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- Equinumerosity abstract "In mathematics, two sets A and B are equinumerous if there exists a one-to-one correspondence (a bijection) between them, i.e. if there exists a function from A to B such that for every element y of B there is exactly one element x of A with f(x) = y. This definition can be applied to both finite and infinite sets and allows one to state that two sets have the same size even if they are infinite.The study of cardinality is often called equinumerosity (equalness-of-number). The terms equipollence (equalness-of-strength) and equipotence (equalness-of-power) are sometimes used instead. The statement that two sets A and B are equinumerous is usually denotedor , or Georg Cantor, the inventor of set theory, showed in 1874 that there is more than one kind of infinity, specifically that the collection of all natural numbers and the collection of all real numbers, while both infinite, are not equinumerous (see Cantor's first uncountability proof). In a controversial 1878 paper, Cantor explicitly defined the notion of "power" of sets and used it to prove that the set of all natural numbers and the set of all rational numbers are equinumerous, and that the Cartesian product of even a countably infinite number of copies of the real numbers is equinumerous to a single copy of the real numbers. Cantor's theorem from 1891 implies that no set is equinumerous to its power set. This allows the definition of greater and greater infinite sets starting from a single infinite set.Equinumerous finite sets have the same number of elements. Equinumerosity has the characteristic properties of an equivalence relation. Equinumerous sets are said to have the same cardinality, and the cardinal number of a set is the equivalence class of all sets equinumerous to it. The statement that any two sets are either equinumerous or one has a smaller cardinality than the other is equivalent to the axiom of choice. Unlike finite sets, some infinite sets are equinumerous to proper subsets of themselves.".
- Equinumerosity wikiPageID "373128".
- Equinumerosity wikiPageRevisionID "606586966".
- Equinumerosity hasPhotoCollection Equinumerosity.
- Equinumerosity subject Category:Basic_concepts_in_infinite_set_theory.
- Equinumerosity subject Category:Cardinal_numbers.
- Equinumerosity type Abstraction100002137.
- Equinumerosity type BasicConceptsInInfiniteSetTheory.
- Equinumerosity type CardinalNumber113597585.
- Equinumerosity type CardinalNumbers.
- Equinumerosity type Cognition100023271.
- Equinumerosity type Concept105835747.
- Equinumerosity type Content105809192.
- Equinumerosity type DefiniteQuantity113576101.
- Equinumerosity type Idea105833840.
- Equinumerosity type Measure100033615.
- Equinumerosity type Number113582013.
- Equinumerosity type PsychologicalFeature100023100.
- Equinumerosity comment "In mathematics, two sets A and B are equinumerous if there exists a one-to-one correspondence (a bijection) between them, i.e. if there exists a function from A to B such that for every element y of B there is exactly one element x of A with f(x) = y. This definition can be applied to both finite and infinite sets and allows one to state that two sets have the same size even if they are infinite.The study of cardinality is often called equinumerosity (equalness-of-number).".
- Equinumerosity label "Equinumerosity".
- Equinumerosity label "Equipotência".
- Equinumerosity label "Gelijkmachtigheid".
- Equinumerosity label "Équipotence".
- Equinumerosity label "等势".
- Equinumerosity sameAs Équipotence.
- Equinumerosity sameAs Gelijkmachtigheid.
- Equinumerosity sameAs Equipotência.
- Equinumerosity sameAs m.020pvc.
- Equinumerosity sameAs Q2914225.
- Equinumerosity sameAs Q2914225.
- Equinumerosity sameAs Equinumerosity.
- Equinumerosity wasDerivedFrom Equinumerosity?oldid=606586966.
- Equinumerosity isPrimaryTopicOf Equinumerosity.