continuum hypothesis

American  

noun

Mathematics.

1. 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.

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continuum hypothesis British  

noun

1. maths the assertion that there is no set whose cardinality is greater than that of the integers and smaller than that of the reals

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Etymology

Origin of continuum hypothesis

First recorded in 1935–40

Example Sentences

For example, you could append the statement “The continuum hypothesis is true” to the group of axioms.

From Scientific American • Jul. 13, 2023

In the latest paper, Yehudayoff and his collaborators show that the problem of learnability, expressed in a suitable sense, is equivalent to the continuum hypothesis.

From Nature • Jan. 7, 2019

But he was not able to prove this continuum hypothesis, and nor were many mathematicians and logicians who followed him.

From Nature • Jan. 7, 2019

Throughout the first half of the 20th century, mathematicians tried to resolve the continuum hypothesis by studying various infinite sets that appeared in many areas of mathematics.

From Scientific American • Sep. 16, 2017

In 1963 a mathematician, Paul Cohen, proved that this puzzle, the so-called continuum hypothesis, was neither provable nor disprovable, thanks to Gödel’s incompleteness theorem.

From "Zero: The Biography of a Dangerous Idea" by Charles Seife