  The Majorana representation of spin-$\frac{n}{2}$ quantum states by sets of
points on a sphere allows a realization of SU(n) acting on such states, and
thus a natural action on the two-dimensional sphere $S^2$. This action is
discussed in the context of the proposed connection between $SU(\infty)$ and
the group $SDiff(S^2)$ of area-preserving diffeomorphisms of the sphere. There
is no need to work with a special basis of the Lie algebra of SU(n), and there
is a clear geometrical interpretation of the connection between the two groups.
It is argued that they are {\it not} isomorphic, and comments are made
concerning the validity of approximating groups of area-preserving
diffeomorphisms by SU(n).
