Definition:Ordering/Notation

Definition
Symbols frequently used to define a general ordering relation are variants on $\preceq$ or $\le$, although the latter 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.