Symbols:Set Theory/Proper Subset

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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 \subsetneq .

The $\LaTeX$ code for \(\subsetneqq\) is \subsetneqq .


$\subset$ 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.