User blog comment:Edwin Shade/Negatively Indexed Epsilon Numbers/@comment-1605058-20171224230129/@comment-30754445-20171225050307

Actually, it is quite plain to see that ε-1 is ω, because it is the only ordinal in the relevant interval which is a limit of power towers of a smaller ordinal. Edwin Shade's original intuitive hunch was correct.

The rest is quite arbitrary, though.

One could argue, for example, that ε-2 is actually 1 if we define ε numbers as "ordinals which cannot be built from smaller ordinals using +,x,^".