continuum hypothesis
Based on the Random House Dictionary, © Random House, Inc. 2012.
Cite This Source
00:10
00:09
00:08
00:07
00:06
00:05
00:04
00:03
00:02
00:01
| the smallest number that is a common multiple of a given set of numbers |
| one of the positive or negative numbers 1, 2, 3, or zero |
| 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 | |
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009
Cite This Source
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.
Cite This Source
