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The term 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.

Latest revision as of 17:21, February 13, 2006

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The term 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.

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