Ripheus23

The three other examples show how some very simple examples of infinite computations in aleph-space interconnect via the hyperoperator sequence. Namely, the +++ sequence leads into the *** sequence before the exponential sequence, and each can be represented by the next highest operator using aleph-omega and aleph-zero: so {aleph-omega * aleph-zero}, {aleph-omega ^ aleph-zero}, and {aleph-omega ^^ aleph-zero}.

The anchor conjecture: that 2 ^a 2 = 4, for all a whatsoever, even ordinals of any transfinite cardinality. This equation is sometimes referred to as the anchor of transfinality. During the apocalypse of the Final Power, it was instead discovered that using the heart operator on {2, 2} goes not to 4, but to 4-aleph.*

*Not to be confused with aleph-4. 4-aleph is the fourth apex number, those that end at the apex of transfinality.

*Further refinements have led me to suspect that aleph-4 tetrated by aleph-4 might in fact be aleph-omega(4)*5.