| viXra.org > Set Theory and Logic > viXra:2308.0146 |
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| viXra.org > Set Theory and Logic > viXra:2308.0146 |
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Set Theory and Logic |
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Authors: Nhat-Anh Phan
For a given infinite countable set A, we demonstrate that A is an infinite countableset if and only if A is equal to an infinite countable set indexed to the infinity. Saidotherwise we demonstrate that A is an infinite countable set iff there exists an infinite numberof non-empty, distinct elements a_i ǂ ∅, i ∈ N∗, ∀i, j ∈ N∗, i ǂ j, a_i ǂ a_j such thatA = U_{+∞}_{i=1} {a_i}. At this occasion, for infinite countable sets constituted by the union of two giveninfinite countable sets A and B, Au2032 = [A ∪ B]P(Au2032), we introduce the notion of undeterminedinfinite countable set in order to designate infinite countable sets for whichan explicit indexation is not determined meanwhile such indexation must necessarilyexist.
Comments: 22 Pages. In French - Copyright All rights reserved
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[v1] 2023-08-23 00:17:02
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