Sets


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Sets

Definition 2.1   a pre-ordered set is a set with the property that, between any two objects, there is at most one arrow. This entails that there exists a binary relation R between the objects of the pre-ordered set, such that the following holds:
  1. aRa (reflexivity)
  2. if aRb and bRc then aRc (transitivity)

Definition 2.2:   a poset is a pre-ordered set with the extra property of being antisymmetric: $ pRq\hspace{.2in}and\hspace{.2in}qRp\hspace{.2in}\Rightarrow p=q$



Cecilia Flori 2006-11-19