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{MPLTEXT 1 0 60 "################### #########################################" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "#Conway chained arrow notation calculator, using a l ist" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "#implementation. a-> b->c->d = [a,b,c,d]." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "#Ve rsion 1.0, 17/4/2008, (c) I.N. Galidakis. See:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "#http://en.wikipedia.org/wiki/Conway_chained_ar row_notation" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "########### #################################################" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "##################################################### #######" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "#Length of the l ist L" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "Len:=L->nops(L):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "######################### ###################################" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "#T if list is a single number a." }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 22 "L1:=L->type(L,posint):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "############################################# ###############" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "#T if li st is [a,b], some numbers a,b." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "L2:=L->Len(L)=2 and type(L[1],posint) and type(L[2],posint):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "######################### ###################################" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "#T if list is [a,b,c], some numbers a,b,c." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "L3:=L->Len(L)=3 and type(L[1 ],posint) and type(L[2],posint) and type(L[3],posint):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "################################### #########################" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "#Definition for Conway Rule #1: X->p->q+1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "R1:=proc(L)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "local l,X,p,q,iY,F,cX;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "l:=Le n(L);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "p:=L[l-1];if not type(p,p osint) then ERROR(`Cannot apply Rule #1: p=`,p,` has to be evaluated f irst`);fi;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 103 "q:=L[l];if not type( q,posint) then ERROR(`Cannot apply Rule #1: q=`,q,` has to be evaluate d first`);fi;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "X:=L[1..l-2];" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "F:=[op(X),Y,q-1];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "if p>1 then " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 " for cX from 2 to p-1 do " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 " \+ F:=subsop(Len(F)-1=F,F);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 " od;" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 " iY:=[seq(Len(F)-1,cX=1..p-1)];" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 " F:=subsop(iY=X,F);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "fi;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "########################## ##################################" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "#Definition for Conway Rule #2: X->1 = X" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "R2:=proc(L)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "option remember;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "local LN,i;LN:=L;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "if Len(LN) >=2 then" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 " for i from 1 to Len(LN ) do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 " if LN[i]=1 then" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 " LN:=subsop(i=NULL,LN);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 " elif type(LN[i],list) then" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 " LN[i]:=R2(LN[i]);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 " fi;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 " od;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 " LN:=[seq(LN[i],i=1..Len(LN))];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "fi;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "######################### ###################################" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "#Definition for Conway Rule #3: X->Y = X^Y" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "R3:=proc(L)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "option remember;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "local LN,i,p,k;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "LN:=L;" } }{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "if Len(LN)>=2 then" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 " for i from 1 to Len(LN) do" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 19 " if L2(LN[i]) then" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 " p:=L[i,1]^L[i,2];#power" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 52 " LN:=[op(LN[1..i-1]),p,seq(LN[k],k=i+1..Len(LN))];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 " elif Len(LN[i])>=2 then" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 20 " LN[i]:=R3(LN[i]);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 " fi;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 " od;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 " LN:=[seq(LN[i],i=1..Len(LN))];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "fi;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "########################## ##################################" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "#Removes spurious brackets: I.e. [a]->a" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "R4:=proc(L)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "option remember;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "local LN,i;LN:=L;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "if Len(L)> =2 then" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 " for i from 1 to Len(LN) do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 " if type(LN[i],list) then" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 " if Len(LN[i])=1 then" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 58 " while type(LN[i],list) do LN:=subsop( i=LN[i,1],LN);od;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 " else" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 " LN[i]:=R4(L[i]);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 " fi;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 " f i;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 " od;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 " LN:=[seq(LN[i],i=1..Len(LN))];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "fi;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "############################ ################################" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "# Print the final number (if possible)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "CP:=proc(L)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "local LN;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "LN:=L;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "if L1(LN) then" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 " printf(`%d`,LN);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "elif L 2(LN) then" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 " printf(`%d^%d`,LN[1] ,LN[2]);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "elif Len(LN)=2 then" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "### WARNING: note that `I` is no lo nger of type `^`\n" }{MPLTEXT 1 0 57 " printf(`(`);CP(LN[1]);printf(`^ `);CP(LN[2]);printf(`)`);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "elif L 3(LN) then" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 39 " printf(`%d^(%d)%d`,L N[1],LN[3],LN[2]);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "elif Len(LN)= 3 then" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 80 " printf(`(`);CP(LN[1]);pr intf(`^(`);CP(LN[3]);printf(`)`);CP(LN[2]);printf(`)`);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "else" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 51 " ERR OR(`Cannot print number. Not reduced enough.`);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "fi;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "############################ ################################" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "#Wiki examples worked out. Final answer is given in terms of" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "#Ackermann numbers, a^(b )c = a^...^c, where %^(b)% denotes b" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "#Knuth Up-Arrows, to avoid excessive calculations." } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "########################## ##################################" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "L:=[4,3,2];" }}{PARA 0 "" 0 "" {TEXT 211 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "R1(%);#rule #1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "R4(%);#remove spurious brackets" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "R2(%);#rule #2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "R3(%);#rule #3" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 25 "CP(%);#print final number" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "########################################## ##################" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "L:=[2 ,2,4];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "R1(%);#rule #1" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "R4(%);#remove spurious bra ckets" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "R1(%);#rule #1" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "R4(%);#remove spurious agai n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "R1(%);#rule #1" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "R4(%);#remove spurious" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "R2(%);#rule #2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "CP(%);#print" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "############################################## ##############" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "L:=[2,4,3 ];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "R1(%);#rule #1" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "R4(%);#remove spurious brack ets" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "#[2,2,2]=2^(2)2=2^^2 =2^2=4, so L becomes:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "L: =[2,[2,4,2],2];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "R1(%);#C annot apply rule #1, before p resolves first. Hence we need:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "Q:=[2,4,2];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "R1(%);#rule #1" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 31 "R4(%);#remove spurious brackets" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "R2(%);#rule #2" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 14 "R3(%);#rule #3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "R3(%);#again" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "CP(%);#print" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "#Hence ," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "L:=[2,2^16,2];" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "CP(%);#print" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "#a tower of 2's with height 2^16" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "########################## ##################################" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "L:=[2,3,2,2];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "R1(%);#rule #1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "R 2(%);#rule #2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "R3(%);#rul e #3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "R1(%);#rule #1" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "R4(%);#remove spurious brack ets" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "Q:=[2,2,7];" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R1(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R4(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R1(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R4(%);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R1(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R4(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R1(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R4(%);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R1(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R4(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R1(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R4(%);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R2(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "CP(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "#Hence (step 4 on this example on Wiki)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "L:=[2,4,7];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R1(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R4 (%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "M:=[2,2,6];" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R1(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R4(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R1(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R4(%);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R1(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R4(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R1(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R4(%);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R1(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R4(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R2(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "CP(%);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "#Hence," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "L:=[2,[2,4,6],6];" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 11 "M:=[2,4,6];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R1(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R4(%);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "N:=[2,2,5];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R1(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R4(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R1 (%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R4(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R1(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R4(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R1 (%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R4(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R2(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "CP(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "#H ence," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "M:=[2,[2,4,5],5];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "#Hence," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "L:=[2,[2,[2,4,5],5],6]; #this is step 8 i n Wiki for this example." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "#Now repeat for M=[2,4,5], etc." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "############################################################" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "L:=[3,2,2,2];" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R1(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R2(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R3(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "CP(%); #Fina l answer is 3^^^^^^^^^2, larger than the previous!!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "########################################## ##################" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "#A %l argish% example..." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "L:=[9 ,9,9,2];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R1(%);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R2(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R3(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 103 "CP(%);#Final answer is 9^...^9, with (9^((9^((9^((9^((9^((9^(9^ (387420489)9)9))9))9))9))9))9) arrows!!!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "L:=[3,3,3];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R1(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R4(%);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "M:=[3,3,2];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R1(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R4(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R2 (%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R3(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "CP(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "#Hence," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 " L:=[3,3^27,2];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "CP(%):" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }