Set Difference with Self is Empty Set

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


 * $S \setminus S = \varnothing$

Proof
From Subset of Itself:
 * $S \subseteq S$

From Set Difference with Superset is Empty Set‎ we have:
 * $S \subseteq T \iff S \setminus T = \varnothing$

Hence the result.

Also see

 * Set Difference with Empty Set is Self