Number Language Creator Number

NLCN (Number Language Creator Number) is R(R(10^100,10^100),R(10^100,10^100)) using the R function. This number was coined by Thisisapasswordsothere on 8/08/24https://sites.google.com/view/amr073snumbers/number-language-creator-number Retrieved Aug 7 2024 (NZT, may appear as 7/08/24 for some of you)
The function R(a,b) is the largest finite number you can make using "a" symbols which are defined using another set of symbols. This function scans over every single symbol until it reaches the end without reseting (which is a function to reset the scanning, without reseting the symbols or variables).
== Known values of R(a,b) ==
There aren't many of these, so extending this will be helpful.
S(n,4)≥n because of the rule: a>Sa. Since this function scans over the characters until it reaches the end without reseting, for each symbol, "a" (aka the answer variable) increases by 1. So XX is 2 because it first scans the first X, adds 1 to "a" and doesn't reset, then it scans the second X, adds one to "a" and doesn't reset, then it halts. At the end "a" is equal to 2. This function basically counts the amount of symbols, so S(1,4) can be X inputted in to this rule, S(2,4) can be XX inputted in to this rule, and so on.
S(a,b+3)≥ab (for b>0): This is true because of the rule: "a>...b S's...a" which is the same as the last, but it adds b to a for each character.
S(a,71)≥a2^a because of this code:
(Sx_0=S)=(x_1>Sx_1)((x_0=S)A(NSx_1=S))=((C>XX)(Sx_1>x_1))((x_0=S)A(Sx_1=S))=(a>Sa)(A_S=NaN)=((x_0>S)(N(Sx_1=S)=R))
which is pretty complicated, but we can simplify it:
(Sx_0=S)=(x_1>Sx_1): If x_0+1=1 then set x_1 to x_1+1
((x_0=S)A(NSx_1=S))=((C>XX)(Sx_1>x_1)): if x_0=1 and not x_1+1=1, then: change the current character to XX and set x_1+1 to x_1 (which is subtracting 1).
((x_0=S)A(Sx_1=S))=(a>Sa): if x_0=1 and x_1+1=1 then set a to a+1
(A_S=NaN)=((x_0>S)(N(Sx_1=S)=R)): if the character 1 after is Not a Number, then set x_0 to 1 and if not x_1+1=1 then reset.
This basically counts the symbols and stores it in the variable x_1. Once done counting, it sets x_0 to 1 and resets. Then it duplicates the X's, subtracts 1 from x_1 and resets, it keeps doing this until x_1=0. Once x_1=0, it counts all the X's and stores it inside the answer variable.
== Source ==
Category:Uncomputable
Category:Numbers based off of Rayo's number
Category:Numbers by Thisisapasswordsothere