Definition:Ordering/Notation

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Definition

Symbols used to denote a general ordering relation are usually variants on $\preceq$, $\le$ and so on.

On $\mathsf{Pr} \infty \mathsf{fWiki}$, to denote a general ordering relation it is recommended to use $\preceq$ and its variants:

$\preccurlyeq$
$\curlyeqprec$

To denote the conventional ordering relation in the context of numbers, the symbol $\le$ is to be used, or its variants:

$\leqslant$
$\leqq$
$\eqslantless$


The symbol $\subseteq$ is universally reserved for the subset relation.


$a \preceq b$

can be read as:

$a$ precedes, or is the same as, $b$.

Similarly:

$a \preceq b$

can be read as:

$b$ succeeds, or is the same as, $a$.


If, for two elements $a, b \in S$, it is not the case that $a \preceq b$, then the symbols $a \npreceq b$ and $b \nsucceq a$ can be used.


Sources