I was looking at particular examples and I observed that they were always reflective, antisymmetric and transitive.
Is the relation $\geq$ always a partial order for the real numbers and integers
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discrete-mathematics
relations
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0And so are $\leq$, $=$. – 2012-12-07
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1@copper.hat I would think that equality "$=$" is not antisymmetric ;-) – 2012-12-07
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0I was trying to be discrete... – 2012-12-07
1 Answers
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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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0so is it a partial order or what? they're suggesting that it's not. – 2012-12-08
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0*If the relation is defined in the way I suspect it is*, then it is a partial order. Just in case I'm thinking of the wrong one, how are you defining the relation? – 2012-12-08
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0In particular, I was assuming the natural order of the real numbers induced the relation. That gives a (non-strict) total order. It also totally orders every subset of the reals, and so partially orders them. – 2012-12-08