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Continuum (mathematics)

In mathematics, the word continuum sometimes denotes the real line. Somewhat more generally a continuum is a linearly ordered set that is "densely ordered", i.e., between any two members there is another, and lacks gaps, i.e., every non-empty subset with an upper bound has a least upper bound. By that definition, the long line is a continuum, as are various other sets besides the real line.

The "cardinality of the continuum" is the cardinality of the real line. The continuum hypothesis is sometimes stated by saying that no cardinality lies between that of the continuum and that of the natural numbers.