## FANDOM

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This my extended Rayo's notation (this is meant to be an extension of Rayo's).

## Base

Let's say we have "x". We're going to set x to $((10^{100}\uparrow^{10^{100}}10^{100})\&_{10^{100}}10^{100})$ using BEAF notation. Now that we have x we're going to do this $(x![\underbrace{x,x,...,x}_{\text{x times}}])?$. This is a Superplex ($S$ or $S_{0}$)

## Small Uncomputable Numbers (SUN's)

For any small (not really small) uncomputable numbers- we don't use an array notation. Instead we say, $S_{n}=\underbrace{Rayo_{S_{n-1}}(Rayo_{S_{n-1}}(...Rayo_{S_{n-1}}(n)))}_{\text{n times}}$.

### Names

$S_{0}$ is a Superplex
$S_{1}$ is a Super-duperplex
$S_{2}$ is a Super-two-duperplex
$.$
$.$
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$S_{n}$ is a Super-"n"-duperplex

## Mediocre Uncomputable Numbers (MUN's)

Now we have our mediocre uncomputable numbers- we use an array notation. Now we say $S_{n,m}=\underbrace{S_{S_{._{._{._{S_{n}}}}}}}_{\text{m times}}$ (alternatively $S[n,m]$). $S_{10^{100},10^{100}}$ is a Hyperplex.

## Large Uncomputable Numbers (LUN's)

Next are Large Uncomputable Numbers. $S_{n,m,p}=\underbrace{S_{n,S_{n,_{._{._{._{S_{n,m}}}}}}}}_{\text{p times}}$. This pattern of repetition follows, so $S_{n,m,p,q}=\underbrace{S_{n,m,S_{n,m,_{._{._{._{S_{n,m,p}}}}}}}}_{\text{q times}}$.

## Beyond Uncomputable Numbers (BUN's)

These numbers go beyond what the normal array function can show.

### Complexed Numbers (CPN's)

Complexed Numbers can be are the smallest of the BUN's. They are represented by $C[n,m]=S\underbrace{[n,n,...n]}_{\text{m times}}$.

Complexed Numbers can also be represented by $C^{p}[n,m]=C^{p-1}[n,C[n,m]]$. $C^{\text{Hyperplex}}[\text{Hyperplex},\text{Hyperplex}]$ is a Supercomplex.

### Totally Uncomputable Numbers (TUN's)

Totally Uncomputable Numbers are Numbers that cannot be represented by Complexed Numbers. They are represented by $U^{p}[n,m]$. $U^{1}[n,m]=\underbrace{C^{C^{.^{.^{.^{C^{1}[n,n]}}}}[n,n]}[n,n]}_{\text{m times}}$, and $U^{p}[n,m]=\underbrace{U^{U^{.^{.^{.^{U^{1}[n,m]}}}}[n,m]}[n,m]}_{\text{p times}}$.

## Infiniplex Function

A Infiniplex (I call it that because it might as well be infinity) is $I_{0}=U^{\text{Supercomplex}}[\text{Supercomplex},\text{Supercomplex}]$.
$I_{n}=\underbrace{U^{U^{.^{.^{.^{U^{1}[I_{0},I_{0}]}}}}I_{0},I_{0}]}[I_{0},I_{0}]}_{I_{n-1} \text{times}}$.
$\underbrace{I_{I_{._{._{._{0}}}}}}_{I_{0} \text{ times}}$ is an Infinihyperplex.

## Names for Numbers Larger than an Infiniplex

Omegaplex $I_{\omega}$
Infinihyperplex $\underbrace{I_{I_{._{._{._{0}}}}}}_{I_{0} \text{ times}}$
Infinimega $\underbrace{I_{I_{._{._{._{0}}}}}}_{I_{\omega} \text{ times}}$
Omagahyperplex $\underbrace{I_{\omega^{I_{\omega^{.^{.^{.^{I_\omega}}}}}}}}_{I_{\omega} \text{ times}}$