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:
 * $a \sim b$ $a \precsim b$ and $b \precsim a$

The notation $a \prec b$ is defined as:
 * $a \prec b$ $a \precsim b$ and $a \not \sim b$