User blog comment:SuperSpruce/Aleph BEAF!/@comment-35470197-20190131011451

> \{N,N,0,1\}

It is ill-defined in that case, because of the following computation: \begin{eqnarray*} \{N,N,0,1\} & = & \{N,N,\{N,1,0,0\},0\} \\ & = & \{N,N,\{N,1\}\} \\ & = & \{N,N,\aleph_1\} \\ & = & \{N,\{N,N,\underline{\aleph_1 - 1}\},\underline{\aleph_1 - 1}\} \\ \end{eqnarray*} The ordinal or expression like \(\aleph_1 - 1\) is ill-defined. You need to fix the rule 5.

Also, "{N,N,N}= the “aleph-null”th aleph fixed point?" is wrong. It is ill-defined in the same reason. In your formulation, the third entry should be a natural number.