User blog:Googleaarex/Dollar Function: final version Rules

Bracket Notation
\(\cir\) will be anything

\(\bullet\) is group of brackets

0. \(a$\) = \(a\)

1. \(a$b\cir\) = \((a+b)$\cir\)

2. \(a$\bullet [0]\cir \bullet\) = \(a$\bullet a\cir \bullet\)

3. \(a$\bullet [b]\cir \bullet\) = \(a$\bullet \underbrace{[b-1]...[b-1]}_{a}\cir \bullet\)

Extended Bracket Notation
3a. \(a$\bullet [0]_\cir\cir \bullet\) = \(a$\bullet \underbrace{[b-1]_\cir ... [b-1]_\cir}_{a}\cir \bullet\)

4. \(a$\bullet [\cir]_1 \bullet\) = \(a$\bullet [\cir] \bullet\)