Definitions

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  • n. Plural form of cardinality.

Etymologies

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Examples

  • The latter entails that any theory which has a model of any infinite cardinality, will have models of all infinite cardinalities.

    Mathematical logic and multiverses

  • “The monkeys can only represent cardinalities in an approximate way.”

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  • Rejection of Different Infinite Cardinalities: Given the non-existence of infinite mathematical extensions, Wittgenstein rejects the standard interpretation of Cantor's diagonal proof as a proof of infinite sets of greater and lesser cardinalities.

    Wittgenstein's Philosophy of Mathematics

  • Given Wittgenstein's rejection of infinite mathematical extensions, he adopts finitistic, constructive views on mathematical quantification, mathematical decidability, the nature of real numbers, and Cantor's diagonal proof of the existence of infinite sets of greater cardinalities.

    Wittgenstein's Philosophy of Mathematics

  • At the same time, the Löwenheim-Skolem theorem says that every first-order formal theory that has at least one model with an infinite domain, must have models with domains of all infinite cardinalities.

    Philosophy of Mathematics

  • It is not apparent at first that there might be infinite sets of different cardinalities, but once this becomes clear, it follows quickly that the structure so described is rich indeed.

    Set Theory

  • It may be possible to construct sets '' A '' and '' B '' for which there is no way to compare their cardinalities: there is no injective function from '' A '' into

    Conservapedia - Recent changes [en]

  • A and B for which there is no way to compare their cardinalities: there is no injective function from

    Conservapedia - Recent changes [en]

  • Model • cardinality constraints: de fi ne the allowed cardinalities Ongoing Work of instances of a Topic Map object (e.g., a certain role within an association) • type/role constraints: ensure that Topic Map objects are used according to their initial semantic de fi nition (cf. NCPL occurrence-type, topic-type) • scope: can be seen as extension of the foremention item, if applicable using the scope operator

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  • Sets that have cardinality Aleph-naught are said to be "countably infinite", whereas sets with higher cardinalities are not "countable".

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