Definition:Absolute Real Vector Strict Ordering

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Let $x$ and $y$ be elements of the real vector space $\R^n$.

The absolute real vector strict ordering is the strict partial ordering $\ge$ defined on the real vector space $\R^n$ as:

$\forall x, y \in \R^n: x \ge y \iff \forall i \in \left\{ {1, 2, \ldots, n}\right\}: x_i \ge y_i$

Linguistic Note

The name absolute real vector strict ordering has been coined by $\mathsf{Pr} \infty \mathsf{fWiki}$ to name this strict partial ordering which is defined without a name in 1994: Martin J. Osborne and Ariel Rubinstein: A Course in Game Theory.