  We compare the K-theory and K-homology of the well known CAR algebra.
  While the $K_0$ group is infinitely generated, we shows that it pairs
identically to zero with even Fredholm modules over the algebra. We show
further that in fact the even K-homology is trivial, while the odd K-homology
is very large. These results give some insight into the K-homology of
AF-algebras.
