An initial segment of 
,
where 
is a well ordered set, is a set 
for some 
(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).
