While I was in college, a fellow
mathematics
major and I made the conjecture that the
set of all
gross things formed a group (in
TMA's sense, above). It
seemed reasonable - the set was certainly
closed under the
operator of
addition or mixing. For if you mix two
gross things together, the result would
have to be gross, right?
Alas, we were never able to prove our
theory, and unfortunately we came to the
conclusion that it is probably false.
For we could not determine what the identity
element of such a group would be. What
could you add to anything gross that would
not change it, yet was itself gross? The
only candidate was water; but there are
some things that cannot combine with anything
to make water - for example, corned beef
hash.
A side note for math geeks: although the
set of gross things is not a group, the fact
that it is closed under addition means that
you could localize in the ring of all things,
with addition being represented by formal sums
and multiplication represented by mixing.
Which would give you a fairly strange ring.