Talk:Comparability

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I have restricted the definition to partial orders. In the previous version there was inconsistency about the question whether an element is comparable to itself. According to [1] it is. Can the definition be extended? In a preorder, are p and q with pRq and qRp called comparable?--Patrick 13:45, 15 May 2007 (UTC)

[edit] Self-comparability

Since a partial order P is, a fortiori, a relation (mathematics), elements x and y are comparable with respect to P if and only if \{(x,y), (y,x)\} \cap P is nonempty. And the difference between non-strict and strict versions of a partial order is precisely that one is the reflexive closure (resp. reflexive reduction) of the other. So any element x is comparable to itself with respect to P if and only if P is reflexive (non-strict).—PaulTanenbaum 01:20, 6 July 2007 (UTC)