User:Ynought

My largest number so far is Yallun 7 "My website ""Array hierachy"My notation playground

My googolism playground

My : notation
I will try to make this my fastest growing recursive notation.Here it is.

My graph function "E"
I will try to make this my fastest growing graph function.Here it is.

Ordinal notation
Here it is.

A series of numbers "Yallun"
Here it is.

Monster notation(s)
Here it is.

Classes of numbers
\(\mathcal{O}(a,b)\) is the set of all numbers greater than \(a\) and less or equall to \(b\)

When i say \(\wp=\mathcal{O}(a,b)\) that means that \(\wp\) is the set of \(\mathcal{O}(a,b)\)

Alpha
\(\alpha=\mathcal{O}(0,1)\)

Beta
\(\beta=\mathcal{O}(1,10)\)

Gamma
\(\gamma=\mathcal{O}(10,100)\)

Delta
\(\delta=\mathcal{O}(100,10^{100})\)

Epsilon
\(\epsilon=\mathcal{O}(10^{100},^{100}10)\)

Zeta
\(\zeta=\mathcal{O}(^{100}10,G_{100})\) \(G\) is grahams function

Eta
\(\eta=\mathcal{O}(G_{100},f_{\omega^2}(100))\)

Theta
\(\theta=\mathcal{O}(f_{\omega^2}(100),f_{\omega^\omega}(100)\)

Iota
\(\iota=\mathcal{O}(f_{\omega^\omega}(100),f_{\varepsilon_0}(100))\)

Kappa
\(\kappa=\mathcal{O}(f_{\varepsilon_{0 }} (100),f_{\varepsilon_{100 }} (100))\)

Lambda
\(\lambda=\mathcal{O}(f_{\varepsilon_{100 }} (100)),f_{\zeta_0}(100)))\)

Mu
\(\mu=\mathcal{O}(f_{\zeta_{100 }} (100),f_{\eta_0}(100))\)

Nu
\(\nu=\mathcal{O}(f_{\eta_0}(100),f_{\varphi(\omega,0)}(100))\)

Xi
\(\xi=\mathcal{O}(f_{\varphi(\omega,0)}(100),f_{\text{LVO }} (100))\)

Omicron
\(\omicron=\mathcal{O}(f_{\text{LVO }} (100),f_{C(1)}(100))\)

Pi
\(\pi=\mathcal{O}(f_{C(1)}(100),f_{C(\omega)}(100))\)

Rho
\(\rho=\mathcal{O}(f_{C(\omega)}(100),f_{C(C(1))}(100))\)

Tau
\(\tau=\mathcal{O}(f_{C(C(1))}(100),f_{C(C(\omega))}(100))\)

Upsilon
\(\upsilon=\mathcal{O}(f_{C(C(\omega))}(100),f_{C^{100}(\omega)}(100))\)

Phi
\(\phi=\mathcal{O}(f_{C^{100}(\omega)},f_{C(\Omega)}(100))\)

Chi
\(\chi=\mathcal{O}(f_{C(\Omega)}(100),f_{C(\Omega_\Omega)}(100))\)

Psi
\(\psi=\mathcal{O}(f_{C(\Omega_\Omega)}(100),f_{\text{PTO}(\text{SMAH+})}(100))\)

Omega
\(\Omega=\mathcal{O}(f_{\text{PTO}(\text{SMAH+})}(100),n)\) where \(n\) is larger than the halting time of every turing machine with HUGE+ proof of halting with lenght of at most \(^{^{100}100}100\)

Digamma
\(\digamma=\mathcal{O}(n,\omega)\) the \(n\) from \(\Omega\)

Milestones:
1000.Edit:11.03.2019

...

TEST

\(\frac{\omega}{\omega\frac{\omega}{\omega}\frac{\omega}{\omega\frac{\omega}{\omega }} \frac{\omega}{\omega\frac{\omega}{\omega}\frac{\omega}{\omega\frac{\omega}{\omega }}} \frac{\omega}{\omega\frac{\omega}{\omega}\frac{\omega}{\omega\frac{\omega}{\omega }} \frac{\omega}{\omega\frac{\omega}{\omega}\frac{\omega}{\omega\frac{\omega}{\omega }}} }\frac{\omega}{\omega\frac{\omega}{\omega}\frac{\omega}{\omega\frac{\omega}{\omega }} \frac{\omega}{\omega\frac{\omega}{\omega}\frac{\omega}{\omega\frac{\omega}{\omega }}} \frac{\omega}{\omega\frac{\omega}{\omega}\frac{\omega}{\omega\frac{\omega}{\omega }} \frac{\omega}{\omega\frac{\omega}{\omega}\frac{\omega}{\omega\frac{\omega}{\omega }}}}} \frac{\omega}{\omega\frac{\omega}{\omega}\frac{\omega}{\omega\frac{\omega}{\omega }} \frac{\omega}{\omega\frac{\omega}{\omega}\frac{\omega}{\omega\frac{\omega}{\omega }}} \frac{\omega}{\omega\frac{\omega}{\omega}\frac{\omega}{\omega\frac{\omega}{\omega }} \frac{\omega}{\omega\frac{\omega}{\omega}\frac{\omega}{\omega\frac{\omega}{\omega }}} }\frac{\omega}{\omega\frac{\omega}{\omega}\frac{\omega}{\omega\frac{\omega}{\omega }} \frac{\omega}{\omega\frac{\omega}{\omega}\frac{\omega}{\omega\frac{\omega}{\omega }}} \frac{\omega}{\omega\frac{\omega}{\omega}\frac{\omega}{\omega\frac{\omega}{\omega }} \frac{\omega}{\omega\frac{\omega}{\omega}\frac{\omega}{\omega\frac{\omega}{\omega }}}}}} \frac{\omega}{\omega\frac{\omega}{\omega}\frac{\omega}{\omega\frac{\omega}{\omega }} \frac{\omega}{\omega\frac{\omega}{\omega}\frac{\omega}{\omega\frac{\omega}{\omega }}} \frac{\omega}{\omega\frac{\omega}{\omega}\frac{\omega}{\omega\frac{\omega}{\omega }} \frac{\omega}{\omega\frac{\omega}{\omega}\frac{\omega}{\omega\frac{\omega}{\omega }}} }\frac{\omega}{\omega\frac{\omega}{\omega}\frac{\omega}{\omega\frac{\omega}{\omega }} \frac{\omega}{\omega\frac{\omega}{\omega}\frac{\omega}{\omega\frac{\omega}{\omega }}} \frac{\omega}{\omega\frac{\omega}{\omega}\frac{\omega}{\omega\frac{\omega}{\omega }} \frac{\omega}{\omega\frac{\omega}{\omega}\frac{\omega}{\omega\frac{\omega}{\omega }}}}} \frac{\omega}{\omega\frac{\omega}{\omega}\frac{\omega}{\omega\frac{\omega}{\omega }} \frac{\omega}{\omega\frac{\omega}{\omega}\frac{\omega}{\omega\frac{\omega}{\omega }}} \frac{\omega}{\omega\frac{\omega}{\omega}\frac{\omega}{\omega\frac{\omega}{\omega }} \frac{\omega}{\omega\frac{\omega}{\omega}\frac{\omega}{\omega\frac{\omega}{\omega }}} }\frac{\omega}{\omega\frac{\omega}{\omega}\frac{\omega}{\omega\frac{\omega}{\omega }} \frac{\omega}{\omega\frac{\omega}{\omega}\frac{\omega}{\omega\frac{\omega}{\omega }}} \frac{\omega}{\omega\frac{\omega}{\omega}\frac{\omega}{\omega\frac{\omega}{\omega }} \frac{\omega}{\omega\frac{\omega}{\omega}\frac{\omega}{\omega\frac{\omega}{\omega }}}}}}}} \)

\(\frac{3+\frac{3+\frac{3+\frac{3+\frac{3+\frac{3+\frac{3+\frac{3+\frac{3+\frac{3+\frac{3+\frac{3+\frac{3+\frac{3+\frac{3+\frac{3+\frac{3+\frac{3+\frac{3+\frac{3+}{\Omega }}{\Omega}} {\Omega }} {\Omega }} {\Omega }} {\Omega }}{\Omega}} {\Omega }} {\Omega }} {\Omega }} {\Omega }}{\Omega}} {\Omega }} {\Omega }} {\Omega }} {\Omega }}{\Omega}} {\Omega }} {\Omega }} {\Omega}\)

\(2:(3,3,(1))=2:(3,3,(0)(0))=2:(3,3,(0)2)=f_2^2(2):(3,3,(0))(3,3,(0))\)

\(=f_2^2(2):(3,3,(0))(3,3,f_2^2(2))\) from there on it gets too big too write down i a reasonable amount of time and storage space

\(\begin{eqnarray*} & & 2:(0,2) \\ & & =2:((0,1)^{(0,1)},1) \\ & & =2:((0,1)^{((0,0)^{(0,0)},0)},1) \\ & & =2:((0,1)^{((0,0)^{(0)^{(0)}(0)^{(0) }} ,0)},1) \\ & & =2:((0,1)^{((0,0)^{(0)^{(0)}(0)^{2 }} ,0)},1) \\ & & =2:((0,1)^{((0,0)^{(0)^{(0)}((0)^{1})^{1}(((0)^{0})^{0}((0)^{0})^{0})^{1 }} ,0)},1) \end{eqnarray*}\)