\begin{definition}[Definition:Set/Uniqueness of Elements/Multiple Specification]
For a given '''set''', an object is either '''in''' the set or '''not in''' the set.
So, if an element is in a set, then it is in the set '''only once''', however many times it may appear in the definition of the set.
Thus, the set $\set {1, 2, 2, 3, 3, 4}$ is the same set as $\set {1, 2, 3, 4}$.
$2$ and $3$ are in the set, and '''listing''' them twice makes no difference to the set's '''contents'''.
Like the membership of a club, if you're in, you're in -- however many membership cards you have to prove it.
\end{definition}