Definition:Proper Subset/Proper Superset

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Definition

If $S$ is a proper subset of $T$, then $T$ is a proper superset of $S$.

This can be expressed by the notation $T \supsetneqq S$.


Also known as

$S \subsetneqq T$ can also be read as:

$S$ is properly included in $T$, or $T$ properly includes $S$
$S$ is strictly included in $T$, or $T$ strictly includes $S$


The following usage can also be seen for $S \subsetneqq T$:

$S$ is properly contained in $T$, or $T$ properly contains $S$
$S$ is strictly contained in $T$, or $T$ strictly contains $S$


However, beware of the usage of contains: $S$ contains $T$ can also be interpreted as $S$ is an element of $T$.

Hence the use of contains is not supported on $\mathsf{Pr} \infty \mathsf{fWiki}$.


Sources