User blog comment:Moooosey/dco + decord sequence/@comment-35470197-20191009222350/@comment-35470197-20191011121153

Usually, one assumes that b is an additive principal number, i.e. an ordinal presentable as w^c for some c. (Since b is assumed to be a limit, c should be non-zero.) Moreover, a should be a sum of additive principal numbers which are not smaller than b.

For example, your current definition does not work when you consider w^2×3. You can define (a,b) as (w^2×2,w^2), (w^2×2+w,w^2), (w^2+w×100,w^2+w^2), and so on. Please try to compute a+(b[n]) for each choice. Then does this example help you to understand the problem?