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Total preorder
In the mathematical area of order theory, a total preorder over a set X is a preorder ≤ over X that is total; that is, for all a and b in X, it holds that a ≤ b or b ≤ a.
The difference between a total preorder and a total order is that a total preorder (since it is only a preorder) is not required to be antisymmetric.
An example is (X, ≤) where X = {1, 2} and a ≤ b for all a and b in X.
10-26-2009 08:16:03
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The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details