User blog comment:Rgetar/Idea for FGH for larger transfinite ordinals/@comment-35470197-20190702232339/@comment-35470197-20190708095307

> Right, thanks. I deleted this statement, it was not used.

Yes, it was. You actually used because you regard \(S\) as a totally ordered set. The union of totally ordered sets is not necessarily totally ordered when they have inclusions compatible with the orderings.