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A point $x$ in $\mathbb {R} ^{2}$ and the set of all $y$ such that $x\leq y$ (in red). The order here is $x\leq y$ if and only if $x_{1}\leq y_{1}$ and $x_{2}\leq y_{2}.$

In mathematics, an ordered vector space or partially ordered vector space is a vector space equipped with a partial order that is compatible with the vector space operations.

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