Set Difference with Self is Empty Set

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Theorem

The set difference of a set with itself is the empty set:

$S \setminus S = \O$


Proof

From Set is Subset of Itself:

$S \subseteq S$

From Set Difference with Superset is Empty Set‎ we have:

$S \subseteq T \iff S \setminus T = \O$

Hence the result.

$\blacksquare$


Also see


Sources