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.