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Usually a continuum refers to a whole, no part of which can be distinguished from neighboring parts except by arbitrary division.
See:
Continuum (mathematics) - sets such as the real line
Continuum hypothesis - "There is no set whose size is strictly between that of the integers and that of the real numbers."
Continuum mechanics, branch of physics that deals with continuous matter, including both solids and fluids.
The Spacetime
The computer game Continuum aka Subspace.
Language continuum
Continuum is also the name of a publisher
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