Definition of continuum hypothesis in English:

continuum hypothesis

Pronunciation /kənˈtinyo͞oəm hīˈpäTHəsəs/ /kənˈtɪnjuəm haɪˈpɑθəsəs/


  • 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.’