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Lemma: Comparing the Elements of Strictly Ordered Sets
In a strictly ordered set $(V,\prec)$, for all elements \(a,b\in V\) exactly one of the following cases holds:
 Either $a \prec b$ ($a$ is smaller than $b$),
 or $a \succ b$ ($a$ is greater than $b$).
 else $a=b$ ($a$ equals $b$).
Because of these three possibilities, the strict order "$\prec$" is sometimes also called a trichotomous order.
Table of Contents
Proofs: 1
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References
Bibliography
 Reinhardt F., Soeder H.: "dtvAtlas zur Mathematik", Deutsche Taschenbuch Verlag, 1994, 10th Edition
 Hoffmann, D.: "Forcing, Eine EinfÃ¼hrung in die Mathematik der UnabhÃ¤ngigkeitsbeweise", Hoffmann, D., 2018