Set Equality

Two sets $A$ and $B$ are equal if they contain exactly the same elements. You write $A = B$.

Sets $A$ and $B$ are equal if and only if $A \subseteq B$ and $B \subseteq A$. This is the formal definition.

For example, $\{1, 2, 3\} = \{3, 2, 1\}$ because order does not matter. Also, $\{1, 1, 2\} = \{1, 2\}$ because duplicates do not count.