User blog:Bubby3/Stronger Bird's Array notation

Did you know you can make ~ behave like ,, in SAN if you change a few rules.

Everything up to [1[1~3]2] remains unchanged.

Comparisons between mine and Bird's expression.

[1[1[1~3]2~2]2[1~3]2] in my system is equal to [1[1~3]3] in Bird's system.

[1[1[1~3]2~2]3[1~3]2] in my system is equal to [1[1~3]4] in Bird's system.

[1[1[1~3]2~2]1[1[1~3]2~2]2[1~3]2] in my system is equal to [1[1~3]1[1~3]2] in Bird's system.

[1[2[2~3]2~2]2[1~3]2] in my system is equal to [1[2~3]2] in Bird's system.

[1[1\2[1~3]2~2]2[1~3]2] in my system is equal to [1[1/2~3]2] in Bird's system.

[1[1[1[1~3]2~2]2[1~3]2~2]2[1~3]2] in my system is equal to [1[1[1~3]2~3]2] in Bird's system.

[1[1[1[1[1~3]2~2]2[1~3]2~2]2[1~3]2~2]2[1~3]2] in my system is equal to [1[1[1[1~3]2~3]2~3]2] in Bird's system.

[1[1~3]3] in my system is equal to [1[1~4]2] in Bird's system.

[1[1~3]1,2] in my system is equal to [1[1~1,2]2] in Bird's system.

[1[1~3]1[1[1~3]2~2]2] in my system is equal to [1[1~1[1~3]2]2] in Bird's system.

[1[1~3]1[1~3]2] in my system is equal to [1[1~1~2]2] in Bird's system.

[1[2~3]2] in my system is equal to [1[1[2/32]2]2] in Bird's system.

[1[1/2~3]2] in my system is equal to [1[1[1/2/32]2]2] in Bird's system.

[1[1[1~3]2~3]2] in my system is equal to [1[1[1~2/32]2]2] in Bird's system.

[1[1[2~3]2~3]2] in my system is equal to [1[1[1[2/32]2/32]2]2] in Bird's system.

[1[1~4]2] in my system is equal to [1[1[1/33]2]2] in Bird's system.

[1[1~3]2[1~4]2] in my system is equal to [1[1~2[1/33]2]2] in Bird's system.

[1[1[1~4]2~3]2[1~4]2] in my system is equal to [1[1[1/33]3]2] in Bird's system.

[1[1~4]3] in my system is equal to [1[1[1/34]2]2] in Bird's system.

[1[1~4]1[1~4]2] in my system is equal to [1[1[1/31/32]2]2] in Bird's system.

[1[2~4]2] in my system is equal to [1[1[1[2/42]2]2]2] in Bird's system.

[1[1~5]2] in my system is equal to [1[1[1[1/43]2]2]2] in Bird's system.

[1[1~6]2] in my system is equal to [1[1[1[1[1/53]2]2]2]2] in Bird's system.

[1[1~7]2] in my system is equal to [1[1[1[1[1[1/63]2]2]2]2]2] in Bird's system.

[1[1~1,2]2] in my system is equal to the limit of Hierarchical Hyper-Nested Array Notation.

[1[1~1/2]2] in my sistem is equal to the limit of Bird's Array notation.

We beat BAN with only 2-hyperseperators. How far can this notation go?

[1[1~1~2]2] has level \(\psi_I(0)\)

[1[1~1~2]3] has level \(\psi_I(1)\)

[1[1~1~2]1[1~1~2]2] has level \(\psi_I(I)\)

[1[1~1~2]1[1~1~2]1[1~1~2]2] has level \(\psi_I(I^2)\)

[1[2~1~2]2] has level \(\psi_I(I^\omega)\)

[1[1[1~1~2]2~1~2]2] has level \(\psi_I(I^I)\)

[1[1~2~2]2] has level \(\psi_I(\varepsilon_{I+1})\) or \(\psi_{\Omega_{I+1}}(0)\)

[1[1~3~2]2] has level \(\psi_{\Omega_{I+2}}(0)\)

[1[1~1[1~1~2]2~2]2] has level \(\psi_{\Omega_{I*2}}(0)\)

[1[1~1~3]2] has level \(\psi_{I_2}(0)\)

[1[1~1~1~2]2] has level \(\psi_{I(1,0)}(0)\)

[1[1[2/32]2]2] has level \(\psi_{I(\omega,0)}(0)\)