  We compute the set of naive pointed homotopy classes of endomorphisms of the
projective line P^1 over the spectrum of a field. Our computation compares well
with Fabien Morel's one of the motivic pointed homotopy classes of
endomorphisms of P^1: there is an a priori monoid structure on the set of naive
homotopy classes such that canonical map from this monoid to group of motivic
homotopy classes is a group completion.
