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: