Horst Herrlich
Abstract
Given a sequence (Xn )n∊N of pairwise disjoint 2-element sets. Can ∪ n∊N Xn be rearranged as a union ∪ i∊I Yi of a family (Yi )i∊I of pairwise disjoint 2-element sets, indexed by an uncountable set I? It will be shown that in the absence of the Axiom of Choice, this strange phenomenon can indeed occur.
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Given a sequence (Xn )n∊N of pairwise disjoint 2-element sets. Can ∪ n∊N Xn be rearranged as a union ∪ i∊I Yi of a family (Yi )i∊I of pairwise disjoint 2-element sets, indexed by an uncountable set I? It will be shown that in the absence of the Axiom of Choice, this strange phenomenon can indeed occur.
Key concepts: Uncountable set, Disjoint sets, Mathematics, Combinatorics, Pairwise comparison, Sequence (biology), Element (criminal law), Disjoint union (topology)