User blog comment:JHeroJr/Why I need a system that inductively defines set theories for each ordinal/@comment-35470197-20200109233744

> Some ordinals have more than one fundamental sequence,

Some? Any non-zero limit ordinal has more than one fundamental sequence.

> so in this case α[n] is α's fundamental sequence with the smallest terms.

Ill-defined because there does not exists such a fundamental sequence in general.