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.


\(\ds a\) \(\preceq\) \(\ds b\) can be read as: \(\quad\) $a$ precedes, or is the same as, $b$
\(\ds a\) \(\preceq\) \(\ds b\) can be read as: \(\quad\) $b$ 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.


When the symbols $\le$ and its variants are used, it is common to interpret them as follows:

\(\ds a\) \(\le\) \(\ds b\) can be read as: \(\quad\) $a$ is less than, or is the same as, $b$
\(\ds a\) \(\le\) \(\ds b\) can be read as: \(\quad\) $b$ is greater than, or is the same as, $a$


Sources