Empty
set : In set theory, the
set
without any members a.k.a. the void set. It's standard definition is {x:
x≠x}
i.e. the set of things that are not identical to themselves, and it is often written as Ø, so that Ø={x: x≠x}.
Accordingly, this is the way to speak of nothing in settheory. Since
in set theory two sets are equal iff they have the same elements, the
empty set is unique (whence "the"), and since one set is included in
another iff there is no element in the other set that is not in the one,
the empty set is included in every set, and so also included in itself,
though it is no element of itself.
Also, the powerset of
Ø is {Ø, {Ø}}, which is one convenient technical way in set theory to
generate something like the counterpart of
truthvalues.
