User:Cloudy176/Croutonillion

''This content in this article was invented by Googology Wiki users. It is in no way part of the "googological canon" :)''

Croutonillion is a groundbreakingly pointless googologism, consisting of a ridiculous sequence of totally arbitrary steps. It is constantly under construction, so please edit this page and add to it!

Croutonillion is the mother of all salad numbers &mdash; a gross parody of many new googologists' attempts to create large numbers, following the misguided philosophy that "if it's more complicated, it's bigger."

Definition
"X" refers to the result of the previous operation. Start with googoltriplex.


 * 1) X{X}X
 * 2) BB(X)
 * 3) megafuga(booga(X))
 * 4) X-xennaplex
 * {X, X / 2}
 * 1) (Rayo's number)X
 * 2) BB(X) (repeat this step Y times, where Y is the value of Clarkkkkson on January 1, googolgong CE)
 * 3) \(f_{\Gamma_0}(X)\)
 * 4) giggol-X-plex
 * 5) X!!!...!!! (nested factorials, meameamealokkapoowa oompa times)
 * 6) gongulus-(2X + 1)-plex
 * 7) TREE(TREE(TREE(...TREE(X)...))) (X nested functions)
 * 8) ceil(Xpi)
 * {X, X | 2}
 * 1) Ξ(X). Do this step Y times, where Y is computed with the following steps:
 * 2) Set Y = 3.
 * 3) Y{Y}(Y + 2) (Y copies of ^)
 * 4) falpha(Y) in FGH, where alpha is Goucher's ordinal
 * 5) T(Y) (Torian)
 * 6) Circle(Y) (Steinhaus-Moser notation). Do this googol times.
 * 7) E10#^^#X (with X copies of #)
 * Let f(x) be the result when going through all the steps up and excluding 16-th. Go in reverse order, and start with X.
 * 1) f(TREE(X))th apocalyptic number
 * 2) fgoober bunch(x)
 * 3) X@X@X@X@X@X@X (legiattic array of)
 * 4) X^^^^^X
 * 5) X^^^^^^X
 * 6) X^^^^^^^X
 * 7) X^^^^^^^^X
 * 8) f(x){f(x)}f(x)
 * 9) SCG(TREE(SCG(TREE(SCG(f(x) + tritri) + supertet) + superpent) + superhex) + supersept) + Moser
 * 10) Exploding Tree Function(X)
 * 11) Rayo 13<\sup>(X)
 * Create an alternate version of Croutonillion by stopping here (do the 103X + 3). Call this alternate C.
 * 1) ΣX(C)
 * 2) X^^^^^^^^^^^^^X
 * 3) XvvvvvvvvvvvvvX (down arrows)
 * 4) X -> X -> X -> X -> X (chained arrows)
 * {X, X (1) 2}
 * 1) X$ (Pickover's superfactorial)
 * 2) gag-X
 * 3) Xsuper gongulus
 * 4) {X & L}10,10
 * X!
 * 1) H(H(...(X)...)) (X nested functions), repeat grangoldex times.
 * 2) Same as step 15.
 * 3) {10,100 //...// 2} (X /'s)
 * 4) Repeat 142857 1337  times for step 1 to step 40.
 * 5) X{meameamealokkapoowa oompa}(101337)
 * 6) {googolplexian,X,X}
 * 7) greagol-X-threx, then gigangol-X-tetrex, then gorgegol-X-pentex, and so on googol times
 * 8) E100#100...100#100#(X+1) (googol 100's)
 * 9) X-illion
 * 10) X&&...&&X (X &'s)
 * 11) E100#^#X
 * 12) googolplexiangoogolplexian X
 * YX, where Y is lynz at May 1 meameamealokkapoowa-arrowa A.D.
 * 1) terrible tethrathoth-ex-terrible tethrathoth-...-ex-terrible tethrathoth (X terrible tethrathoth's)
 * 2) Rayo(Rayo(X) + 3)
 * 3) Ackermann(X, X)
 * 4) BH(X) starting with a size-X chain of \(\Gamma_0\)s
 * 5) Circle(Circle(X)) (Friedman's circle theorem, not SMN)
 * 6) Length of the Goodstein sequence starting with X
 * 7) X-illion-illion-illion-...-illion-illion-illion, faxul times
 * 8) BOX_M~X X
 * 9) X(Xth digit of pi + 1)
 * 10) Arx(X,X,X,...,X,X,X) (with X X's)
 * 11) \(f_{X}(X)\), repeat X times
 * 12) G(X)
 * 13) E(Y)Y#^^...^^#^#Y (X ^'s), where Y is googolplex.
 * 14) Repeat X times for step 1 to step 63.
 * 15) Repeat X times for step 1 to step 64.
 * 16) Repeat X times for step 1 to step 65.
 * 17) Repeat X times for step 1 to step 66.
 * 18) Repeat X times for step 1 to step 67.
 * 19) Repeat X times for step 1 to step 68.
 * 20) Repeat X times for step 1 to step 69.
 * 21) Repeat X times for step 1 to step 70.
 * 22) 10^^X
 * 23) X^^10
 * 24) X^^X
 * 25) {L & L & L...L & L & L,X}X,X (X L's)
 * 26) 75*75...75*75*X (X 75's)
 * 27) Graham's Number*X*Y, where Y is Step 5.
 * 28) Rayo(X)
 * 29) SCG(SCG(SCG(SCG(X)+googol)+googolplex)+googolplexian)
 * 30) TREE(TREE(TREE(TREE(X)+googol)+googolplex)+googolplexian)
 * 31) Rayo(Rayo(Rayo(Rayo(X)+googol)+googolplex)+googolplexian)
 * 32) Ξ(Ξ(Ξ(Ξ(X)+googol)+googolplex)+googolplexian)
 * 33) Arx(Arx(Arx(Arx(X)+googol)+googolplex)+googolplexian)
 * 34) BH(X) expect for hydra using TFB labels instead of omegas
 * 35) Repeat steps 1-84 until number of repetitions gets OVER 9000 (i.e. 9001 times)
 * 36) Repeat X times for step 85.
 * 37) Repeat X times for step 86.
 * 38) Repeat X times for step 87.
 * 39) Repeat X times for step 88.
 * {X,X (X) X,X}
 * {X,X,X} & X
 * 1) \(1000^{X^{SCG^{SCG^{SCG^{SCG^{SCG^X(X)}(X)}(X)}(X)}(X)}}\)
 * 2) E100#^#^#X
 * 3) E100#^^#^#X
 * 4) E100#^^^#^#X
 * 5) E100#^^^^^^^^^^^^^^^^#^#X + X
 * 6) E100#^^^^^#^#X
 * 7) E100#^^^^^^#^#X
 * 8) E100#^^^^^^^#^#X
 * 9) X{61}X
 * 10) Arx(X,X,X,X)
 * 11) Arx(X,X,X,X,X)
 * 12) 1337133713371337...1337133713371337 (X 1337's)
 * 13) X+1
 * 14) X&&&...&&&X, with X copies of &
 * 15) H(X), Chris Bird's H function
 * 16) H(X), hyperfactorial
 * 17) m1(X), fusible margin function
 * 18) SCGX(X)
 * 19) X -> X -> X -> X -> X
 * 20) cg(X), Conway &amp; Guy's function
 * 21) C(X), Hurford's C function
 * 22) Xi(X)
 * 23) X!!!!! (nested factorial, not multi) or ((((X!)!)!)!)!
 * 24) First Mersenne prime after X, if it exists. Otherwise it is the first number with abundance X.
 * 25) X^^5
 * 26) {10, 100, X, 3, 3, 7, X}
 * 27) {10, 100 (1337) X}
 * 28) TREEX(X) (repeat this step humongulus times)
 * 29) Rayo(X) (repeat this step humongulus + 1 times)
 * 30) A(X, X) (Ackermann function; repeat this step humongulus + 2 times)
 * 31) X^^^X (repeat this step humongulus + 3 times)
 * 32) giggol-X-plex
 * Create an alternate version of Croutonillion by stopping here. Call this number C2.
 * 1) SCG(SCG(C2 + X) + X) + XC2
 * 2) C*C2*X
 * 3) X!X, Nested Factorial Notation.
 * 4) X^^^C
 * {X,1337,100}
 * 1) {9001,9001,C,X}
 * GX
 * 1) Graham's Number{C}X
 * 2) goo-X-ol
 * 3) X-oogol
 * 4) X{27}X
 * 5) 103(X+1), repeat 1000000 times.
 * 6) 2(First prime after log2(X))
 * 7) X-ty-Xs (X copies of X concatenated)
 * 8) X$ (superfactorial, repeat 50 times)
 * 9) Rayo(X)
 * 10) X![X([X([X])X])X] in hyperfactorial array notation
 * 11) {X&L,X}X,X Repeat this for meameamealokkapoowa oompa times. (Note: all Xs are Xs from croutonillion
 * 12) Repeat step 1 then step 1,2 then step 1,2,3.... then... step 1,2,...,141 for meameamealokkapoowa oompa-brecewah times.
 * 13) X$$$...$$$ w/ X$$$...$$$  w/ X$$$...$$$ ....... w/ X$$$...$$$ w/X with X$$$...$$$ w/ X X's.
 * 14) X{X{X$$$...$$$}X}X, with X $'s.
 * 15) GG X NESTED GRAHAM!!! Looks like expanded to 2.
 * 16) Repeat step 1 to 145 for X times. Then do that X times. Then do that X times. Then do that X times. ... Then do that X times. Then do that X times. with X 'Then do that X times'. And, X is changing every step!
 * 17) The number of steps in gijswijt's sequence needed to reach X.
 * 18) Amount of terms in the harmonic series needed to reach X.
 * 19) Define the whole process up to here as the function C(n). Then, define the fast-growing-crouton as follows:
 * 20) * \(C_0(n) = C(n)\)
 * 21) * \(C_{\alpha+1}(n) = C^n_\alpha(C^n(n))\), where \(C^n\) denotes function iteration
 * 22) * \(C_\alpha(n) = C_{\alpha[n]}(n)\) iff \(\alpha\) is a limit ordinal
 * 23) * fundamental sequences are as normal
 * 24) *The value to carry on in the definition is \(C_{ψ_0(Ω_ω)}(X)\)
 * 25) X in a X-gon using Steinhaus-Moser notation
 * 26) Repeat step the last step. X times.
 * 27) G(G(...(X)...)) (G(G(...(X)...)) (...G(G(...(X)...)) (X G's)... G's) G's), X layers.
 * AX, let A0 = X and An = X!(A(n-1)).
 * 1) Age of Jonathan Bowers in the year X^3 C.E. in Planck times.
 * 2) X&&&&&X
 * 3) return value of D(D(D(D(D(X))))) in loader.c
 * 4) S(X), Chris Bird's S function.
 * 5) S(S(...(3)...)), X S's
 * 6) I(X), iota function at 12:00 AM, January 1 X A.D.
 * 7) X$[U(X)] using dollar function and U function
 * 8) FGH(6,[X2])
 * 9) Repeat step 1 then step 1,2 then step 1,2,3.... then... step 1,2,...,161 for X times.
 * 10) \((X^100)^{100^X})^{100^{X^X}}\)
 * 11) \(\lfloor(10 \uparrow e) \uparrow\uparrow X\rfloor\)
 * 12) \(X \uparrow_{,_{(\uparrow\uparrow)\uparrow}\uparrow} X\), using this.
 * 13) \(X\$[[X],_{X,\text{S}(X),\text{SCG}(X+\text{KAI U~})}]\)
 * 14) \(\sum^{X}_{i=1}\Sigma(i)\)
 * 15) X+IPieces-Cetes Supercluster Complex(X) iota function at X minutedexes after January 1 X A.D, but with  all the functions in the Pieces-Cetes Supercluster complex.
 * 16) \(\sum^{X}_{j=1}\sum^{j}_{i=1}\Sigma(i)\)
 * 17) Repeat the steps 1 to 169 Rayo(X) times.
 * 18) X![[<1(X)2>1] ]
 * 19) 10*1010, let create a function:
 * 20) n*1m = n+m
 * 21) n*lm = Xm
 * 22) X1 = X
 * 23) XY+1 = n*l-1n...n*l-1n (XY n's)
 * 24) Gen(X, X, X, ..., X) with X X's using this
 * 25) X^X
 * 26) X^^X
 * 27) X^^^X
 * 28) X^^^^^^^^^^^^^^^^^^^X
 * 29) X{X}X
 * 30) XX with X pairs of curly braces
 * 31) X+1
 * 32) X*2
 * {X,X[X/2]X} using BAN
 * 1) \(X^{X+1}\)
 * 2) \(f_{\varepsilon_X+1}(X)\)
 * 3) \(Rayo^{Rayo(X)}(Rayo(X))\)
 * 4) Repeat step 1, then step 1 and 2, then step 1,2 and 3 until 1,2,3,....,183,184,185 for \(\Xi^{\Xi(X)}(\Sigma_X(X))^{\text{Fish number  7}}\$[[0]_2]\)bracewah times
 * 5) Fish number X
 * 6) X![X]![X]![X]!........[X]![X]![X] with X![X] quantity of [X]!
 * 7) X+IHercules Corona Borealis Great Wall(Fish number X) iota function at \(\Xi^{\Xi(X)}(\Sigma_X(X))^{\text{Fish number 7}}\$[[0]_2]\)bracewah times minutedexes after January 1 X A.D, but with all the functions in the Hercules Corona Borealis Great Wall.
 * 8) XC C2
 * Create an alternate version of Croutonillion by stopping here. Call this number C3.
 * 1) C3![C2![C![X]]]
 * 2) Repeat step 191 X^^2 times
 * 3) Repeat step 192 X^^3 times
 * 4) Repeat step 193 X^^4 times
 * 5) Repeat step 194 X^^5 times
 * 6) Repeat step 195 X^^6 times
 * 7) Repeat step 196 X^^7 times
 * 8) Repeat step 197 X^^8 times
 * 9) Repeat step 198 X^^9 times
 * 10) Repeat step 199 X^^10 times
 * 11) X![1,2,3,4...........X-2,X-1,X]
 * 12) X$ into X$-gons
 * 13) repeat step 1 to 202 for X^(grand Sprach Zarathustra) times (grand Sprach Zarathustra=E100{#&#&#&#&#&#&#&#&#&#& ... &#&#&#&#&#&#&#&#&#&#}100w/Sprach   Zarathustra #s)
 * 14) XX&X using BEAF
 * 15) $$X\rightarrow X\rightarrow X\rightarrow X$$
 * 16) $$E[X]X\#\#X$$
 * 17) $$E[X]X\#\uparrow^X\#X$$
 * 18) $$E[X]X\#\uparrow^{\#\uparrow^{\#}\#}\#X$$
 * 19) $$X \rightarrow X \rightarrow X \rightarrow X \rightarrow X$$ using Conway's chained arrow in hypermathmatics
 * 20) $$X$$ inside a $$2X$$-sided polygon
 * 21) $$\Sigma(X)$$
 * 22) $$Rayo^X(X)$$
 * 23) $$X+1$$
 * 24) $$X\times2$$
 * 25) $$X\uparrow X$$
 * 26) $$X\uparrow^{X}X$$
 * 27) $$X\rightarrow X = X \uparrow_{1}\uparrow X$$ using this
 * 28) $$\{X, X[1\backslash1\backslash2]X\}$$
 * 29) Repeat steps 1 to 218
 * 30) Repeat steps 1 to 219
 * 31) Repeat steps 1 to 220
 * 32) Repeat steps 1 to 221
 * Create an alternate version of Croutonillion by stopping here. Call this number C4.
 * 1) \(C4\uparrow^{C3\uparrow^{C2\uparrow^{C}C2}C3}C4
 * 2) \(C4\underbrace{\uparrow_{\uparrow_{..._{\uparrow_{\uparrow}}}}}_{C3\underbrace{\uparrow_{\uparrow_{..._{\uparrow_{\uparrow}}}}}_{C2\underbrace{\uparrow_{\uparrow_{..._{\uparrow_{\uparrow}}}}}_{C\underbrace{\uparrow_{\uparrow_{..._{\uparrow_{\uparrow}}}}}_{X}C}C2}C3}C4\)
 * 3) Aarexhydra(x)
 * 4) X + C4
 * 5) X + C3
 * 6) X + C2
 * 7) X + C
 * 8) 10^X
 * 9) X{34}X
 * 10) $$f_\omega(X)$$
 * 11) $$f_{\Gamma_0}(X)$$
 * 12) $$f_{\theta(\Omega^\omega)}(X)$$
 * 13) $$f_{\theta(\Omega^\Omega)}(X)$$
 * 14) $$f_{\theta(\varepsilon_{\Omega+1})}(X)$$
 * 15) $$f_{\theta(\theta_1(\omega))}(X)$$
 * 16) $$f_{\theta(\theta_1(\Omega))}(X)$$
 * 17) $$f_{\theta(\theta_1(\Omega_2))}(X)$$
 * 18) $$f_{\theta(\theta_I(0))}(X)$$
 * 19) $$f_{\theta(\theta_M(0))}(X)$$
 * 20) $$f_{\theta(\theta_K(0))}(X)$$
 * Create an alternate version of Croutonillion by stopping here. Call this number C5.
 * 1) (E100{#&#&#&#&#&#&#&#&#&#& ... &#&#&#&#&#&#&#&#&#&#}100#Sprach Zarathustra100 w/Sprach Zarathustra #s)^X^N, where  N is \(SCG^{N2}(X)\), where N2 is \(SCG^{N3}(X)\), where N3 is \(SCG^{N4}(X)\), where N4 is \(SCG^{N5}(X)\), where N5 is \(SCG^X(X)\).
 * 2) X{X}X (X copies of ^)
 * 3) BB(X)
 * 4) X-xennaplex
 * 5) (Rayo's number)^X
 * 6) Repeat all steps 1-
 * Create an alternate version of Croutonillion by stopping here. Call this number C6.
 * 1) X + C6
 * 2) X + C5
 * 3) X + C4
 * 4) X + C3
 * 5) X + C2
 * 6) X + C
 * 7) 10^X
 * 8) X{34}X
 * 9) $$f_\omega(X)$$
 * 10) $$f_{\Gamma_0}(X)$$
 * 11) $$f_{\theta(\Omega^\omega)}(X)$$
 * 12) $$f_{\theta(\Omega^\Omega)}(X)$$
 * 13) $$f_{\theta(\varepsilon_{\Omega+1})}(X)$$
 * 14) $$f_{\theta(\theta_1(\omega))}(X)$$
 * 15) $$f_{\theta(\theta_1(\Omega))}(X)$$
 * 16) $$f_{\theta(\theta_1(\Omega_2))}(X)$$
 * 17) $$f_{\theta(\theta_I(0))}(X)$$
 * 18) $$f_{\theta(\theta_M(0))}(X)$$
 * 19) $$f_{\theta(\theta_K(0))}(X)$$
 * 20) repeat step 1, step1-2, step 1-2-3,........, step 1-2-3-......400-401 for {[(X$)!(X$)]![(X$)!(X$)]}$ times.
 * 21) Go into reverse order till step 1 (the first one of all this construction) then repeat this process {X![X$]}!{{[X$)!(X$)]![(X$)!(X$)]}$} times.
 * 22) \(X\text{%}\), Warp Notation
 * 23) \(X\text{%}\text{%}\)
 * 24) \(X\text{%}_2\)
 * 25) \(X\text{%}_{\text{%}}\)
 * 26) \(X(1)\)
 * 27) \(X(1)_{(1)}\)
 * 28) \(X(2)\)
 * 29) \(X((1))\)
 * 30) \(X(0_1)\)
 * 31) \(X(0_{0_1})\)
 * 32) \(X(0 \rightarrow 1)\)
 * 33) \(X(0 \rightarrow_2 1)\)
 * 34) \(X(0 \rightarrow_{0_1} 1)\)
 * 35) \(X(0 \rightarrow_{0 \rightarrow 1} 1)\)
 * 36) \(X(0 (1)\rightarrow 1)\)
 * 37) \(X(0 (0 \rightarrow 1)\rightarrow 1)\)
 * 38) X{2320}X
 * 39) $$R_0(X)$$
 * 40) $$R_0(X)=Rayo(X)$$
 * 41) $$R_{\alpha+1}(X)=R_\alpha^X(X)$$
 * 42) $$R_\alpha(X)=R_{\alpha[X]}(X)$$ if $$\alpha$$ is a limit ordinal
 * 43) $$R_\omega(X)$$
 * 44) $$R_{\varepsilon_0}(X)$$
 * 45) $$R_{\Gamma_0}(X)$$
 * 46) $$R_{\theta(\theta_I(0))}(X)$$
 * 47) $$R_{\theta(\theta_M(0))}(X)$$
 * 48) $$R_{\theta(\theta_K(0))}(X)$$
 * 49) Repeat steps 1 to 427 {C, C2, [C3] C4, C4 [C5[C5]C5] C6, C6, C6} times (using BAN)

Croutonillion is $$10^{3X+3}$$.

Guidelines

 * Be creative. Repeat steps, go back and loop.
 * Avoid FGH for non-recursive ordinals. It can grow pretty slowly at first.
 * Explain any notation that may be unclear.
 * Define everything (e.g. "Rayo's function with X-th order logic" -- what's Xth order logic?).