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Undo revision 615409 by ArnoldFriend (Talk) didn't see the link to linear order above
Mathematically, '''continuum''' can refer to the [[Real_line|real line]], its [[Cardinality|cardinality]] <math>\mathfrak{c}</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>\mathfrak{c}</math>.
Mathematically, '''continuum''' can refer to the [[Real_line|real line]], its [[Cardinality|cardinality]] <math>\mathfrak{c}</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>\mathfrak{c}</math>.
The continuum is called so because it was the first (and most prominent) [[Continuous|continuous]] set studied by mathematicians. No additional numbers may be added to the continuum (real line) without losing its dense [[linear order]]. Since the [[Complex_number|complex numbers]] add the [[Imaginary_number|imaginary number]], i, to the real line, this is one reason they have no natural linear order.
The continuum is called so because it was the first (and most prominent) [[Continuous|continuous]] set studied by mathematicians. No additional numbers may be added to the continuum (real line) without losing its dense linear order. Since the [[Complex_number|complex numbers]] add the [[Imaginary_number|imaginary number]], i, to the real line, this is one reason they have no natural linear order.
[[Category:Mathematics]]
[[Category:Mathematics]]