Definition:Strict Ordering/Notation

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

On, 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, 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.

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.