User blog comment:Edwin Shade/An Injection From The Countable Ordinals To The Reals/@comment-30754445-20171219174932/@comment-30754445-20171219185024

Interesting.

Is there a gurantee that this sequence will, indeed, be different for any two ordinals?

One thing is for sure: under this interpertation, the vast majority of real numbers don't represent any ordinal at all. This is why I thought Edwin wanted to encode the actual fundamental sequences rather than only their length.