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/Let \(*\) is anything and \(*_2\) is rest of \(()\)-array.

0. \(En = 10^n\)

0a. \(E(n)m = n^m\)

1. \(E* n(\#)m = \underbrace{E*E* ... E*E*}_{m} n\)

2. \(E* n((*_2)*\#)l = E* \underbrace{n(*_2)n ... n(*_2)n}_{l}\)

3. \(E* n(*_2 \#)l = E* n(*_2 l)n\)

Note: \(\#^1 = \#\), \(\#^2 = \#\#\), \(\#^3 = \#\#\#\), etc.

Numbers

  • Gooline = \(E100(\#)100\)
  • Gooduoline = \(E100(\# * 2)100\)
  • Gootrioline = \(E100(\# * 3)100\)
  • Goosquare = \(E100(\#^2)100\)
  • Goolinesquare = \(E100(\#^2 + \#)100\)
  • Gooduosquare = \(E100(\#^2*2)100\)
  • Goocube = \(E100(\#^3)100\)
  • Goomega = \(E100(\#^\#)100\)
  • Goomegaline = \(E100(\#^{\# + 1})100\)
  • Goomegamega = \(E100(\#^{\#*2})100\)
  • Goomquare = \(E100(\#^{\#^2})100\)
  • Goomube = \(E100(\#^{\#^3})100\)
  • Googiga = \(E100(\#^{\#^\#})100\)
  • Googuare = \(E100(\#^{\#^{\#^2}})100\)
  • Gootera = \(E100(\#^{\#^{\#^\#}})100\)
  • Goopeta = \(E100(\#^{\#^{\#^{\#^\#}}})100\)
  • Googooline = \(E100(E(\#)\#(\#)\#)100\)
  • Googoosquare = \(E100(E(\#)\#(\#^2)\#)100\)
  • Googoomega = \(E100(E(\#)\#(\#^\#)\#)100\)
  • Googoogooline = \(E100(E(\#)\#(E(\#)\#(\#)\#)\#)100\)

Extension!

Let \(E* n(*_2 \#_1)l\) is \(E* n(\underbrace{*_2 E(\#)\#(... (*_2 E(\#)\#(\#)\#) ...)\#}_{l})n\).

And \(E* n(*_2 \#_x)l\) is \(E* n(\underbrace{*_2 E(\#_{x-1})\#_{x-1}(... (*_2 E(\#_{x-1})\#_{x-1}(\#_{x-1})\#_{x-1}) ...)\#_{x-1}}_{l})n\).

0. \(En = 10^n\)

0a. \(E(n)m = n^m\)

1. \(E* n(\#)m = \underbrace{E*E* ... E*E*}_{m} n\)

2. \(E* n((*_2)*\#)l = E* \underbrace{n(*_2)n ... n(*_2)n}_{l}\)

3. \(E* n(*_2 \#)l = E* n(*_2 l)n\)

4. \(E* n(*_2 \#_x)l = E* n(\underbrace{*_2 E(\#_{x-1})\#_{x-1}(... (*_2 E(\#_{x-1})\#_{x-1}(\#_{x-1})\#_{x-1}) ...)\#_{x-1}}_{l})n\)

4a. \(* \#_0 * = * \# *\)

Extension of Extension!!

Let \(E* n(\#_{,1})l = E* n(\underbrace{\#_{\#_{,...}}}_{l})n\). Then \(E* n(\#_{,1}\#_{,1})l = E* n(\underbrace{\#_{,1}\#_{\#_{,1}\#_{,...}}}_{l})n\), \(E* n(\#_{,1}^\#)l = E* n(\underbrace{\#_{,1}\#_{,1} ... \#_{,1}\#_{,1}}_{l})n\), etc.

Let \(*_3\) is rest of \(\#\)-array.

5. \(E* n(*_2 \#_{,,...,,x+1 *_3})l = E* n(\underbrace{*_2 \#_{,,...,*_2 \#_{,,...,\#_{...},x *_3},x *_3}}_{l})n\)

5a. \(E* n(*_2 \#_{*_3 ,})l = E* n(*_2 \#_{*_3})l\)

Forever extending...

Support \(,^2 = ,,\), \(,^3 = ,,,\), etc.

6. \(E* n(*_2 \#_{,,...,,^{y}x+1 *_3})l = E* n(*_2 \#_{,,...,\underbrace{,,...,,}_{y}x+1 *_3})l\)

Forever extending... II

First, we have \(E* n(*_2 \#_{,_{1}x+1})m = E* n(*_2 \#_{\underbrace{,^{,^{... ,^{,1,_{1}x}1,_{1}x ...}1,_{1}x}1,_{1}x}_{m}})n\).

Then \(E* n(*_2 \#_{,_{2}x+1})m = E* n(*_2 \#_{,_{1}^{,_{1}^{... ,_{1}^{,_{1},_{2}x},_{2}x ...},_{2}x},_{2}x})m\), \(E* n(*_2 \#_{,_{3}x+1})m = E* n(*_2 \#_{,_{2}^{,_{2}^{... ,_{2}^{,_{2},_{3}x},_{3}x ...},_{3}x},_{3}x})m\), etc.

Rules coming soon!

On the next level...

Coming Soon!

Full Ruleset

  1. \(En = 10^n\)
    1. \(E(n)m = n^m\)
  2. \(E* n(\#)m = \underbrace{E*E* ... E*E*}_{m} n\)
  3. \(E* n((*_2)*\#)l = E* \underbrace{n(*_2)n ... n(*_2)n}_{l}\)
  4. \(E* n(*_2 \#)l = E* n(*_2 l)n\)
  5. \(E* n(*_2 \#_x)l = E* n(\underbrace{*_2 E(\#_{x-1})\#_{x-1}(... (*_2 E(\#_{x-1})\#_{x-1}(\#_{x-1})\#_{x-1}) ...)\#_{x-1}}_{l})n\)
    1. \(* \#_0 * = * \# *\)
  6. \(E* n(*_2 \#_{,,...,,x+1 *_3})l = E* n(\underbrace{*_2 \#_{,,...,*_2 \#_{,,...,\#_{...},x *_3},x *_3}}_{l})n\)
    1. \(E* n(*_2 \#_{*_3 ,})l = E* n(*_2 \#_{*_3})l\)
  7. \(E* n(*_2 \#_{,,...,,^{y}x+1 *_3})l = E* n(*_2 \#_{,,...,\underbrace{,,...,,}_{y}x+1 *_3})l\)

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