Set Theory and Logic

    

One First Crucial Theorem for the Re-foundation of Elementary Set Theory and the Teaching of That Discipline to Future Generations

Authors: Nhat-Anh Phan

For a given infinite countable set A = U_{i∈N∗}{a_i }, ∀i ∈ N∗ , a_i≠∅, we demonstrate that it is legitimate to partition A in a finite or infinite number of infinite countable sub-sets when the initial order of indexation of the elements of A maintains a strictly increasing order in each sub-set. At this occasion we introduce two new formalism allowing to signify the fact that it is A that has been partitioned and the fact that A and the latter partition of A belong to the same class comprising infinitely many infinite countable sets constituted by the same infinite countable sub-sets that constitute the partition of A.

Comments: 14 Pages. Copyright. All rights reserved.

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[v1] 2022-10-21 01:42:43

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