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This next extension is pretty obvious. I turned the LEVEL to an array.

More Rules

Let \# and \#^* represent rest of ARRAY/LEVEL. For \#, there MUST be a rest of ARRAY/LEVEL but for \#^*, it's optional.

Let a, b, and c_n be COUNTING NUMBERS.

As usual, here are the new rules:

  • a(1)\{0\} = a (I know. The LEVEL has a different numbering system unlike the ARRAY)
  • a(c_1,c_2,\cdots)\{\#, 0\} = a(c_1,c_2,\cdots)\{\#\}
  • a(c_1,c_2,\cdots)\{\underbrace{0, 0, \cdots, 0}_{n}, b, \#^*\} = a(c_1,c_2,\cdots)\{\underbrace{a, a, \cdots, a}_{n}, b-1, \#^*\}
  • a(c_1 + 1, c_2,\cdots)\{0\} = a(c_1, c_2,\cdots)\{\underbrace{a, a, \cdots, a}_{a}\}
  • a(\underbrace{1, 1, \cdots, 1}_{n}, c+1, \#^*)\{0\} = a(\underbrace{a, a, \cdots, a}_{n}, c, \#^*)\{0\}
  • a(c, \#^*)\{b, \#^*\} = a\uparrow^ca(c, \#^*)\{b-1, \#^*\}
  • a(\#, 1)\{\#\} = a(\#)\{\#\}

Simple enough.

Stuff

Let's try to evaluate 2(1, 2)\{1\}.

2(1, 2)\{1\}

  • =4(1,2)\{0\}
  • =4(4,1)\{0\}
  • =4(4)\{0\}
  • =\text{Superquadribal}

We can rewrite our numbers too!

  • \text{Biblex} = \text{Bibal}(1,2)\{0\}
  • \text{Bidublex} = \text{Biblex}(1,2)\{0\}

Extending further

As you can see right now, this notation can be further extended to include a multidimensional ARRAY and a hyperdimensional LEVEL! We can even probably add multiple BASEs! Great!

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