Definition:Strict Ordering/Notation

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Definition

Symbols used to denote a general strict ordering are usually variants on $\prec$, $<$ and so on.

On $\mathsf{Pr} \infty \mathsf{fWiki}$, to denote a general strict ordering it is recommended to use $\prec$.

To denote the conventional strict ordering in the context of numbers, the symbol $<$ is to be used.


The symbol $\subset$ is deprecated on $\mathsf{Pr} \infty \mathsf{fWiki}$, as it is ambiguous in the literature, and this can be a cause of confusion and conflict.

Hence the symbols $\subsetneq$ and $\subsetneqq$ are used for the (proper) subset relation.


$a \prec b$

can be read as:

$a$ (strictly) precedes $b$.

Similarly:

$a \prec b$

can also be read as:

$b$ (strictly) succeeds $a$.


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


Sources