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I have made some interesting stuff.

Y function

Y(n) is defined as the maximal output of a notation uses n rules, for the final output of Y(n), you must place n in all the variables.

  • In the base rule you may use addition once, or multiplication once, or exponentation once.
  • The other rules are based on recursion.
  • Default value is 0.
  • The recursion is based on a base value.
Y function
Type Uncomputable
Grow rate \(\omega_1^\text{CK}\)


Y(1) = 2 , using f(a) = a+a

Y(2) ≥ mega, using f(a,0) = \(a^{a}\) and f(a,b) = f(f(...(f(f(a,b-1),b-1),b-1)...),b-1) with a nests

Y(3) \(\geq f_{\varepsilon_0}(3)\) - uses my bracket notation

Y(4) \(\geq f_{\Gamma_0}(4)\) - uses my 4-rule extended bracket notation

Y(5) \(\geq f_{\vartheta(\Omega^\omega)}(5)\)

3 rules of bracket notation +

a$[0,0...0,0,b#] = a$[0,0,0,[0,0,0,[0,0,0,[...[0,0,0,[0,0...0,0,b-1#],b-1#]...],b-1#],b-1#],b-1#]

[#0] = #


Y(6) \(\geq f_{\vartheta(\Omega^\Omega)}(6)\)

Rules of Y(5) +

a$([0]) = a$[a,a,a...a,a,a] with a a's


Y(7) \(\geq f_{\vartheta(\varepsilon_{\Omega+1})}(7)\) Uses my Linear Array Notation

Y(8) \(\geq f_{\vartheta(\Omega_{2})}(8)\) Uses my Extended Array Notation

Second Y function

Second Y function
Type Uncomputable
Grow rate \(\omega_1^{CK} 2\)ωCK1 ×2
  • In the base rule you may use the normal Y function
  • The other rules are based on recursion.
  • Default value is 0.
  • The recursion is based on a base value.

¥ function

The output of ¥(n) is the biggest number definable using n characters of text in any language , but you may not use ¥ function in the definition, e.g. ¥(7) = ¥(¥(9))

Ultimate ₩ythagoras Number = ¥1000(1000) >> Hollom's number

Hollom's number takes 3500 symbols to define.

Numbers with Y functions

Y(1000) = Omega Y Universe

\(Y_2(1000)\) = Omega Y Multiverse

¥(1000) = Alpha-Omega Universe Ultimate

Omega-Amazing ₩ythagoras Universe  = ¥1000(1000)

Hyper € Notation

This is my variant of Hyper E notation.

E# and xE# are the same, but the E = €

E^ = €\(\downarrow\) , same rules but downarrows.

€@a#\(\downarrow_{c@}\)#b = €@#(...((#\(\downarrow_{c-1@}\#))\downarrow_{c-1@}\)#)...\(\downarrow_{c-1@}\)#)\(\downarrow_{c-1@}\)#a b nests

€@a#\(\downarrow_{\#}\)#b = €@a#\(\downarrow_{b}\)#a

also, limit is only \(\zeta_0\) for €a#\(\downarrow_{\#\downarrow_{\#\downarrow_{...{\#\downarrow_{\#}\#}...}\#}\#}\)#a with a nests

Dollars function

See blog post about dollars function.

Dollars function
Based on Exponentation
Grow rate >> \(f_{\psi_I(0)}(n)\)

KAI X~

a!(0@) = a!

a!(b) = ((...((a!(b-1#))!(b-1#))...)!(b-1#))!(b-1#)

a!(@,0,b#) = a!(@,a,b-1#)

'# can be anything

@ is a row of zeroes


\(A_{0}(a)\) = a!(a,a,a...a,a,a)

\(B_{0}(a)\) = \(A_{(a,a,a...a,a,a)}(a)\)

\(\Gamma_{0}(a)\) = \(B_{(a,a,a...a,a,a)}(a)\)

arrays work the same.

X(1) = Omega_75!(75!)

X(n) = Omega_(X(n-1)!)(X(n-1)!)



U = 75!(75!(...(75!(75!))...) with 75! nests

U~ = X(X(X(...(X(X(U)))...))) with U nests

KAI(1) = X(X(X(...(X(X(U~)))...))) with U~ nests

KAI(n) = X(X(X(...(X(X(KAI(n-1))))...))) with KAI(n-1) nests

KAI U~ = KAI(U~)

KAI X~ = KAI(KAI(...(KAI(KAI(KAI U~)))...)) with KAI U~ nests.

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