Definition:Ordering/Notation

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

On, 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, while $\le$ is usually used in the context of numbers.


 * $a \preceq b$

can be read as:
 * $a$ precedes, or is the same as, $b$.

Alternatively:
 * $a \preceq b$

can be read as:
 * $b$ succeeds, or is the same as, $a$.

A symbol for an ordering can be reversed, and the sense is likewise inverted:


 * $a \preceq b \iff b \succeq a$

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.