Symbols:Set Theory/Proper Subset
- $\subsetneq$ or $\subsetneqq$
$S \subsetneq T$ and $S \subsetneqq T$ both mean:
- $S$ is a proper subset of $T$
In other words, $S \subseteq T$ and $S \ne T$.
The $\LaTeX$ code for \(\subsetneq\) is
The $\LaTeX$ code for \(\subsetneqq\) is
$\subset$ is sometimes used to mean:
- $S$ is a subset of $T$
in the sense that $S$ is permitted to equal $T$.
That is, for which we have specified as $S \subseteq T$.
Although many sources use this interpretation, it is emphatically not recommended, as it can be the cause of considerable confusion.