Definition of continuum hypothesis in US English:

continuum hypothesis


  • The assertion that there is no transfinite cardinal between the cardinal of the set of positive integers and that of the set of real numbers.

    • ‘In 1938, logician Kurt Godel proved that the continuum hypothesis is consistent with the standard axioms of set theory.’
    • ‘The main focus of the 1964 paper is the continuum hypothesis, an interesting case study for Godel's philosophical view.’
    • ‘In set theory he made important contributions to the axiom of choice and to the continuum hypothesis.’
    • ‘If, on the other hand, if we decide to not include the continuum hypothesis, then the situation is undetermined.’
    • ‘A good axiom, he felt, should help mathematicians settle not only the continuum hypothesis but also many other questions about Cantor's hierarchy of infinite sets.’