User blog comment:Ubersketch/Homomorphism between Cantor's normal form of finite degree and primitive sequence system/@comment-35470197-20190809223713/@comment-35470197-20190810021717

It is obvious. If you do not assume any compatibility of the structure of ordinal notations, then you can map any term to \(0\). If you want to assume the bijectivity, you can bijectively factor through \(\mathbb{N}\). It does not give analysis, though.