bunny again notation analysis (NO EXPLANATION)

Introduction[]

I'm pretty sure this siho guy's gonna find out the entire world does not revolve around him, his country, his belief, and stuff like that, whatever, idk.

—tat1101

Harry's notation is a googologist's notation created by bunny again yesterday, for bunny again himself he is actually not active anywhere either on wiki googology or miraheze googology, but yesterday he seemed to have created a notation quite quickly, he said that he wanted to get to phi (w,0) but the analysis is still stuck at epsilon and has not increased,

the definition is very similar to my extended hyper e notation or obilique notation, until now obilique notation is still undergoing a naive extension called Prettisimo I-IV, until now I haven't developed it and I plan to replace it with a better one, so far I haven't gotten there yet to epsilon nought, but let's start my analysis

$n[1]=f_{\omega }$

$n[1]2=f_{\omega +1}$

$n[1]3=f_{\omega +2}$

$n[1]4=f_{\omega +3}$

$n[1][1]=f_{\omega 2}$ (the [1] diagonalize)

$n[1][1]1=f_{\omega 2+1}$

$n[1][1]2=f_{\omega 2+2}$

$n[1][1]3=f_{\omega 2+3}$

$n[1][1][1]=f_{\omega 3}$

$n[1][1][1]1=f_{\omega 3+1}$

$n[1][1][1]2=f_{\omega 3+2}$

Until now it is very clear that this notation is similar to hyper e in general

$n[1][1][1][1]=f_{\omega 4}$

$n[1][1][1][1][1]=f_{\omega 5}$

$n[1][1][1][1][1][1]=f_{\omega 6}$

$n[2]=f_{\omega ^{2}}$

$n[2]1=f_{\omega ^{2}+1}$

$n[2]2=f_{\omega ^{2}+2}$

$n[2]3=f_{\omega ^{2}+3}$

$n[2][1]=f_{\omega ^{2}+\omega }$

Pay attention carefully, don't misunderstand

$n[2][1]1=f_{\omega ^{2}+\omega +1}$

$n[2][1]2=f_{\omega ^{2}+\omega +2}$

$n[2][1][1]=f_{\omega ^{2}+\omega 2}$

look very similar to extended hyper e notation

$n[2][1][1][1]=f_{\omega ^{2}+\omega 3}$

$n[2][2]=f_{\omega ^{2}2}$

Maybe by now you have seen my obilique notation pattern

$n[2][2][1]=f_{\omega ^{2}2+\omega }$

$n[2][2][1][1]=f_{\omega ^{2}2+\omega 2}$

$n[2][2][1][1][1]=f_{\omega ^{2}2+\omega 3}$

$n[2][2][2]=f_{\omega ^{2}3}$

$n[2][2][2][2]=f_{\omega ^{2}4}$

$n[2][2][2][2][2]=f_{\omega ^{2}5}$

$n[3]=f_{\omega ^{3}}$

Second movement[]

$n[3]1=f_{\omega ^{3}+1}$

$n[3][1]=f_{\omega ^{3}+\omega }$

$n[3][1][1]=f_{\omega ^{3}+\omega 2}$

$n[3][1][1][1]=f_{\omega ^{3}+\omega 3}$

$n[3][1][1][1][1]=f_{\omega ^{3}+\omega 4}$

$n[3][2]=f_{\omega ^{3}+\omega ^{2}}$

$n[3][2][1]=f_{\omega ^{3}+\omega ^{2}+\omega }$

$n[3][2][2]=f_{\omega ^{3}+\omega ^{2}2}$

$n[3][2][2][2]=f_{\omega ^{3}+\omega ^{2}3}$

$n[3][3]=f_{\omega ^{3}2}$

$n[3][3][3]=f_{\omega ^{3}3}$

$n[3][3][3][3]=f_{\omega ^{3}4}$

$n[4]=f_{\omega ^{4}}$

$n[4][1]=f_{\omega ^{4}+\omega }$

$n[4][1][1]=f_{\omega ^{4}+\omega 2}$

$n[4][1][1][1]=f_{\omega ^{4}+\omega 3}$

$n[4][1][1][1][1]=f_{\omega ^{4}+\omega 4}$

$n[4][2]=f_{\omega ^{4}+\omega ^{2}}$

$n[4][2][1]=f_{\omega ^{4}+\omega ^{2}+\omega }$

$n[4][2][1][1]=f_{\omega ^{4}+\omega ^{2}+\omega 2}$

$n[4][2][1][1][1]=f_{\omega ^{4}+\omega ^{2}+\omega 3}$

$n[4][2][2]=f_{\omega ^{4}+\omega ^{2}+\omega ^{2}}$

$n[4][2][2][2]=f_{\omega ^{4}+\omega ^{2}2}$

$n[4][3]=f_{\omega ^{4}+\omega ^{3}}$

$n[4][3][3]=f_{\omega ^{4}+\omega ^{3}2}$

$n[4][4]=f_{\omega ^{4}2}$

Look at the pattern, that so similar to obilique notation, so then

$n[4][4][4]=f_{\omega ^{4}3}$

$n[4][4][4][4]=f_{\omega ^{4}4}$

$n[4][4][4][4][4]=f_{\omega ^{4}5}$

$n[5]=f_{\omega ^{5}}$

$n[6]=f_{\omega ^{6}}$

$n[7]=f_{\omega ^{7}}$

$n[[1]]=f_{\omega ^{\omega }}$

Third movement[]

$n[[1]]1=f_{\omega ^{\omega }+1}$

$n[[1]]2=f_{\omega ^{\omega }+2}$

$n[[1]]3=f_{\omega ^{\omega }+3}$

$n[[1]][1]=f_{\omega ^{\omega }+\omega }$

$n[[1]][1][1]=f_{\omega ^{\omega }+\omega 2}$

$n[[1]][1][1][1]=f_{\omega ^{\omega }+\omega 3}$

$n[[1]][2]=f_{\omega ^{\omega }+\omega ^{2}}$

$n[[1]][2][2]=f_{\omega ^{\omega }+\omega ^{2}2}$

$n[[1]][2][2][2]=f_{\omega ^{\omega }+\omega ^{2}3}$

$n[[1]][3]=f_{\omega ^{\omega }+\omega ^{3}}$

$n[[1]][4]=f_{\omega ^{\omega }+\omega ^{4}}$

$n[[1]][5]=f_{\omega ^{\omega }+\omega ^{5}}$

$n[[1]][[1]]=f_{\omega ^{\omega }2}$

how can we continue it again

$n[[1]][[1]][[1]]=f_{\omega ^{\omega }3}$

$n[[1]][[1]][[1]][[1]]=f_{\omega ^{\omega }4}$

$n[[1]][[1]][[1]][[1]][[1]]=f_{\omega ^{\omega }5}$

$n[[1]][[1]][[1]][[1]][[1]][[1]]=f_{\omega ^{\omega }6}$

$n[[1]1]=f_{\omega ^{\omega +1}}$

$n[[1]1][[1]]=f_{\omega ^{\omega +1}+\omega ^{\omega }}$

$n[[1]1][[1]][[1]]=f_{\omega ^{\omega +1}+\omega ^{\omega }2}$

$n[[1]1][[1]][[1]][[1]]=f_{\omega ^{\omega +1}+\omega ^{\omega }3}$

$n[[1]1][[1]][[1]][[1]][[1]]=f_{\omega ^{\omega +1}+\omega ^{\omega }4}$

$n[[1]1][[1]1]=f_{\omega ^{\omega +1}2}$

$n[[1]1][[1]1][[1]1]=f_{\omega ^{\omega +1}3}$

$n[[1]1][[1]1][[1]1][[1]1]=f_{\omega ^{\omega +1}4}$

$n[[1]2]=f_{\omega ^{\omega +2}}$

$n[[1]2][[1]]=f_{\omega ^{\omega +2}+\omega ^{\omega }}$

$n[[1]2][[1]][[1]]=f_{\omega ^{\omega +2}+\omega ^{\omega }2}$

$n[[1]2][[1]][[1]][[1]]=f_{\omega ^{\omega +2}+\omega ^{\omega }3}$

$n[[1]2][[1]][[1]][[1]][[1]]=f_{\omega ^{\omega +2}+\omega ^{\omega }4}$

$n[[1]2][[1]2]=f_{\omega ^{\omega +2}2}$

$n[[1]2][[1]2][[1]2]=f_{\omega ^{\omega +2}3}$

$n[[1]2][[1]2][[1]2][[1]2]=f_{\omega ^{\omega +2}4}$

$n[[1]3]=f_{\omega ^{\omega +3}}$

$n[[1]3][1]=f_{\omega ^{\omega +3}+\omega }$

$n[[1]3][2]=f_{\omega ^{\omega +3}+\omega ^{2}}$

$n[[1]3][3]=f_{\omega ^{\omega +3}+\omega ^{3}}$

$n[[1]3][[1]]=f_{\omega ^{\omega +3}+\omega ^{\omega }}$

$n[[1]3][[1]3]=f_{\omega ^{\omega +3}2}$

$n[[1]3][[1]3][[1]3]=f_{\omega ^{\omega +3}3}$

$n[[1]3][[1]3][[1]3][[1]3]=f_{\omega ^{\omega +3}4}$

$n[[1]4]=f_{\omega ^{\omega +4}}$

$n[[1]5]=f_{\omega ^{\omega +5}}$

$n[[1][1]]=f_{\omega ^{\omega 2}}$

Maybe at this point you will see a pattern of cascading e notation

$n[[1][1]][[1][1]]=f_{\omega ^{\omega 2}2}$

$n[[1][1]][[1][1]][[1][1]]=f_{\omega ^{\omega 2}3}$

$n[[1][1]][[1][1]][[1][1]][[1][1]]=f_{\omega ^{\omega 2}4}$

$n[[1][1]1]=f_{\omega ^{\omega 2+1}}$

$n[[1][1]2]=f_{\omega ^{\omega 2+2}}$

$n[[1][1]3]=f_{\omega ^{\omega 2+3}}$

$n[[1][1]4]=f_{\omega ^{\omega 2+4}}$

$n[[1][1][1]]=f_{\omega ^{\omega 3}}$

$n[[1][1][1][1]]=f_{\omega ^{\omega 4}}$

$n[[1][1][1][1][1]]=f_{\omega ^{\omega 5}}$

$n[[2]]=f_{\omega ^{\omega ^{2}}}$

$n[[2]][[2]]=f_{\omega ^{\omega ^{2}}2}$

just follow the pattern

$n[[2]][[2]][[2]]=f_{\omega ^{\omega ^{2}}3}$

$n[[2]][[2]][[2]][[2]]=f_{\omega ^{\omega ^{2}}3}$

$n[[2]1]=f_{\omega ^{\omega ^{2}+1}}$

$n[[2]2]=f_{\omega ^{\omega ^{2}+2}}$

$n[[2]3]=f_{\omega ^{\omega ^{2}+3}}$

$n[[2][1]]=f_{\omega ^{\omega ^{2}+\omega }}$

$n[[2][1][1]]=f_{\omega ^{\omega ^{2}+\omega 2}}$

$n[[2][1][1][1]]=f_{\omega ^{\omega ^{2}+\omega 3}}$

$n[[2][2]]=f_{\omega ^{\omega ^{2}2}}$

$n[[2][2][1]]=f_{\omega ^{\omega ^{2}2+1}}$

$n[[2][2][1][1]]=f_{\omega ^{\omega ^{2}2+2}}$

$n[[2][2][2]]=f_{\omega ^{\omega ^{2}3}}$

$n[[2][2][2][2]]=f_{\omega ^{\omega ^{2}4}}$

$n[[2][2][2][2][2]]=f_{\omega ^{\omega ^{2}5}}$

$n[[3]]=f_{\omega ^{\omega ^{3}}}$

$n[[3]][[3]]=f_{\omega ^{\omega ^{3}}2}$

$n[[3]][[3]][[3]]=f_{\omega ^{\omega ^{3}}3}$

$n[[3]][[3]][[3]][[3]]=f_{\omega ^{\omega ^{3}}4}$

$n[[3]1]=f_{\omega ^{\omega ^{3}+1}}$

$n[[3]2]=f_{\omega ^{\omega ^{3}+2}}$

$n[[3]3]=f_{\omega ^{\omega ^{3}+3}}$

$n[[3][1]]=f_{\omega ^{\omega ^{3}+\omega }}$

$n[[3][1][1]]=f_{\omega ^{\omega ^{3}+\omega 2}}$

$n[[3][1][1][1]]=f_{\omega ^{\omega ^{3}+\omega 3}}$

$n[[3][2]]=f_{\omega ^{\omega ^{3}+\omega ^{2}}}$

$n[[3][3]]=f_{\omega ^{\omega ^{3}+\omega ^{3}}}$

$n[[3][3]]=f_{\omega ^{\omega ^{3}2}}$

$n[[3][3][3]]=f_{\omega ^{\omega ^{3}3}}$

$n[[3][3][3][3]]=f_{\omega ^{\omega ^{3}4}}$

$n[[3][3][3][3][3]]=f_{\omega ^{\omega ^{3}5}}$

$n[[4]]=f_{\omega ^{\omega ^{4}}}$

$n[[5]]=f_{\omega ^{\omega ^{5}}}$

$n[[6]]=f_{\omega ^{\omega ^{6}}}$

$n[[7]]=f_{\omega ^{\omega ^{7}}}$

$n[[[1]]]=f_{\omega ^{\omega ^{\omega }}}$