User blog comment:Fejfo/bitstring lexographical notation/@comment-35470197-20190913005559/@comment-30869823-20190913221710

Yes, that seems like it is a well-defined way to encode ordinals in bitstrings. However I don't like how it uses a system of fundamental sequences below \( \alpha \) to define encodings upto \( \alpha \). That effectively means it needs to get it's strength from somewhere else (the place where the fundamental sequences are defined). Althoug it might still be useful for constructing an explicit well-ordering on bitstrings/natural numbers (in binary they are almost bitstrings) from an ordinal.