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).
