Karl Jones: Created page with "In the mathematical field of set theory, the '''continuum''' means the real numbers, or the corresponding (infinite) cardinal number, c. =..."

2016-09-22T15:45:47Z

Created page with "In the mathematical field of set theory, the '''continuum''' means the real numbers, or the corresponding (infinite) cardinal number, c. =..."

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In the [[Mathematics|mathematical]] field of [[set theory]], the '''continuum''' means the [[Real number|real numbers]], or the corresponding (infinite) cardinal number, c.

== Description ==

[[Georg Cantor]] proved that the [[cardinality]] c is larger than the smallest infinity, namely, aleph 0.

He also proved that c equals aleph 0 2^ 0, the cardinality of the [[power set]] of the [[Natural number|natural numbers]].

The [[cardinality of the continuum]] is the size of the set of real numbers. The continuum hypothesis is sometimes stated by saying that no cardinality lies between that of the continuum and that of the natural numbers, aleph 0.

== See also ==

* [[Cardinality of the continuum]]
* [[Suslin's problem]]

== External links ==

* [https://en.wikipedia.org/wiki/Continuum_(set_theory) Continuum (set theory)] @ Wikipedia

[[Category:Mathematics]]
[[Category:Set theory]]

Continuum (set theory) - Revision history

Karl Jones: Created page with "In the mathematical field of set theory, the '''continuum''' means the real numbers, or the corresponding (infinite) cardinal number, c. =..."