power of the continuum

…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…

…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.