## FANDOM

10,837 Pages

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.