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 using BEAF notation. Now that we have x we're going to do this . This is a Superplex ( or )

## Small Uncomputable Numbers (SUN's)

For any small (not really small) uncomputable numbers- we don't use an array notation. Instead we say, .

### Names

is a Superplex

is a Super-duperplex

is a Super-two-duperplex

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 (alternatively ). is a Hyperplex.

## Large Uncomputable Numbers (LUN's)

Next are Large Uncomputable Numbers. . This pattern of repetition follows, so .

## 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 .

Complexed Numbers can also be represented by . is a Supercomplex.

### Totally Uncomputable Numbers (TUN's)

Totally Uncomputable Numbers are Numbers that cannot be represented by Complexed Numbers. They are represented by . , and .

## Infiniplex Function

A Infiniplex (I call it that because it might as well be infinity) is .

.

is an Infinihyperplex.

## Names for Numbers Larger than an Infiniplex

Omegaplex

Infinihyperplex

Infinimega

Omagahyperplex