Observe this incredible sequence
\( \\[15pt]
{(a)\^\^a = a^{a-1} = N_a\,^{a^a} \,=\, N_a\,^{N_a\,^{a^2}} \,=\,
N_a\,^{N_a\,^{N_a\,^{2a}}} \,=\,
N_a\,^{N_a\,^{N_a\,^{N_a\,^{ln_{a}(2^a)+a}}}} \,=\, ...
} \)
This hints that the zeration \( \\[15pt]
{a\circ a=ln_{N_a}(2)+a } \), which is even another argument in favor of \( \\[15pt]
{a\circ b=ln_{?}(?^a+?^b) } \), but also hints about what is below zeration, and maybe it can explored over tetration.
-Is trivial that the former sequence of towers converge to \( \\[15pt]
{ a^{a-1} } \).
-Is puzzling that the exponent (2+a) is missing.
\( \\[15pt]
{(a)\^\^a = a^{a-1} = N_a\,^{a^a} \,=\, N_a\,^{N_a\,^{a^2}} \,=\,
N_a\,^{N_a\,^{N_a\,^{2a}}} \,=\,
N_a\,^{N_a\,^{N_a\,^{N_a\,^{ln_{a}(2^a)+a}}}} \,=\, ...
} \)
This hints that the zeration \( \\[15pt]
{a\circ a=ln_{N_a}(2)+a } \), which is even another argument in favor of \( \\[15pt]
{a\circ b=ln_{?}(?^a+?^b) } \), but also hints about what is below zeration, and maybe it can explored over tetration.
-Is trivial that the former sequence of towers converge to \( \\[15pt]
{ a^{a-1} } \).
-Is puzzling that the exponent (2+a) is missing.
