User blog comment:Googleaarex/Fundamental sequences for my ordinal notation/@comment-1605058-20170225174736/@comment-1605058-20170225195721

@Denis: Nothing in the blog post indicates that, and even if it did. Besides, the same problem applies to all further FSes as well, and there is no well-established system of closed forms.

@Aarex: Not fixed. First of all, \(\alpha+\beta=\beta\) for \(\beta>\alpha\) is, to say the least, wrong, as for example \(\alpha=1,\beta=2\) shows. Second, even assuming \(\alpha\leq\beta\), you still give multiple FSes to many ordinals - consider \(\alpha=\omega+n,\beta=\omega\).