Set equality

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Definition
 Set equality Two sets $A\,$ and $B\,$, are said to be equal (or identical) if they consist of exactly the same elements, in which case we write $A=B\,$. If one of the sets contains an element not in the other, we say the sets are unequal and we write $A\neq B\,$.

Examples

1. The sets $\lbrace7,3,11,2,5\rbrace\,$ and $\lbrace11,7,5,3,2\rbrace\,$ are equal since both consist of the five prime numbers $2,3,5,7\,$ and $11\,$. the order in which numbers appear is irrelevant.

2. The sets $\lbrace\delta,\alpha,\alpha,\alpha,\omega,\omega,\xi\rbrace\,$ and $\lbrace\delta,\alpha,\omega,\xi\rbrace\,$ are equal even though, in the first set element $\alpha\,$ is listed three times and element $\omega\,$ is listed twice. Both sets contain the four elements $\alpha,\delta,\xi,\omega\,$ and no others.