User blog comment:Ikosarakt1/Fast-growing hierarchy/@comment-5529393-20130619110333/@comment-5150073-20130619134433

This problem appears because w < w^2, and to determine what ordinal is larger we need special algorithm to compare them. Is it so necessary? Ordinals like w+w^2 or w^2+w+w^2 I shall call "unproper" ordinals, but if we initially plug proper ordinal into FGH, can it eventually lead to the unproper?