User blog comment:Googleaarex/My new site/@comment-75.109.190.23-20160718222825

Hello Aarex Tiaokhiao. My name is Samuel. I am a huge fan of your work with large numbers. I would like to ask some questions about your Extended Up Arrow Notation part 4. it's about these 5 numbers on the web page that i copied and pasted to this comment below. Could you show me the steps to go from Otoperoogol to Otopersuperoogol to Osquartoperoogol to Otoquaroogol to Opoperoogol?

Dimensional/Nested Array Up-arrow We defined a ↑,1↑ b, which is equal to a ↑,,...,,↑ a (b ,'s). Then a ↑,1↑↑ b = a ↑,,...,,↑,1↑ a (b ,'s), a ↑,1↑↑↑ b = a ↑,,...,,↑,1↑↑ a (b ,'s), etc.Then a ↑,1,↑ b = a ↑_{,1...↑_{b}...} a (b nested, a_b = ab), a ↑_{,1,1↑} b = a ↑_{,1,,...,,↑} a (b ,'s), a ↑_{,2↑} b = a ↑_{,1,1...,1,1↑} a (b ,1's), a ↑_{,3↑} b = a ↑_{,2,2...,2,2↑} a (b ,3's), etc.So the limit is ↑_{,_{,_{...}↑}↑} level.Dimensional/Nested Array Up-Arrow Rules a #↑ b = a # a ... a # a (b a's)a ##↑ b = a ####...#### a (b ##'s)a # @_{,,...,,#↑,...} # b = a # @_{,,...,... # @_{,,...,,#,...} # ...,#,...} # a (b nested) (@ is ↑ or ,)↑_{#,#...#,#,} = ↑_{#,#...#,#}a #,_{#↑}#↑ b = a #,_{#},_{#}...,_{#},_{#}↑,_{#↑}# a (b ,#'s)Dimensional/Nested Array Up-Arrow Analysis ↑_{,_{1}↑} has cardinal I(w,0) = W(W{2}^w)↑_{,↑,↑_{1}↑} has cardinal W(W{2}^w+1)↑_{,,↑,↑_{1}↑} has cardinal W(W{2}^w+W{2})↑_{,_{1}↑↑} has cardinal I(w,1) = W(W{2}^w*2)↑_{,_{1},↑} has cardinal I(w+1,0) = W(W{2}^{w+1})↑_{,_{1},_{1}↑} has cardinal I(w*2,0) = W(W{2}^{w*2})↑_{,_{2}↑} has cardinal I(w^2,0) = W(W{2}^w^2)↑_{,_{↑_{↑}}↑} has cardinal I(w^w,0) = W(W{2}^w^w)↑_{,_{↑_{,↑}}↑} has cardinal I(W,0) = W(W{2}^W)↑_{,_{↑_{,↑_{,,↑}}}↑} has cardinal I(psi_I(0),0) = W(W{2}^W(W(W{2})))↑_{,_{↑_{,,↑}}↑} has cardinal I(I,0) = W(W{2}^W(W{2}))↑_{,_{↑_{,_{,↑}↑}}↑} has cardinal I(I(w,0),0) = W(W{2}^W(W{2}^w))↑_{,_{↑_{,_{,↑}↑}}↑} has cardinal I(1,0,0) = W(W{2}^W(W{2}^W{2}))↑_{,_{↑_{,_{,↑}↑}},↑} has cardinal I(1,1,0) = W(W{2}^{W(W{2}^W{2})+1})↑_{,_{↑_{,_{,↑}↑}},_{↑_{,_{↑_{,_{,↑}↑}}↑}}↑} has cardinal I(1,I(1,0,0),0) = W(W{2}^{W(W{2}^W{2})+W(W{2}^W(W{2}^W{2}))})↑_{,_{↑_{,_{,↑}↑}},_{↑_{,_{,↑}↑}}↑} has cardinal I(2,0,0) = W(W{2}^{W(W{2}^W{2})*2})↑_{,_{↑_{,_{,↑}↑}↑_{,_{,↑}↑}}↑} has cardinal I(1,0,0,0) = W(W{2}^{W(W{2}^W{2})^2})↑_{,_{↑_{,_{,↑}↑}↑}↑} has cardinal I(M^w,0) = W(W{2}^{W(W{2}^W{2})^w})↑_{,_{↑_{,_{,↑}↑}↑_{,_{,↑}↑}}↑} has cardinal I(M^M,0) = W(W{2}^{W(W{2}^W{2})^W(W{2}^W{2})})On mahlo cardinals...↑_{,_{,↑}↑} has cardinal M = W(W{2}^W{2})↑_{,_{,↑}↑↑} has cardinal M_2 = W(W{2}^W{2}*2)↑_{,_{,↑},↑} has cardinal M(1,0) = W(W{2}^{W{2}+1})↑_{,_{,↑},,↑} has cardinal M(2,0) = W(W{2}^{W{2}+2})↑_{,_{,↑},_{1}↑} has cardinal M(w,0) = W(W{2}^{W{2}+w})↑_{,_{,↑},_{↑}↑_{,_{,↑}↑}} has cardinal M(M,0) = W(W{2}^{W{2}+W(W{2}^W{2})})↑_{,_{,↑},_{↑_{,_{,↑},_{,↑}↑}}↑} has cardinal M(1,0,0) = W(W{2}^{W{2}+W(W{2}^{W{2}*2})})↑_{,_{,↑},_{↑_{,_{,↑},_{,↑}↑}}↑} has cardinal M(1,0,0,0) = W(W{2}^{W{2}+W(W{2}^{W{2}*2})^2})↑_{,_{,↑},_{,↑},_{↑_{,_{,↑},_{,↑},_{,↑}↑}}↑} has cardinal Xi(3,0) = W(W{2}^{W{2}*2})↑_{,_{,↑},_{,↑},_{↑_{,_{,↑},_{,↑},_{,↑}↑}}↑} has cardinal W(W{2}^{W{2}*2+W(W{2}^{W{2}*3})})↑_{,_{,↑},_{,↑},_{,↑}↑} has cardinal Xi(4,0) = W(W{2}^{W{2}*3})↑_{,_{↑,↑}↑} has cardinal Xi(w,0) = W(W{2}^{W{2}*w})↑_{,_{↑_{,_{,↑}↑},↑}↑} has cardinal Xi(M,0) = W(W{2}^{W{2}*W(W{2}^W{2})})↑_{,_{↑_{,_{↑,↑}↑},↑}↑} has cardinal Xi(Xi(w,0),0) = W(W{2}^{W{2}*W(W{2}^{W{2}*w})})↑_{,_{↑_{,_{,↑↑}↑},↑}↑} has cardinal Xi(1,0,0) = W(W{2}^{W{2}*W(W{2}^W{2}^2)})↑_{,_{,↑↑}↑} has cardinal K = W(W{2}^W{2}^2)↑_{,_{,↑↑}↑↑} has cardinal K_2 = W(W{2}^W{2}^2*2)↑_{,_{,↑↑},↑} has cardinal K(1,0) = W(W{2}^{W{2}^2+1})↑_{,_{,↑↑},_{,↑}↑} has Mahlo Compact Cardinal = W(W{2}^{W{2}^2+W{2}})↑_{,_{,↑↑},_{,↑↑}↑} has Compact Compact Cardinal = W(W{2}^{W{2}^2*2})↑_{,_{↑,↑↑}↑} has w-ex-Compact Cardinal = W(W{2}^{W{2}^2*w})↑_{,_{↑_{,_{,↑↑↑}↑},↑↑}↑} has cardinal W(W{2}^{W{2}^2*W(W{2}^W{2}^3)})↑_{,_{,↑↑↑}↑} has Ultimate Cardinal = W(W{2}^W{2}^3)↑_{,_{,↑1}↑} has Stage-w Cardinal = W(W{2}^W{2}^w)↑_{,_{,↑_{,_{,↑}↑}}↑} has Stage-M Cardinal = W(W{2}^W{2}^W(W{2}^W{2}))↑_{,_{,↑_{,_{,,↑}↑}}↑} has cardinal W(W{2}^W{2}^W(W{2}^W{2}^W{2}))↑_{,_{,,↑}↑} has cardinal W(W{2}^W{2}^W{2})↑_{,_{,,↑},↑} has cardinal W(W{2}^{W{2}^W{2}+1})↑_{,_{,,↑},_{,,↑}↑} has cardinal W(W{2}^{W{2}^W{2}*2})↑_{,_{,↑,↑}↑} has cardinal W(W{2}^W{2}^{W{2}+1})↑_{,_{,,↑↑}↑} has cardinal W(W{2}^W{2}^{W{2}*2})↑_{,_{,,,↑}↑} has cardinal W(W{2}^W{2}^W{2}^2)↑_{,_{,_{1}↑}↑} has cardinal W(W{2}^W{2}^W{2}^w)↑_{,_{,_{,↑}↑}↑} has cardinal W(W{2}^W{2}^W{2}^W{2})Dimensional/Nested Array Up-Arrow Numbers Osuperoogol = 10↑_{,_{1}↑}100Osuperoogolplex = 10↑_{,_{1}↑}10↑_{,_{1}↑}100Osuperiggol = 10↑_{,_{1}↑}↑_{,_{1}↑}100Duosuperoogol = 10↑_{,_{1}↑↑}100Omegesuperoogol = 10↑_{,_{1},↑}100Oduosuperoogol = 10↑_{,_{1},_{1}↑}100Otriosuperoogol = 10↑_{,_{1},_{1},_{1}↑}100Osquaroogol = 10↑_{,_{2}↑}100Ocuberoogol = 10↑_{,_{3}↑}100Otoperoogol = 10↑_{,_{↑_1}↑}100Otopersuperoogol = 10↑_{,_{↑_{1}↑}↑}100Osquartoperoogol = 10↑_{,_{↑_{1}↑_{1}}↑}100Otoquaroogol = 10↑_{,_{↑_2}↑}100Opoperoogol = 10↑_{,_{↑_↑_1}↑}100Oomeger-peroogol = 10↑_{,_{↑_{,↑}}↑}100Ooomeger-per-peroogol = 10↑_{,_{↑_{,_{↑_{,↑}}↑}}↑}100Oomegeroogol = 10↑_{,_{,↑}↑}100Oduomegeroogol = 10↑_{,_{,↑↑}↑}100Oogigeroogol = 10↑_{,_{,,↑}↑}100Oosuperoogol = 10↑_{,_{,_{1}↑}↑}100Oosquaroogol = 10↑_{,_{,_{2}↑}↑}100Ootoperoogol = 10↑_{,_{,_{↑_1}↑}↑}100Ooomegeroogol = 10↑_{,_{,_{,↑}↑}↑}100Ounomegeroogol = 10↑_{,_{...,↑...}↑}10 (100 ,'s)Ounomegeroogolplex = 10↑_{,_{...,↑...}↑}10 (Ounomegeroogol ,'s)CommentsYou do not have permission to add comments.Sign in|Report Abuse|Print Pag