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The statement removed is not true. One could add a number at either end of the real line, define the order in the obvious way and one would still have a continuum.
Mathematically, '''continuum''' can refer to the [[Real_line|real line]], its [[Cardinality|cardinality]] <math>2^{\aleph_0}</math>, or any [[Continuous|continuous]] [[Connected_(topology)|connected]] [[Dense_subset|dense]] [[Linear_order|linear order]]. Generally, when mathematicians say "the continuum", they are referring to one of the first two possibilities (context clarifies which one). The [[Continuum_hypothesis|Continuum Hypothesis]] conjectures that there is no set of cardinality bigger than that of the [[natural number]]s <math>\aleph_0</math>, but smaller than the cardinality of the set of the real numbers, <math>2^{\aleph_0}</math>.
Mathematically, '''continuum''' can refer to the [[Real_line|real line]], its [[Cardinality|cardinality]] <math>2^{\aleph_0}</math>, or any [[Continuous|continuous]] [[Connected_(topology)|connected]] [[Dense_subset|dense]] [[Linear_order|linear order]]. Generally, when mathematicians say "the continuum", they are referring to one of the first two possibilities (context clarifies which one). The [[Continuum_hypothesis|Continuum Hypothesis]] conjectures that there is no set of cardinality bigger than that of the [[natural number]]s <math>\aleph_0</math>, but smaller than the cardinality of the set of the real numbers, <math>2^{\aleph_0}</math>.
[[Category:Mathematics]]
[[Category:Mathematics]]