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Ordinal Notations 0 : Up to the Gamma Fixed Point
Introducing some low level ordinal notations. Using
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CSBN - Chronolegend's Square Bracket Notation Level 1
- Concepts
- Numbers: non-negative integers, represented by lower case letters.
- Strings: Collections of numbers and separators, represented by capital letters
- Non-Empty String: A string that contains at least one number and zero or more separators.
- Main String: A string that is not a substring nor enclosed by square brackets.
- Separators: Numbers enclosed by square brackets []
- Substrings: Strings that are parts of another string
- Argument: A number at the end of the main string, the letter n is reserved for it.
- Syntax Rules
- A number ends the main string
- Except in the main string, Separators must always be inbetween two numbers
- Strings can be zero, or they can be empty, except this would create an illegal string (check above rule)
- If the main string contai…
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CCBN - Chronolegends Curly Bracket Notation
Step 1: {0}n = n^n
Step 2: {X+1}n = {X}...{X}n with n {X}'s