Suppose that A, B and C are three muturally disjoint sets and suppose that
Thenand
where well orderingmeans 'A is less than B' and well ordering
means 'B is less than C'. Applying these successively we obtain
and
butand
both mean exactly the same, namely that A is less than B and B is less than C, so we can write
hence
Ifwe can write
Ifwe can write
Ifwe can write