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I was looking at particular examples and I observed that they were always reflective, antisymmetric and transitive.

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    I was trying to be discrete...2012-12-07

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Indeed, it is (if you're using the $\ge$ relation that I think you are). In fact, it's a total order, since comparability holds, as well.

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    In particular, I was assuming the natural order o$f$ the real numbers induced the relation. That gives a (non-strict) total order. It also totally orders every subset o$f$ the reals, and so partially orders them.2012-12-08