User blog comment:Edwin Shade/An Injection From The Countable Ordinals To The Reals/@comment-30754445-20171219174932/@comment-30754445-20171219180601

Alemagno,

It seems that Edwin Shade wants to concatante entire fundamental sequences in some fashion, instead of what you did there.

It is the same idea, though.

At any rate, both systems seem to have the same problem: What's Ordname(ω+1)? Or any other ordinal which contains ω as part of its fundamental sequence? Since Ordname(ω) is a nonterminating decimal, you can't concatanate anything to it.