Definition 1.4.24 (Succession).  Let S, T be sets,  be a partial order on S,  be a partial order on T. We define:

This definition constructs a partial order on the disjoint union of two sets S and T from partial orders on S and T. Elements of S are always considered smaller than elements of T. This is used to define addition of ordinal numbers (see $../Numbers/Ordinal/sum).