Definition:Preordering/Notation

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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