As a pedagogical device for describing functions such as the one

below

           |
           |                  +-----------------
           |                 /:
           |                / :
           |               /  :
           |              /   :
           |             /    :
           |            /     :
      -----+------------------------------------
           |                  a
           |

where two formulae, f1 and f2, are necessary for adjoining domains but the function is continous at the boundary point, I usually write the description in the form

        f(x) = f1(x) for x =< a
        f(x) = f2(x) for x >= a

The astute reader will note that the domains overlap, but that

f1(a) = f2(a), so no semantic ambiguity obtains.

[ This RFC was put into machine readable form for entry ] [ into the online RFC archives by Naoki Matsuhira 5/97 ]