We construct explicit generators of the K-theory and K-homology of the
coordinate algebra of `functions' on quantum projective spaces. We also sketch
a construction of unbounded Fredholm modules, that is to say Dirac-like
operators and spectral triples of any positive real dimension.Comment: 8 pages, no figures, dcpic, pdflatex. v2: 8 pages, minor changes,
final version to appears in JK