Definition:Improper Subset/Also defined as

Improper Subset: Also defined as
Let us consider treatments of set theory which categorise the empty set $\O$ as a proper subset.

Then an improper subset $S$ of a set $T$ is such that:
 * $S = T$

As this is merely a matter of nomenclature, this distinction should not be of great importance.

However, it is wise to make sure which usage is intended when it is encountered.