contiuumhypoteesiin
The Continuum Hypothesis, often referred to in Finnish as "kontiinin hypoteesi" or sometimes mistakenly written as "contiuumhypoteesiin," is a statement in set theory concerning the possible sizes of infinite sets. It asks whether there exists an infinite set whose cardinality is strictly between that of the set of natural numbers and the set of real numbers. In terms of cardinal numbers, the hypothesis can be expressed as: there is no cardinal number \( \kappa \) such that \( \aleph_0 < \kappa < 2^{\aleph_0} \).
The hypothesis was first formulated by Georg Cantor in 1874 as part of his work on the
In 1940, Kurt Gödel proved that the Continuum Hypothesis cannot be disproved from the standard axioms of
The independence result has had profound implications for mathematics, illustrating that the axioms of set theory