Symbols:Set Theory/Proper Superset

Proper Superset

 * $\supset$, $\supsetneq$ or $\supsetneqq$

$S \supset T$ means $S$ is a proper superset of $T$, in other words, $S \supseteq T$ and $S \ne T$.

The symbols $\supset$, $\supsetneq$ and $\supsetneqq$ are equivalent.

Also denoted as
It should be noted that use in the literature of subset-type symbols is haphazard.

Many authors use exclusively $\supset$, even when the inclusion is not strict, reserving $\supsetneq$ or $\supsetneqq$ for strict inclusions.

If in doubt, one cannot go wrong by writing $\supseteq$, the reader can then consider it an ongoing exercise to determine which inclusions are strict.