Set Theory and Logic

    

One Second Crucial Theorem for the Refoundation of Elementary Set Theory and the Teaching of that Discipline to Future Generations

Authors: Nhat-Anh Phan

For a given infinite countable set constituted by the union of infinitely many non-empty, finite or infinite countable, disjoint sub-sets A = {i∈N*}[A_i]_P(A) , ∀i ∈ N* , A_i ≠ ∅, ∀i, j ∈ N* , i ≠ j, A_i ∩ A_j = ∅, we demonstrate that it is legitimate to partition A in a finite or infinite number of sub-sets that are themselves constituted by a finite or infinite number of sub-sets of A when the initial order of indexation of the sub-sets of A maintains a strictly increasing order in each sub-set.

Comments: 15 Pages. Copyright. All rights reserved.

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[v1] 2022-11-17 11:20:31

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