Let 
be a well ordered set. Then the set 
for some 
is called an initial segment of 
(Rubin 1967, p. 161; Dauben 1990, pp. 196-197; Moore
1982, pp. 90-91). This term was first used by Cantor, who also proved that if
and 
are well ordered sets
that are not order isomorphic, then exactly one
of the following statements is true:
1. 
is order isomorphic to an initial segment of
, or
2. 
is order isomorphic to an initial segment of
(Dauben 1990, p. 198).
