In
mathematics, the continuum hypothesis (abbreviated CH) is a
hypothesis, advanced by
Georg Cantor, about the possible sizes of
infinite sets. Cantor introduced the concept of
cardinality to compare the sizes of infinite sets, and he gave two proofs that cardinality of the set of
integers is strictly smaller than that of the set of
real numbers. His proofs, however, give no indication of the extent to which the cardinality of the natural numbers is less than that of the real numbers. Cantor proposed the continuum hypothesis as a possible solution to this question. It states:There is no set whose size is strictly between that of the integers and that of the real numbers. In light of Cantor's theorem that the sizes of these sets cannot be equal, this hypothesis states that the set of real numbers has minimal possible cardinality. The name of the hypothesis comes from the term
the continuum for the real numbers.
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