Definition, Betydelse & Synonymer | Engelska ordet CARDINALITY

Definition av CARDINALITY

1. (matematik) kardinalitet

Exempel på hur man kan använda CARDINALITY i en mening

• Two sets have the same cardinality if, and only if, there is a one-to-one correspondence (bijection) between the elements of the two sets.
• In mathematics, cardinality describes a relationship between sets which compares their relative size.
• In mathematics, the empty set or void set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.
• The number of elements of a finite set is a natural number (possibly zero) and is called the cardinality (or the cardinal number) of the set.
• Cantor's diagonal argument shows that the power set of a set (whether infinite or not) always has strictly higher cardinality than the set itself (or informally, the power set must be larger than the original set).
• Like the other axioms of countability, separability is a "limitation on size", not necessarily in terms of cardinality (though, in the presence of the Hausdorff axiom, this does turn out to be the case; see below) but in a more subtle topological sense.
• The uncountability of a set is closely related to its cardinal number: a set is uncountable if its cardinal number is larger than aleph-null, the cardinality of the natural numbers.
• For every vector space there exists a basis, and all bases of a vector space have equal cardinality; as a result, the dimension of a vector space is uniquely defined.
• Multiple occurrences of identical elements have no effect on the cardinality of a set or its contents.
• The set of all integer sequences is uncountable (with cardinality equal to that of the continuum), and so not all integer sequences are computable.
• The axiom schema is motivated by the idea that whether a class is a set depends only on the cardinality of the class, not on the rank of its elements.
• However, the cardinality of the set of functions in the closed linear span is the cardinality of the continuum, which is the same cardinality as for the set of polynomials.
• Continuum hypothesis, a conjecture of Georg Cantor that there is no cardinal number between that of countably infinite sets and the cardinality of the set of all real numbers.
• This notation is meant to be suggestive of the fact that the cardinality of the disjoint union is the sum of the cardinalities of the terms in the family.
• Rubin, use the term transfinite cardinal to refer to the cardinality of a Dedekind-infinite set in contexts where this may not be equivalent to "infinite cardinal"; that is, in contexts where the axiom of countable choice is not assumed or is not known to hold.
• In mathematics, the rank, Prüfer rank, or torsion-free rank of an abelian group A is the cardinality of a maximal linearly independent subset.
• Then we can apply the axiom of replacement to replace each element of that powerset of x by the initial ordinal number of the same cardinality (or zero, if there is no such ordinal).
• Further, all the maximal algebraically independent subsets have the same cardinality, known as the transcendence degree of the extension.
• In mathematics, particularly in set theory, the aleph numbers are a sequence of numbers used to represent the cardinality (or size) of infinite sets that can be well-ordered.
• In 1973 he and John Hopcroft published the Hopcroft–Karp algorithm, the fastest known method for finding maximum cardinality matchings in bipartite graphs.

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