Definition:Preordering/Notation

Definition

Symbols used to denote a general preordering relation are usually variants on $\lesssim$, $\precsim$ or $\precapprox$.

A symbol for a preordering can be reversed, and the sense is likewise inverted:

$a \precsim b \iff b \succsim a$

The notation $a \sim b$ is defined as:

$a \sim b$ if and only if $a \precsim b$ and $b \precsim a$

The notation $a \prec b$ is defined as:

$a \prec b$ if and only if $a \precsim b$ and $a \not \sim b$

Sources

• 1991: Roger B. Myerson: Game Theory ... (previous) ... (next): $1.2$ Basic Concepts of Decision Theory