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In mathematics, particularly in set theory, the beth numbers are a certain sequence of infinite cardinal numbers (also known as transfinite numbers), conventionally written , where is the second Hebrew letter (beth). The beth numbers are related to the aleph numbers, but unless the generalized continuum hypothesis is true, there are numbers indexed by that are not indexed by .

Attributes	Values
rdf:type	yago:WikicatCardinalNumbers yago:Abstraction100002137 yago:CardinalNumber113597585 yago:DefiniteQuantity113576101 yago:Measure100033615 yago:Number113582013
rdfs:label	Funkce beth (cs) Beth-Funktion (de) Beth number (en) Beth (nombre) (fr) Numero beth (it) ベート数 (ja) 베트 수 (ko) Beet-getal (nl) Skala betów (pl) Бет-число (ru) ℶ 數 (zh)
rdfs:comment	Funkce Beth pojmenovaná po druhém písmenu hebrejské abecedy zapisovaná rovněž jako je jedním ze způsobů zápisu určitých nekonečných kardinálních čísel v teorii množin. (cs) Die Beth-Funktion, benannt nach dem zweiten Buchstaben des hebräischen Alphabets und auch als geschrieben, ist eine in der Mengenlehre, genauer in der Theorie der Kardinalzahlen, verwendete Aufzählung gewisser unendlicher Kardinalzahlen. (de) In mathematics, particularly in set theory, the beth numbers are a certain sequence of infinite cardinal numbers (also known as transfinite numbers), conventionally written , where is the second Hebrew letter (beth). The beth numbers are related to the aleph numbers, but unless the generalized continuum hypothesis is true, there are numbers indexed by that are not indexed by . (en) Dans la théorie des ensembles ZFC (avec axiome du choix), les nombres beth désignent une hiérarchie de nombres cardinaux indexée par les ordinaux, obtenue à partir du dénombrable en prenant le cardinal de l'ensemble des parties pour successeur, et la borne supérieure (ou réunion) pour passer à la limite. La notation de ces nombres utilise la deuxième lettre de l'alphabet hébreu, ou ב. (fr) In matematica, e più precisamente in teoria degli insiemi, il numero beth indica una particolare successione di numeri cardinali. Il simbolo è bet, , la seconda lettera dell'alfabeto ebraico. La successione è parametrizzata sui numeri ordinali e definita per induzione transfinita come segue: (it) 数学において、無限基数はヘブライ文字（）の右下に順序数の添え字をつけて表される（アレフ数参照）。2番目のヘブライ文字 ב（）は関連した方法で使われるが、によって表されるすべての数を表しているとは限らない。 (ja) 집합론에서 베트 수(ℶ數, 영어: beth number)는 가산 무한 집합의 거듭된 멱집합들의 크기들을 나타내는 표기법이다. (ko) In de wiskunde is een beet-getal de kardinaliteit van een herhaalde machtsverzameling van de natuurlijke getallen . De beetgetallen worden aangeduid met de Hebreeuwse letter (beet), de tweede letter van het Hebreeuwse alfabet. de kardinaliteit van . is de kardinaliteit van de machtsverzameling , is de kardinaliteit van de machtsverzameling van , enz. (nl) Skala betów – rosnący ciągły ciąg liczb kardynalnych indeksowany wszystkimi liczbami porządkowymi, w którym każdy kolejny wyraz jest mocą zbioru wszystkich podzbiorów wyrazu poprzedniego. (pl) 和阿列夫数類似，ℶ 數（读作Beth数）也是一系列超窮基數。阿列夫数的構造相對複雜，初學者較難掌握，而在連續統假設下，阿列夫数與 ℶ 數等價，下面介紹 ℶ 數的概念： * 可數集（如自然數集）的基數標記爲，下一個 ℶ 數被定義爲上一個 ℶ 數的冪集的基數，卽：等等 (zh) Числа бет в математике — кардинальные числа, характеризующие мощность бесконечного множества.Последовательность бесконечных кардинальных чисел обычно записывается как , где названа по второй букве еврейского алфавита (бет). (ru)
dct:subject	Infinity Cardinal numbers
Wikipage page ID	393359 (xsd:integer)
Wikipage revision ID	1088520156 (xsd:integer)
Link from a Wikipage to another Wikipage	Cantor's theorem Cardinality of the continuum Power set Bet (letter) Holomorphic Virginia Commonwealth University Infinite set Limit ordinal Transfinite induction Complex number Continuous function Countably infinite Analytic function Mathematics Function (mathematics) Generalized continuum hypothesis Multiset Continuum hypothesis Transcendental numbers Stone–Čech compactification Strong limit cardinal Computable number Computable set Zermelo–Fraenkel set theory Total order Irrational number Aleph null Aleph number Algebraic number Euclidean space Finite set Oxford University Press Cardinal number Fractal Hebrew alphabet Infinity Cardinal numbers Supremum Thomas Forster Transfinite number Transfinite recursion Transitive set Dover Publications Axiom of choice Integer Natural number Rational number Real analytic function Real number Sequence Set (mathematics) Set theory Von Neumann universe Real line Subset Uncountable Uncountable set Ur-element Borel determinacy Finite sequence Pure set Cardinal exponentiation Uncomputable real number
sameAs	Beth number Beth number Beth number Beth number Beth number

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