What does cardinal number mean?
Definitions for cardinal number
car·di·nal num·ber
This dictionary definitions page includes all the possible meanings, example usage and translations of the word cardinal number.
Princeton's WordNet
cardinal number, cardinalnoun
the number of elements in a mathematical set; denotes a quantity but not the order
Wiktionary
cardinal numbernoun
A number used to denote quantity; a counting number.
cardinal numbernoun
A word that expresses a countable quantity; a cardinal numeral.
cardinal numbernoun
A generalized kind of number used to denote the size of a set, including infinite sets.
Wikipedia
Cardinal number
In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality (size) of sets. The cardinality of a finite set is a natural number: the number of elements in the set. The transfinite cardinal numbers, often denoted using the Hebrew symbol ℵ {\displaystyle \aleph } (aleph) followed by a subscript, describe the sizes of infinite sets. Cardinality is defined in terms of bijective functions. 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 the case of finite sets, this agrees with the intuitive notion of size. In the case of infinite sets, the behavior is more complex. A fundamental theorem due to Georg Cantor shows that it is possible for infinite sets to have different cardinalities, and in particular the cardinality of the set of real numbers is greater than the cardinality of the set of natural numbers. It is also possible for a proper subset of an infinite set to have the same cardinality as the original set—something that cannot happen with proper subsets of finite sets.
ChatGPT
cardinal number
A cardinal number is a number that indicates quantity or "how many". It represents the size or amount of a set, such as zero, one, two, three, etc. In more advanced mathematics, the concept of a cardinal number is extended to infinite sets, with different sizes of infinity having different cardinal numbers.
Wikidata
Cardinal number
In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality of sets. The cardinality of a finite set is a natural number – the number of elements in the set. The transfinite cardinal numbers describe the sizes of infinite sets. Cardinality is defined in terms of bijective functions. Two sets have the same cardinality if and only if there is a bijection between them. In the case of finite sets, this agrees with the intuitive notion of size. In the case of infinite sets, the behavior is more complex. A fundamental theorem due to Georg Cantor shows that it is possible for infinite sets to have different cardinalities, and in particular the cardinality of the set of real numbers is greater than the cardinality of the set of natural numbers. It is also possible for a proper subset of an infinite set to have the same cardinality as the original set, something that cannot happen with proper subsets of finite sets. There is a transfinite sequence of cardinal numbers: This sequence starts with the natural numbers including zero, which are followed by the aleph numbers. The aleph numbers are indexed by ordinal numbers. Under the assumption of the axiom of choice, this transfinite sequence includes every cardinal number. If one rejects that axiom, the situation is more complicated, with additional infinite cardinals that are not alephs.
Matched Categories
Numerology
Chaldean Numerology
The numerical value of cardinal number in Chaldean Numerology is: 8
Pythagorean Numerology
The numerical value of cardinal number in Pythagorean Numerology is: 9
Translations for cardinal number
From our Multilingual Translation Dictionary
- hooftelwoordAfrikaans
- nombre cardinalCatalan, Valencian
- kardinální čísloCzech
- rhif prifolWelsh
- kardinaltalDanish
- Grundzahlwort, Grundzahl, Kardinalzahl, bestimmtes ZahlwortGerman
- απόλυτος αριθμόςGreek
- número cardinal, adjetivo cardinalSpanish
- hulga võimsus, põhiarv, kardinaalarvEstonian
- zenbaki kardinalBasque
- kardinaaliluku, peruslukuFinnish
- nombre cardinalFrench
- bunuimhirIrish
- számosság, tőszámnév, tőszámHungarian
- numero cardinaleItalian
- 基数, 集合数Japanese
- hoofdtelwoord, bepaald telwoordDutch
- liczebnik główny, liczba kardynalnaPolish
- número cardinal, numeral cardinalPortuguese
- număr cardinal, numeral cardinal, cardinalRomanian
- количественное числительное, кардинальное число, мощность множестваRussian
- kardinaltal, grundtalSwedish
- số đếm, số lượngVietnamese
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"cardinal number." Definitions.net. STANDS4 LLC, 2024. Web. 25 Apr. 2024. <https://www.definitions.net/definition/cardinal+number>.
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