Set equality

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Set equality

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


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

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

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