Tiered Arrow Notation

This page will show you how powerful TAN can be. Surpassing Katakana's Extended Arrow Notation's Limit.

First, the usual arrows.
a ↑ b = a * a * a * a * a * a ... [b times]
a ↑↑ b = a ↑ a ↑ a ↑ a ↑ a ↑ a ... [b times]
a ↑↑↑ b = a ↑↑ a ↑↑ a ↑↑ a ↑↑ a ↑↑ a ... [b times]

In general...
a ↑ᶜ b = a ↑ᶜ ⁻ ¹ a ↑ᶜ ⁻ ¹ a ↑ᶜ ⁻ ¹ a ↑ᶜ ⁻ ¹ a ↑ᶜ ⁻ ¹ a ... [b times]

Now its time for the big guns.
a ⇑ b = a ↑ᵇ a = a{b}a = a [↑] b
Boogol = 10 ⇑ 100 = 10 ↑¹⁰⁰ 10 = 10{100}10 = 10 [↑] 100
a ⇑↑ b = a ⇑ a ⇑ a ⇑ a ⇑ a ⇑ a ... [b times] = a{{1}}b = a [↑]↑ b
G₆₄ = 3 ⇑↑ 65 = 3{{1}}65 = 3 [↑]↑ 65
a ⇑↑↑ b = a ⇑↑ a ⇑↑ a ⇑↑ a ⇑↑ a ⇑↑ a ... [b times] = a{{2}}b = a [↑]↑↑ b

(TBA)