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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
They are arranged along a post-creole continuum which has acrolectal at one end and basilectal at the other.
The only crack we see in the idea of the continuum comes from quantum theory.
Human maturation is a gradual process, a continuum rather than a sharp change.
I've always written about the gay experience as part of the continuum of the world.
The Kelso sand dune habitat is composed of a continuum of inclines, that vary from flat to steep.
The lymphatic system is a physiological continuum, yet the inguinal lymph nodes are traditionally divided into two anatomical groups.

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