Why isnt pentation defined as
\( pent(z) = sexp^{[z]}(x_0) = \) lim \( sexp^{[n]}( L' ^z slog^{[n]}(x_0)) \)
Do you really believe lim \( sexp^{[n]}(f(L,L',z)) = \) lim \( sexp^{[n]}( L' ^z slog^{[n]}(x_0)) \) where \( f \) is a simple elementary function ?
Afterall approximating slog^[n] with an elementary function seems wrong/divergent ?
Lim \( sexp^{[n]}(x+y) \) is usually very different from lim \( sexp^{[n]}(x) \) even if \( y \) is small or getting smaller with growing \( n \).
Also its not defined as lim \( sexp^{[n]}(L' ^{z-n}) \).
I assume its (your def of pentation in the paper) meant as an acceleration of lim \( sexp^{[n]}(L' ^{z-n}) \).
If not that would appeal weird and dubious to me.
Is that acceleration really a big improvement ?
Still reading and thinking , I dont have much time ...
regards
tommy1729
\( pent(z) = sexp^{[z]}(x_0) = \) lim \( sexp^{[n]}( L' ^z slog^{[n]}(x_0)) \)
Do you really believe lim \( sexp^{[n]}(f(L,L',z)) = \) lim \( sexp^{[n]}( L' ^z slog^{[n]}(x_0)) \) where \( f \) is a simple elementary function ?
Afterall approximating slog^[n] with an elementary function seems wrong/divergent ?
Lim \( sexp^{[n]}(x+y) \) is usually very different from lim \( sexp^{[n]}(x) \) even if \( y \) is small or getting smaller with growing \( n \).
Also its not defined as lim \( sexp^{[n]}(L' ^{z-n}) \).
I assume its (your def of pentation in the paper) meant as an acceleration of lim \( sexp^{[n]}(L' ^{z-n}) \).
If not that would appeal weird and dubious to me.
Is that acceleration really a big improvement ?
Still reading and thinking , I dont have much time ...
regards
tommy1729
