Negation cannot be conceived as, for example, "not-x". We must assume a
group to which x could belong, but does not. "Not-x" is incomplete, it
holds a suppressed term.

In the same way, sets must also hold suppressed terms. For example, the
set 'items marked only with ones', is not a bona-fide set. This is
because sets portray properties that are not properties of individual
elements or their totalities but are properties of a particular type of
membership. From the perspective of the totality of individual elements,
the defining property of a set is its emergent property.

Thus a bouquet is a set of flowers, but a set of flowers per se is
simply an unnamed and uninstantiated set as it displays no emergent
property.

A distinction can be made here between negation and sets.

Badiou gives
us an example of Cohen's - 'items marked only with ones' which he claims
can only be instantiated by elements marked by zero. This, I think is to
model the suppressed term on the idea of that offered by negation, and
is wrong for that reason: Negation switches groups - "not-x" merely
suppresses the presentation of that other group. For sets, there are as
many types of membership as there are sets. This is because an emergent
property - the defining characteristic of a set, is unique and arises
independently of individual elements. in other words, elements
distinguish negation, but emergent properties distinguish sets.