User blog comment:Cloudy176/Hyperfactorial array notation: Analysis part 1/@comment-1605058-20130507200045

The thing I like most about hyperfactorial notation is that it is non-trivial that every array can be evaluated. BEAF and BAN can be proven to do so by transfinite induction (just like in FB100Z's ordinal BEAF), but for this it isn't obvious that arrays never explode to infinte depth