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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 COUNTING 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, \#\} = a(c)\{\underbrace{a, a, \cdots, a}_{\text{n}}, b-1, \#\}
  • 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\}


Numbers

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. :)

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