## FANDOM

10,828 Pages

This notation is based on the Steinhaus-Moser Notation. For now let's call this BA and not BAL. (BASE, ARRAY, LEVEL; no LEVEL for now :P )

## Definition

Let $\#$ denote rest of array. Let $a$ and $b$ be natural numbers.

Rules:

• $a\{0\} = a$ (a is called the BASE)
• $a\{\#, 0\} = a\{\#\}$ (I chose 0 for some reason)
• $a\{\underbrace{0, 0, \cdots, 0}_{\text{n}}, b + 1, \#\} = a\{\underbrace{a, a, \cdots, a}_{\text{n}}, b, \#\}$
• $a\{b, \#\} = a^a\{b-1, \#\}$

Obviously, the ARRAY is inside the curly braces.

## Others

I found that:

• $\text{Mega} = 2\{0, 2\} = 256\{256\}$

$a\{0, b\}$ represents $a$ inscribed in a $b+3$-gon in Steinhaus-Moser Notation. Therefore,

• $\text{Moser} = 2\{0, 2\{0, 2\}-3\} = 2\{0, \text{Mega}-3\}$

## Numbers

### Bal Series

Cannibal

$\text{Cannibal} = 0$

It ate itself.

Unibal

$\text{Unibal} = 1\{1\} = 1$

Yes, I had to define this. :)

Bibal

$\text{Bibal} = 2\{2, 2\}$

This is equal to 256 inside a pentagon.

Tribal

$\text{Tribal} = 3\{3, 3, 3\}$

Yay, it's in the dictionary! LOL

$\text{Quadribal} = 4\{4, 4, 4, 4\}$

Skip a few ...

Decabal

$\text{Decabal} = 10\{10, 10, 10, 10, 10, 10, 10, 10, 10, 10\}$

King Bal

$\text{King Bal} = 2218\{\underbrace{2218, 2218, \cdots, 2218}_{2218}\}$

I like this one. XD

That's it for now. In the next part, I will redefine these numbers to make them look simpler. I'll post Part 2 sometime later. :)