Cantor's paradox
In set theory, Cantor's paradox is derivable from the theorem that there is no greatest cardinal number, so that the collection of "infinite sizes" is itself infinite. The difficulty is handled in axiomatic set theory by declaring that this collection is not a set but a proper class; in von Neumann–Bernays–Gödel set theory it follows from this and the axiom of limitation of size that this proper class must be in bijection with the class of all sets. Thus, not only are there infinitely many infinities, but this infinity is larger than any of the infinities it enumerates.
primaryTopic
Cantor's paradox
In set theory, Cantor's paradox is derivable from the theorem that there is no greatest cardinal number, so that the collection of "infinite sizes" is itself infinite. The difficulty is handled in axiomatic set theory by declaring that this collection is not a set but a proper class; in von Neumann–Bernays–Gödel set theory it follows from this and the axiom of limitation of size that this proper class must be in bijection with the class of all sets. Thus, not only are there infinitely many infinities, but this infinity is larger than any of the infinities it enumerates.
has abstract
Em teoria dos conjuntos, o par ...... nto das partes desse conjunto.
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Georg Cantor beschrieb in den ...... swerte Lösung der Problematik.
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In de verzamelingentheorie is ...... lingentheorie inconsistent is.
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In matematica il paradosso di ...... eoria intuitiva degli insiemi.
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In set theory, Cantor's parado ...... f this theory is inconsistent.
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Le paradoxe de Cantor, ou para ...... rdinaux n'est pas un ensemble.
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Paradoks zbioru wszystkich zbi ...... nie zbioru wszystkich zbiorów.
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Парадо́кс Ка́нтора — парадокс ...... ние такого множества возможно.
@ru
在数学中，康托尔悖论是集合论的一个定理，即没有最大的基数，所 ...... 是不充足的。在其後的各個公理化集合論中，這個悖論已經被解決。
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comment
Em teoria dos conjuntos, o par ...... nor que um dos seus elementos.
@pt
Georg Cantor beschrieb in den ...... n diesen Briefen bilden die äl
@de
In de verzamelingentheorie is ...... oneindigheden die hij opsomt!
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In matematica il paradosso di ...... gli infiniti che esso enumera.
@it
In set theory, Cantor's parado ...... the infinities it enumerates.
@en
Le paradoxe de Cantor, ou para ...... Pour lui, cela montre que le p
@fr
Paradoks zbioru wszystkich zbi ...... nie zbioru wszystkich zbiorów.
@pl
Парадо́кс Ка́нтора — парадокс ...... ние такого множества возможно.
@ru
在数学中，康托尔悖论是集合论的一个定理，即没有最大的基数，所 ...... 是不充足的。在其後的各個公理化集合論中，這個悖論已經被解決。
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label
Cantor's paradox
@en
Cantorsche Antinomie
@de
Paradoks zbioru wszystkich zbiorów
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Paradosso di Cantor
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Paradox van Cantor
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Paradoxe de Cantor
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Paradoxo de Cantor
@pt
Парадокс Кантора
@ru
康托尔悖论
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