans on a spiritual continuum, a karmic wheel, rather than in a divided world of good and evil.

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