Partially Ordered SetYou are currentlybrowsing as guest. Click here to log in 

Suppose you have a collection of objects. For two of them it might be obvious that, in some sense A is bigger than B, but others might be harder to compare.
Cake tins, for example. If A can hold B, then A is clearly bigger than B. However, it may be that C can't hold D, and D can't hold C. Using the concept of "can contain", the ordering between these tins is incomplete. It is a partial ordering.
With this example in mind we have the following definition of a PartiallyOrdered Set:
Irreflexive versionA set X is partially ordered by R if:

Reflexive versionA set X is partially ordered by R if:

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