Definition:Set/Uniqueness of Elements/Equality of Sets

Definition
By definition of set equality

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.