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This is the final blog post I will write about Dollars function.

What to solve first?

In order of importance:

• numbers with the lowest & level (Ultimate Array Notation III)

• numbers with least & symbols (Ultimate Array Notation II)

• many &'s solve on lowest to highest & order (Ultimate Array Notation I)

• brackets with the lowest arrow level (Extended Array Notation)

• brackets with the least number of entries (Array Notation)

• brackets with the lowest level (Extended Bracket Notation)

• least nested bracket with the smallest brackets in it (Bracket Notation)

All brackets have the same a$.

Symbols

◆ can be anything

○ is a high-level bracket

◇ is a string of symbols, & and [0] brackets between them

◈ is a string of symbols

The black square is a group of brackets.

Default

An non-indexed thing deafults to 1:

[0] = \([0]_1\)

[0 \(\rightarrow\) 1] = [0 \(\rightarrow_1\) 1]

[0 \(\rightarrow_0\) 1] = [0,1]

[0]&3 = [0](&_1)3

Bracket Notation - Extended Array Notation

In a picture to make it better readable

Dollar function 1





























Ultimate Array Notation I, II, III

Ultimate Array Notation 1 and 2



















FGH

Bracket Notation: \(\varepsilon_0\)

Extended Bracket Notation: \(\Gamma_0\)

Linear Array Notation: \(\vartheta(\varepsilon_{\Omega+1})\)

analysis here

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