for all bounded sequences , while mapping the constant sequence to . (i) Show that if is a ultrafilter, show that there exists a unique *-homomorphism with the property that for every , one has if and only if is -large. (ii) Conversely, show that all *-homomorphisms from to arise in this fashion, and that a *-homomorphism arises from a nonprincipal ultrafilter if and only if it extends the limit f