# A complete organize on finite subsets of an ordered clique Answer

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A complete organize on finite subsets of an ordered clique

Let $$(A,<)$$ breathe an ordered clique. Then I outline an ordering on the clique of finite subsets of $$A$$ as follows. I say that $$Xprec Y$$ if and provided that the smallest component of $$Xtriangle Y$$ (the symmetric dissimilarity) is contained in $$X$$. An simple, however not utterly trifling, commentary is that $$prec$$ really defines a complete organize on the household of finite subsets of $$A$$. My query is whether or not this development is well-known.

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