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- Cardinality_of_the_continuum abstract "In set theory, the cardinality of the continuum is the cardinality or “size” of the set of real numbers , sometimes called the continuum. It is an infinite cardinal number and is denoted by or (a lowercase fraktur script "c").The real numbers are more numerous than the natural numbers . Moreover, has the same number of elements as the power set of . Symbolically, if the cardinality of is denoted as , the cardinality of the continuum isThis was proven by Georg Cantor in his 1874 uncountability proof, part of his groundbreaking study of different infinities, and later more simply in his diagonal argument. Cantor defined cardinality in terms of bijective functions: two sets have the same cardinality if and only if there exists a bijective function between them.Between any two real numbers a < b, no matter how close they are to each other, there are always infinitely many other real numbers, and Cantor showed that they are as many as those contained in the whole set of real numbers. In other words, the open interval (a,b) is equinumerous with This is also true for several other infinite sets, such as any n-dimensional Euclidean space (see space filling curve). That is, The smallest infinite cardinal number is (aleph-naught). The second smallest is (aleph-one). The continuum hypothesis, which asserts that there are no sets whose cardinality is strictly between and implies that .".
- Cardinality_of_the_continuum wikiPageID "1574901".
- Cardinality_of_the_continuum wikiPageRevisionID "606202483".
- Cardinality_of_the_continuum hasPhotoCollection Cardinality_of_the_continuum.
- Cardinality_of_the_continuum id "5708".
- Cardinality_of_the_continuum title "cardinality of the continuum".
- Cardinality_of_the_continuum subject Category:Cardinal_numbers.
- Cardinality_of_the_continuum subject Category:Infinity.
- Cardinality_of_the_continuum subject Category:Set_theory.
- Cardinality_of_the_continuum type Abstraction100002137.
- Cardinality_of_the_continuum type CardinalNumber113597585.
- Cardinality_of_the_continuum type CardinalNumbers.
- Cardinality_of_the_continuum type DefiniteQuantity113576101.
- Cardinality_of_the_continuum type Measure100033615.
- Cardinality_of_the_continuum type Number113582013.
- Cardinality_of_the_continuum comment "In set theory, the cardinality of the continuum is the cardinality or “size” of the set of real numbers , sometimes called the continuum. It is an infinite cardinal number and is denoted by or (a lowercase fraktur script "c").The real numbers are more numerous than the natural numbers . Moreover, has the same number of elements as the power set of .".
- Cardinality_of_the_continuum label "Cardinalidade do contínuo".
- Cardinality_of_the_continuum label "Cardinality of the continuum".
- Cardinality_of_the_continuum label "Cardinalità del continuo".
- Cardinality_of_the_continuum label "Kardinaliteit van het continuüm".
- Cardinality_of_the_continuum label "Kontinuum (Mathematik)".
- Cardinality_of_the_continuum label "Puissance du continu".
- Cardinality_of_the_continuum label "连续统的势".
- Cardinality_of_the_continuum label "連続体濃度".
- Cardinality_of_the_continuum sameAs Mohutnost_kontinua.
- Cardinality_of_the_continuum sameAs Kontinuum_(Mathematik).
- Cardinality_of_the_continuum sameAs Puissance_du_continu.
- Cardinality_of_the_continuum sameAs Cardinalità_del_continuo.
- Cardinality_of_the_continuum sameAs 連続体濃度.
- Cardinality_of_the_continuum sameAs Kardinaliteit_van_het_continuüm.
- Cardinality_of_the_continuum sameAs Cardinalidade_do_contínuo.
- Cardinality_of_the_continuum sameAs m.05cn9k.
- Cardinality_of_the_continuum sameAs Q1535547.
- Cardinality_of_the_continuum sameAs Q1535547.
- Cardinality_of_the_continuum sameAs Cardinality_of_the_continuum.
- Cardinality_of_the_continuum wasDerivedFrom Cardinality_of_the_continuum?oldid=606202483.
- Cardinality_of_the_continuum isPrimaryTopicOf Cardinality_of_the_continuum.