axiom of dependent choice wikipedia - EAS
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https://en.wikipedia.org/wiki/Axiom_of_dependent_choiceIn mathematics, the axiom of dependent choice, denoted by , is a weak form of the axiom of choice () that is still sufficient to develop most of real analysis. It was introduced by Paul Bernays in a 1942 article that explores which set-theoretic axioms are needed to develop analysis.
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Xem thêmUnlike full , is insufficient to prove (given ) that there is a non-measurable set of real numbers, or that there is a set of real numbers without the property of Baire or without the perfect set property. This follows because the Solovay model satisfies ,
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Xem thêmVăn bản Wikipedia theo giấy phép CC-BY-SAMục này có hữu ích không?Cảm ơn! Cung cấp thêm phản hồiAxiom of choice - Wikipedia
https://en.wikipedia.org/wiki/Axiom_of_choiceThere are several weaker statements that are not equivalent to the axiom of choice, but are closely related. One example is the axiom of dependent choice (DC). A still weaker example is the axiom of countable choice (ACω or CC), which states that a choice function exists for any countable set of nonempty sets. These axioms are sufficient for many proofs in elementary mathematical analysis, and are consistent with some principles, such as the Lebesgue measura…
Wikipedia · Nội dung trong CC-BY-SA giấy phépAxiom of dependent choice - WikiMili, The Best Wikipedia ...
https://wikimili.com/en/Axiom_of_dependent_choiceIn mathematics, the axiom of dependent choice, denoted by , is a weak form of the axiom of choice that is still sufficient to develop most of real analysis. It was introduced by Paul Bernays in a 1942 article that explores which set-theoretic axioms are needed to develop analysis.
Axiom of dependent choice - zxc.wiki
https://de.zxc.wiki/wiki/Axiom_der_abhängigen_AuswahlThe axiom of dependent choice (from English axiom of dependent choice or principle of dependent choice for short DC) is an axiom of set theory. It is a weak version of the axiom of choice , but it is sufficient in analysis , for example , to show the equivalence of continuity and continuity of sequences .
Axiome du choix dépendant — Wikipédia
https://fr.wikipedia.org/wiki/Axiome_du_choix_dépendant- L'axiome peut s'énoncer comme suit[2] : pour tout ensemble non videX, et pour toute relation binaire R sur X, si l'ensemble de définition de R est X tout entier (c'est-à-dire si pour tout a∈X, il existe au moins un b∈X tel que aRb) alors il existe une suite (xn) d'éléments de X telle que pour tout n∈N, xnRxn+1. Noter que cet axiome n'est pas nécessaire pour former, pour chaque entier n…
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Axiom of dependent choice - Wikipedia - it.abcdef.wiki
https://it.abcdef.wiki/wiki/Axiom_of_dependent_choiceDa Wikipedia, l'enciclopedia libera In matematica , l' assioma della scelta dipendente , indicato con , è una forma debole dell'assioma della scelta ( ) che è ancora sufficiente per sviluppare la maggior parte dell'analisi reale . È stato introdotto da Paul Bernays in un articolo del 1942 che esplora quali assiomi della teoria degli insiemi sono necessari per sviluppare l'analisi.
Axiom der abhängigen Auswahl – Wikipedia
https://de.wikipedia.org/wiki/Axiom_der_abhängigen_Auswahl- Sei X {\displaystyle X} eine nichtleere Menge und R ⊆ X 2 {\displaystyle R\subseteq X^{2}} eine definale Relation. Dann gibt es eine Folge ( x n ) n ∈ N {\displaystyle \left(x_{n}\right)_{n\in \mathbb {N} }} in X {\displaystyle X} dergestalt, dass ∀ n ∈ N : R ( x n , x n + 1 ) {\displaystyle \forall n\in \mathbb {N} \colon R\left(x_{n},x_{n+1}\right)} gilt. Auch ohne abhängige Auswahl ka…
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