Bilangan riil: Perbedaan antara revisi

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The reals are [[uncountable set|uncountable]]; that is: while both the set of all [[natural number]]s and the set of all real numbers are [[infinite set]]s, there can be no [[one-to-one function]] from the real numbers to the natural numbers: the [[cardinality]] of the set of all real numbers (denoted <math>\mathfrak c</math> and called [[cardinality of the continuum]]) is strictly greater than the cardinality of the set of all natural numbers (denoted [[aleph number#Aleph-naught|<math>\aleph_0</math>]]). The statement that there is no subset of the reals with cardinality strictly greater than <math>\aleph_0</math> and strictly smaller than <math>\mathfrak c</math> is known as the [[continuum hypothesis]]. It is known to be neither provable nor refutable using the axioms of [[Zermelo–Fraenkel set theory]], the standard foundation of modern mathematics, provided ZF set theory is [[consistency|consistent]].

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