CONTINUUM HYPOTHESIS Definition & Meaning

continuum hypothesis

noun

Mathematics.

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.

continuum hypothesis

noun

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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�y��vlog History and Origins

Origin of continuum hypothesis¹

First recorded in 1935–40

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Example Sentences

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Finding no such set, the mathematician formulated his famous “continuum hypothesis” in 1878.

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As it turns out, the continuum hypothesis belongs to the statements that elude our basic mathematical framework.

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In other words, you could assume the continuum hypothesis to be true and never encounter a contradiction.

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In response, some people are trying to extend the basic framework of the subject to derive a tool from this larger theory to prove or disprove the continuum hypothesis.

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

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