Difference between revisions of "Continuum"
Jump to navigation
Jump to search
(deleting second paragraph, per RSchlafly) |
|||
| Line 1: | Line 1: | ||
Mathematically, '''continuum''' can refer to the [[real line]], its [[cardinality]] <math>\mathfrak{c}</math>, or any [[continuous]] [[Connected_(topology)|connected]] [[Dense_subset|dense]] [[linear order]] without [[endpoint]]s. Generally, when mathematicians say "the continuum", they are referring to one of the first two possibilities (context clarifies which one). The [[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]], its [[cardinality]] <math>\mathfrak{c}</math>, or any [[continuous]] [[Connected_(topology)|connected]] [[Dense_subset|dense]] [[linear order]] without [[endpoint]]s. Generally, when mathematicians say "the continuum", they are referring to one of the first two possibilities (context clarifies which one). The [[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>. | ||
| − | |||
| − | |||
[[Category:Mathematics]] | [[Category:Mathematics]] | ||
Revision as of 19:34, February 16, 2009
Mathematically, continuum can refer to the real line, its cardinality , or any continuous connected dense linear order without endpoints. Generally, when mathematicians say "the continuum", they are referring to one of the first two possibilities (context clarifies which one). The Continuum Hypothesis conjectures that there is no set of cardinality bigger than that of the natural numbers , but smaller than the cardinality of the set of the real numbers .
