Limit ordinal
In set theory, a limit ordinal is an ordinal number that is neither zero nor a successor ordinal. Alternatively, an ordinal λ is a limit ordinal if there is an ordinal less than λ, and whenever β is an ordinal less than λ, then there exists an ordinal γ such that β < γ < λ. Every ordinal number is either zero, or a successor ordinal, or a limit ordinal. For example, ω, the smallest ordinal greater than every natural number is a limit ordinal because for any smaller ordinal (i.e., for any natural number) n we can find another natural number larger than it (e.g. n+1), but still less than ω.
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Limit ordinal
In set theory, a limit ordinal is an ordinal number that is neither zero nor a successor ordinal. Alternatively, an ordinal λ is a limit ordinal if there is an ordinal less than λ, and whenever β is an ordinal less than λ, then there exists an ordinal γ such that β < γ < λ. Every ordinal number is either zero, or a successor ordinal, or a limit ordinal. For example, ω, the smallest ordinal greater than every natural number is a limit ordinal because for any smaller ordinal (i.e., for any natural number) n we can find another natural number larger than it (e.g. n+1), but still less than ω.
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En aroteorio, lima ordonombro ...... das 0 el la limaj ordonombroj.
@eo
En mathématiques et plus préci ...... est pas un ordinal successeur.
@fr
Graniczna liczba porządkowa – ...... ie zaliczają jej do ich grona.
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In set theory, a limit ordinal ...... umber is also a limit ordinal.
@en
Limitní ordinál je ordinální číslo, které nemá předchůdce a není prázdné.
@cs
Un ordinale limite è un numero ...... cardinalità via via crescente:
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Ординал называется предельным, ...... м, если , сингулярным — если .
@ru
极限序数是非零非后继序数的序数。直觉的说,有不能通过后继运算 ...... 教科书包括 0 在极限序数的类中,如。而其他人排除了它,如。
@zh
集合論およびにおける極限順序数(きょくげんじゅんじょすう、英 ...... 数である。を用いれば、任意の無限基数もまた極限順序数となる。
@ja
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En aroteorio, lima ordonombro ...... ize al la en ĉi tiu topologio.
@eo
En mathématiques et plus préci ...... est pas un ordinal successeur.
@fr
Graniczna liczba porządkowa – ...... ie zaliczają jej do ich grona.
@pl
In set theory, a limit ordinal ...... . n+1), but still less than ω.
@en
Limitní ordinál je ordinální číslo, které nemá předchůdce a není prázdné.
@cs
Un ordinale limite è un numero ...... i gli ordinali minori di esso.
@it
Ординал называется предельным, ...... м, если , сингулярным — если .
@ru
极限序数是非零非后继序数的序数。直觉的说,有不能通过后继运算 ...... 教科书包括 0 在极限序数的类中,如。而其他人排除了它,如。
@zh
集合論およびにおける極限順序数(きょくげんじゅんじょすう、英 ...... 数である。を用いれば、任意の無限基数もまた極限順序数となる。
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Graniczna liczba porządkowa
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Lima ordonombro
@eo
Limit ordinal
@en
Limitní ordinál
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Ordinal limite
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Ordinale limite
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Предельный ординал
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极限序数
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極限順序数
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극한 순서수
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