Definition:Proper Subset/Improper

Definition
Let $T$ be a set. The term improper subset is relevant in treatments of set theory which define a proper subset $T$ as a subset $S$ of $T$ such that:
 * $0 \subsetneqq S \subsetneqq T$

Under such a regime, $S$ is an improper subset of $T$ either:
 * $S = T$

or:
 * $S = \O$