Ordinal arithmetic
In the mathematical field of set theory, ordinal arithmetic describes the three usual operations on ordinal numbers: addition, multiplication, and exponentiation. Each can be defined in essentially two different ways: either by constructing an explicit well-ordered set that represents the result of the operation or by using transfinite recursion. Cantor normal form provides a standardized way of writing ordinals. In addition to these usual ordinal operations, there are also the and the .
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Additively indecomposable ordinalAdolf LindenbaumAnne C. MorelArithmetic of ordinalsBachmann–Howard ordinalBaire space (set theory)Canonical formCantor normal formDistributive propertyEpsilon numbers (mathematics)Even and odd ordinalsFast-growing hierarchyFinSetFirst uncountable ordinalFundamental theorem of arithmeticGentzen's consistency proofGeorg CantorGerhard HessenbergGlossary of set theoryHessenberg productHessenberg sumInfinity plus oneIntuitionismKarl HessenbergKleene's OLarge countable ordinalLimit ordinalNatural product of ordinalsNatural sum of ordinalsNear-semiringNimberNormal functionOn Numbers and GamesOrdinal additionOrdinal collapsing functionOrdinal exponentiationOrdinal multiplicationOrdinal notationOrdinal numberPrime ordinal
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Ordinal arithmetic
In the mathematical field of set theory, ordinal arithmetic describes the three usual operations on ordinal numbers: addition, multiplication, and exponentiation. Each can be defined in essentially two different ways: either by constructing an explicit well-ordered set that represents the result of the operation or by using transfinite recursion. Cantor normal form provides a standardized way of writing ordinals. In addition to these usual ordinal operations, there are also the and the .
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Arytmetyka liczb porządkowych ...... ec między nimi pewne analogie.
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En el camp matemàtic de la teo ...... a expenses de la continuïtat.
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En teoría de conjuntos, la ari ...... ordenados que las representan.
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In the mathematical field of s ...... , there are also the and the .
@en
Ordinální aritmetika je jednou ...... užívána pro označení ordinálů.
@cs
我們可在序數上定義若干算術運算，這是對自然數運算的推廣。
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1,022,061,794
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August 2020
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reason
Why are addition and multiplication defined like this?
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Arytmetyka liczb porządkowych ...... niej wyniki niezależnościowe.
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En el camp matemàtic de la teo ...... a expenses de la continuïtat.
@ca
En teoría de conjuntos, la ari ...... ordenados que las representan.
@es
In the mathematical field of s ...... , there are also the and the .
@en
Ordinální aritmetika je jednou ...... užívána pro označení ordinálů.
@cs
我們可在序數上定義若干算術運算，這是對自然數運算的推廣。
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label
Aritmètica ordinal
@ca
Aritmética ordinal
@es
Arytmetyka liczb porządkowych
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Opérations arithmétiques sur les ordinaux
@fr
Ordinal arithmetic
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Ordinální aritmetika
@cs
Transfinite Arithmetik
@de
序數算術
@zh
서수의 산술
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