Notation Array Notation

Notation Array Notation, although it sounds redundant, is a very quickly growing function. It catalogues all the levels of operation. It is also known as NaN (but do not get it confused with Not A Number)!!! The rules for the notation are as follows.

Rules
1. follows a similar rule to that of the Hyper-L notation parenthesis

2. Placed in a parenthesis

3. The first and last number (3,3) tells you which numbers are on each side of the operation

4. the brackets {} tell you the notation level (addition is 1, mult and exp is 2, etc.)

5. They also tell you which level of operation in the notation you are describing

An example: (4{3,2}2)

In this example, 4 and 2 are on both sides of the operation 3 tells you it is Up Arrow Notation 2 tells you there are 2 up arrows separating the 4 and 2

Levels
The levels are:

Level One (addition) = (x{1,1}x) Ex: (3{1,1}1) = 3+1 = 4

Level Two (mult and exp ) = (x{2,1}x) for mult, (x{2,2}x) for single exp Ex: (4{2,1}3) = 4*3 = 12; (4{2,2}3) = 4^3 = 64; (4{2,3}3) = 4^3^3 = 262144

Level Three: (arrow ) = (x{3,n}x) Ex: (10{3,5}6) = 10^^^^^6 (^ is an up arrow)

Level Four: (Conway ) = (x{4,n}x) Ex: (4{4,4}4) = 4->4->4->4 = Conway's Tetratet

Level 5: (Alpha) = (x{5,n}x) Ex: (3{5,6}4} = 3AAAAAA4

For those beyond notation:

Level 29: Not29 (3{29,3}3)

Level 30: Not30 (3{30,3}3)