Set: Definition

As we mentioned, sets are unordered collections. This means that changing the order of the listed elements or repeating any of the elements in a set doesn't change the set: it's still the same set.

Example: All the $3$ sets

• $\{1, 2, 3\}$
• $\{3, 1, 2\}$, and
• $\{1, 2, 2, 3, 1, 3\}$

are just different ways to write out the same exact set: $\{1, 2, 3\}$.

We say that all these set are equal to one another (in $\LaTeX$:

$=$

):

$\{1, 2, 3\} $$\;= \{3, 1, 2\} $$\;= \{1, 2, 2, $$3, 1, 3\}$