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- Two sets are equal, iff they have the same elements:
**forall**`x`,`y`: x = y <=> (**forall**z: z in x <=> z in y). - There exists a set that does not have any elements:
**exists**`x`:**forall**`y`:`y`not in`x`.- We call this set
*empty set*:**0**:=**such**`x`:**forall**`y`:`y`not in`x`. - Because of second axiom,
**0**is well defined:**forall**`y`:`y`not in**0**. - Because of first axiom,
**0**is unique:**forall**`z`: (**forall**`y`:`y`not in`z`) =>`z`=**0**.

- We call this set

Author: Wolfgang Schreiner

Last Modification: October 14, 1999