power of the continuum

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power of the continuum

mathematics

Also known as: alef-one, aleph-one

Learn about this topic in these articles:

continuum hypothesis

In history of logic: The continuum problem and the axiom of constructibility
…natural numbers, called ℵ₁ (aleph-one), is equal to the cardinality of the set of all real numbers. The continuum hypothesis states that ℵ₁ is the second infinite cardinal—in other words, there does not exist any cardinality strictly between ℵ_o and ℵ₁. Despite its prominence, the problem of the continuum…
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set theory of Cantor

In set theory: Cardinality and transfinite numbers
…called denumerable), and ℵ (aleph) is sometimes used for that of the set of real numbers. Then n < ℵ₀ for each n ∊ ℕ and ℵ₀ < ℵ.
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