continuum hypothesis

The continuum hypothesisMathworldPlanetmath that there is no cardinal numberMathworldPlanetmath κ such that 0<κ<20.

An equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath statement is that 1=20.

It is known to be of the axioms of ZFC.

The continuum hypothesis can also be stated as: there is no subset of the real numbers which has cardinality strictly between that of the reals and that of the integers. It is from this that the name comes, since the set of real numbers is also known as the continuumMathworldPlanetmath.

Title continuum hypothesis
Canonical name ContinuumHypothesis
Date of creation 2013-03-22 12:05:29
Last modified on 2013-03-22 12:05:29
Owner rspuzio (6075)
Last modified by rspuzio (6075)
Numerical id 14
Author rspuzio (6075)
Entry type Axiom
Classification msc 03E50
Synonym CH
Related topic AxiomOfChoice
Related topic ZermeloFraenkelAxioms
Related topic GeneralizedContinuumHypothesis
Defines continuum