# Definition:Set/Uniqueness of Elements/Multiple Specification

## Definition

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.