Improper Subset

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**Formal Definition**

If $A$ is any set,then $A$ is the **improper subset of** $A$. Any other subset of $A$ is a **proper subset of** $A$

**Informal Definition**

A subset that is equal to the set, meaning that subset is the set it comes from, is the improper subset.

**Example(s)**

$A=\{1,2,3,4,5\}$, $B=\{1,2,3,4,5\}$ and $B\subseteq A$.

Then, $B$ is the improper subset of $A$. $B = A$.

**Non-example(s)**

$A$ as above. $B=\{1,2,3\}$ and $B\subset A$. Then, $B$ is not the improper subset of $A$.

**Additional Comments**

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