Definition:Absolute Real Vector Ordering

Definition

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

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

As such, it is not generally expected to be seen in this context outside $\mathsf{Pr} \infty \mathsf{fWiki}$.

Sources

• 1994: Martin J. Osborne and Ariel Rubinstein: A Course in Game Theory ... (previous) ... (next): Chapter $1$ Introduction: $1.7$: Terminology and Notation