Infinite descending chain: Difference between revisions

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+#REDIRECT [[Total order#Chains]]
-Given a [[set]] ''S'' with a [[partial order]] <=, an '''infinite descending chain''' is a ''chain'' ''V'', that is, a subset of ''S'' upon which <= defines a [[total order]], such that ''V'' has no ''minimal element'', that is, an element ''m'' such that for all elements ''n'' in ''V'' it holds that ''m'' <= ''v''.
+{{R from merge}}
+{{R to section}}
+[[Category:Order theory]]
+[[Category:Wellfoundedness]]
-As an example, in the set of [[Integer]]s, the chain -1,-2,-3,... is an infinite descending chain, but there exists no infinite chain on the [[Natural number]]s, every chain of natural numbers has a minimal element.