\begin{definition}[Definition:Set/Uniqueness of Elements/Equality of Sets]
By definition of '''set equality'''
{{:Definition:Set Equality/Definition 1}}
So, to take the club membership analogy, if two clubs had exactly the same members, the clubs would be considered as ''the same club'', although they may be given different '''names'''.
This follows from the definition of '''equals''' given above.
Note that there '''are''' mathematical constructs which '''do''' take into account both (or either of) the order in which the elements appear, and the number of times they appear, but these are ''not'' '''sets''' as such.
\end{definition}