continuum hypothesis

noun Mathematics.
a conjecture of set theory that the first infinite cardinal number greater than the cardinal number of the set of all positive integers is the cardinal number of the set of all real numbers.

Origin:
1935–40

Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
Cite This Source Link To continuum hypothesis
Collins
World English Dictionary
continuum hypothesis
 
n
maths the assertion that there is no set whose cardinality is greater than that of the integers and smaller than that of the reals

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009
Cite This Source
Encyclopedia Britannica
Encyclopedia

continuum hypothesis

statement of set theory that the set of real numbers (the continuum) is in a sense as small as it can be. In 1873 the German mathematician Georg Cantor proved that the continuum is uncountable-that is, the real numbers are a larger infinity than the counting numbers-a key result in starting set theory as a mathematical subject. Furthermore, Cantor developed a way of classifying the size of infinite sets according to the number of its elements, or its cardinality. (See set theory: Cardinality and transfinite numbers.) In these terms, the continuum hypothesis can be stated as follows: The cardinality of the continuum is the smallest uncountable cardinal number.

Learn more about continuum hypothesis with a free trial on Britannica.com.

Encyclopedia Britannica, 2008. Encyclopedia Britannica Online.
Cite This Source
Example sentences
The operational significance of the continuum hypothesis in the theory of water movement through soils and aquifers.
Copyright © 2014 Dictionary.com, LLC. All rights reserved.
  • Please Login or Sign Up to use the Recent Searches feature