Continuum Hypothesis

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Continuum hypothesis - In mathematics, the continuum hypothesis is a hypothesis about the possible sizes of infinite sets. Georg Cantor introduced the concept of cardinality to compare the sizes of infinite sets, and he showed that the set of integers is strictly smaller than the set of real numbers.

Alternate hypothesis - The alternate hypothesis, or alternative hypothesis, together with the null hypothesis are the two rival hypothesis whose likelihoods are compared by a statistical hypothesis test. Usually the alternate hypothesis is the possibility that an observed effect is genuine and the null hypothesis is the rival possibility that ...

Forcing (mathematics) - In axiomatic set theory, forcing is a technique, invented by Paul Cohen, for proving consistency and independence results with respect to the Zermelo-Fraenkel axioms. It was first used, in 1962, to prove the independence of the continuum hypothesis and the axiom of choice from Zermelo-Fraenkel set theory.

Freiling's axiom of symmetry - Freiling's axiom of symmetry (AX) is a set-theoretic axiom proposed by Chris Freiling. The conjunction of AX with the axiom of choice entails that the continuum hypothesis does not hold.


Suggested Web Sites

Infinite Ink: The Continuum Hypothesis, by Nancy McGough - History, mathematics, metamathematics, and philosophy of Cantor's Continuum Hypothesis.

The Continuum Hypothesis - A workshop featuring a number of lectures surveying the current insights into the continuum problem and its variations. MSRI, Berkeley, CA, USA; 29 May -- 1 June 2001.

Axiom of Choice and Continuum Hypothesis - Part of the Frequently Asked Questions in Mathematics.

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Albert Einstein Short Biography - ... papers on logic and modal logic by defining translations between them. He also produced celebrated work on the Continuum hypothesis, showing that it cannot be disproven from the axioms. Kurt Gödel is the greatest logician of the ...

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