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

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

Cohen developed a method called “forcing” that demonstrated that the continuum hypothesis is independent of the axioms of mathematics—that is, it couldn’t be proved within the framework of set theory.

From Scientific American • Sep. 16, 2017

He guessed not, a conjecture now known as the continuum hypothesis.

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