1. The problem is to understand what an improper subset is. 2. In set theory, a subset $A$ of a set $B$ is called an improper subset if $A$ is exactly equal to $B$. 3. This means every element of $A$ is in $B$, and $A$ contains all elements of $B$. 4. The notation for improper subset is $A \subseteq B$ where $A = B$. 5. In contrast, a proper subset $A \subset B$ means $A$ is contained in $B$ but $A \neq B$. 6. So, an improper subset is the set itself, not a smaller part of it. Final answer: An improper subset of a set is the set itself.