Cardinality is an inherent property of a set, roughly the number of individual objects it contains, understood through one-to-one correspondences between sets; two sets are equinumerous, or have the same cardinality, if such a correspondence exists between them, and this concept shows that there are different sizes of infinity. A set is countably infinite if it can be placed in one-to-one correspondence with the natural numbers, and uncountable sets, such as the real numbers, are strictly larger. Cardinality was first introduced formally to mathematics by Georg Cantor around the turn of the 20th century and has since become a fundamental concept of mathematics. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
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Countable Set, Concepts Countability is exactly a classification by cardinality: a countable set is one whose cardinality is finite or matches the cardinality of the natural numbers.
Additional Source Countable Set (Wikipedia)Lead section
Infinity, Concepts Cardinality is the concept that gives infinite sets a size at all, and distinguishes different infinite sizes from one another; the concept's own description names infinity directly.
Additional Source Cardinality (Wikipedia)Lead section
Sets, Concepts Cardinality is defined as an inherent property of sets, so the set concept is what the property is measured on.
Additional Source Cardinality (Wikipedia)Lead section
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Source Cardinality (Wikipedia)
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Source Cardinality (Wikipedia)
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1. Cardinality (Wikipedia)
Wikimedia FoundationLead section
cardinality is an inherent property of sets, roughly meaning the number of individual objects they contain, which may be infinite
History section, origin year
In a series of papers beginning with On a Property of the Collection of All Real Algebraic Numbers (1874), Cantor introduced the idea of comparing the sizes of infinite sets, through the notion of one-to-one correspondence.
Attributed To: Georg Cantor, Lead
It is considered to have been first introduced formally to mathematics by Georg Cantor at the turn of the 20th century.
View the Source Countable Set (Wikipedia)
Wikimedia FoundationAssociated With: Countable Set, Lead sectionQuote, Associated With: Countable Set, Lead section
A mathematical set is countable if either it is finite or it can be put in one to one correspondence with the set of natural numbers
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