Definitions for continuum hypothesis
con·tin·u·um hy·poth·e·sis

WiktionaryRate this definition:0.0 / 0 votes

1. continuum hypothesisnoun

   The hypothesis which states that any infinite subset of must have the cardinality of either the set of natural numbers or of itself.

WikipediaRate this definition:0.0 / 0 votes

1. Continuum hypothesis

   In mathematics, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets. It states that there is no set whose cardinality is strictly between that of the integers and the real numbers, or equivalently, that any subset of the real numbers is finite, is countably infinite, or has the same cardinality as the real numbers. In Zermelo–Fraenkel set theory with the axiom of choice (ZFC), this is equivalent to the following equation in aleph numbers: 2 ℵ 0 = ℵ 1 {\displaystyle 2^{\aleph _{0}}=\aleph _{1}} , or even shorter with beth numbers: ℶ 1 = ℵ 1 {\displaystyle \beth _{1}=\aleph _{1}} . The continuum hypothesis was advanced by Georg Cantor in 1878, and establishing its truth or falsehood is the first of Hilbert's 23 problems presented in 1900. The answer to this problem is independent of ZFC, so that either the continuum hypothesis or its negation can be added as an axiom to ZFC set theory, with the resulting theory being consistent if and only if ZFC is consistent. This independence was proved in 1963 by Paul Cohen, complementing earlier work by Kurt Gödel in 1940.The name of the hypothesis comes from the term the continuum for the real numbers.

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1. Continuum hypothesis

   In mathematics, the continuum hypothesis is a hypothesis, advanced by Georg Cantor in 1878, about the possible sizes of infinite sets. It states: Establishing the truth or falsehood of the continuum hypothesis is the first of Hilbert's 23 problems presented in the year 1900. The contributions of Kurt Gödel in 1940 and Paul Cohen in 1963 showed that the hypothesis can neither be disproved nor be proved using the axioms of Zermelo–Fraenkel set theory, the standard foundation of modern mathematics, provided ZF set theory is consistent. The name of the hypothesis comes from the term the continuum for the real numbers.

How to pronounce continuum hypothesis?

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How to say continuum hypothesis in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of continuum hypothesis in Chaldean Numerology is: 2

2. Pythagorean Numerology

   The numerical value of continuum hypothesis in Pythagorean Numerology is: 4

References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Continuum_Hypothesis
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Continuum_Hypothesis
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=continuum hypothesis