User blog comment:P進大好きbot/New Issue on Traditional Analyses/@comment-31663462-20190825021820/@comment-35470197-20190825023707

> you can write an algorithm to compare their values

It is not necessarily true. You need to verify the decidability of the comparison of two ordinals.

Moreover, if it is eventually computable at each pair of two expressions, it is useless in analysis unless you explicitly have an effective way to determine the comparison.