Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License
 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.

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

Rejection of Different Infinite Cardinalities: Given the nonexistence 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.

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.

At the same time, the LÃ¶wenheimSkolem theorem says that every firstorder formal theory that has at least one model with an infinite domain, must have models with domains of all infinite cardinalities.

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.

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

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

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 occurrencetype, topictype) • scope: can be seen as extension of the foremention item, if applicable using the scope operator

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