User blog:King2218/BAL Notation Part 2

This time, I introduce the LEVEL.

New Rules
Let $$\#$$ represent rest of array. (There MUST be a rest of array)

Let a, b, and c be NATURAL NUMBERS.

Rules:


 * $$a(1)\{0\} = a$$ (The number inside the parentheses is the LEVEL.)
 * $$a(c)\{\#, 0\} = a(c)\{\#\}$$
 * $$a(c)\{\underbrace{0, 0, \cdots, 0}_{\text{n}}, b + 1, \#\} = a(c)\{\underbrace{a, a, \cdots, a}_{\text{n}}, b, \#\}$$
 * $$a(c + 1)\{0\} = a(c)\{\underbrace{a, a, \cdots, a}_{a}\}$$
 * $$a(c)\{b, \#\} = a\uparrow^ca(c)\{b-1, \#\}$$

The LEVEL was actually a representation of the number of braces like so:


 * $$3\{\{3\}\} = 3(2)\{3\}$$

Bal Series
I exclude the Cannibal and the Unibal for now.

$$\text{Bibal} = 2(2)\{0\}$$

$$\text{Tribal} = 3(2)\{0\}$$ (just a coincidence here)

$$\text{Quadribal} = 4(2)\{0\}$$

$$\text{Decabal} = 10(2)\{0\}$$

$$\text{King Bal} = 2218(2)\{0\}$$

$$\text{Balgong} = 100000(2)\{0\}$$

Superbal Series
$$\text{Superbibal} = 2(2)\{0\} = \text{Bibal}$$

$$\text{Supertribal} = 3(3)\{0\}$$

$$\text{Superquadribal} = 4(4)\{0\}$$

$$\text{Superdecabal} = 10(10)\{0\}$$

$$\text{Superior Bal} = 2218(2218)\{0\}$$

$$\text{Superbalgong} = 100000(100000)\{0\}$$

Blex Series
$$\text{Biblex} = \text{Bibal}(\text{Bibal})\{0\}$$

$$\text{Triblex} = \text{Tribal}(\text{Tribal})\{0\}$$ (awww it's not a word anymore)

$$\text{Quadriblex} = \text{Quadribal}(\text{Quadribal})\{0\}$$

$$\text{Decablex} = \text{Decabal}(\text{Decabal})\{0\}$$

$$\text{King Blex} = \text{King Bal}(\text{King Bal})\{0\}$$

$$\text{Blexigong} = \text{Balgong}(\text{Balgong})\{0\}$$

Dublex Series
$$\text{Bidublex} = \text{Biblex}(\text{Biblex})\{0\}$$

$$\text{Tridublex} = \text{Triblex}(\text{Triblex})\{0\}$$

$$\text{Quadridublex} = \text{Quadriblex}(\text{Quadriblex})\{0\}$$

$$\text{Decadublex} = \text{Decablex}(\text{Decablex})\{0\}$$

$$\text{King Dublex} = \text{King Blex}(\text{King Blex})\{0\}$$

$$\text{Dublexigong} = \text{Blexigong}(\text{Blexigong})\{0\}$$

and so on...

Next Part?
You might have noticed that I enclosed the LEVEL inside parentheses. It's because I'm also going to turn it into an array! But that will be in Part 3. :)