The finite sequences and the partitions whose members are finite of a set

In this paper, we investigate relationships between \(|\seq(A)|\) and \(|\Part_{\fin}(A)|\) in the absence of the Axiom of Choice, where \(\seq(A)\) is the set of finite sequences of elements in a set \(A\) and \(\Part_{\fin}(A)\) is the set of partitions of \(A\) whose members are finite. We show t...

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Bibliographic Details
Published in:arXiv.org 2023-12
Main Authors: Phansamdaeng, Palagorn, Vejjajiva, Pimpen
Format: Article
Language:English
Online Access:Get full text
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Summary:In this paper, we investigate relationships between \(|\seq(A)|\) and \(|\Part_{\fin}(A)|\) in the absence of the Axiom of Choice, where \(\seq(A)\) is the set of finite sequences of elements in a set \(A\) and \(\Part_{\fin}(A)\) is the set of partitions of \(A\) whose members are finite. We show that \(|\seq(A)|
ISSN:2331-8422