75xsvbj4xS4pgUWgWg3ZB6tqHbsQz1UhpD9gycqmV4QfO64dnb
I don't know whether this sequence terminates or not, this sequence came to my mind when I was studying Godsteinn's theorem but still, maybe this sequence will continue to converge to infinity, maybe you can tell whether this sequence will end or not because I'm a bit no doubt about this, it's not for serious functions like Prss or Godsteinn sequence
actually the definition is quite short, chatgpt has made me the python code for this but still the original idea is my own, chatgpt said that maybe this sequence is unlikely to converge to infinity because the system is continuously cycling, maybe later I will add a new definition
(1) Take a number \(n\) in decimal
(2) Convert \(n)\ to binary number system
(3) Consider the binary representation as…
Reverse mathematics and rank functions for directed graphs
Citation: Hirst, Jeffry L. "Reverse mathematics and rank functions for directed graphs." Archive for Mathematical Logic 39.8 (2000): 569-579.
A rank function for a directed graph $G$ assigns elements of a well ordering to the vertices of $G$ in a fashion that preserves the order induced by the edges. While topological sortings require a one-to-one matching of vertices and elements of the ordering, rank functions frequently must assign several vertices the same value. Theorems stating basic properties of rank functions vary significantly in logical strength. Using the techniques of reverse mathematics, we present results that require the subsystems $\mathbf{R C A}_{0}, \mathbf{A C A}_{0}, \mathbf{A T R}_{0}$, and $\boldsymbol{\Pi}_{1}^{1}-\m…
some point parable imitates cantor normal form
I've actually been stuck in the ordinal ω^ω^ω for a long time and couldn't get out of it, why even though I had applied the Saibian method in inner argument notation but it still didn't work, reaching epsilon was my dream at that time one day I got enlightenment and finally I use a method that I call "the climbing method" this method appears in ordinal analysis, you might call this method CNF or something like that, the climbing method is quite easy to generalize, I will try to give an example, remember that the number at the end is not f_e0 but g_e0 in SGH, in the future I will just use the hardy hierarchy,
an infinite number of marbles are provided and a finite number of pots are also provided,
the exact number of pots is 6.02214076 × 1023…
rough prototype for nothing notation beyond e0 (1000th edit)
This is a prototype that still needs further analysis, this analysis comes from ordinal analysis and could be wrong depending on which fundamental sequence you use because it is different so sorry if there are mistakes because this is still premature, thank you
Nothing notation sub notation:
Basic nothing notation (BNN) up to (imitating multi argument veblen function, not sure, ill defined)
Legional nothing notation (LNN) up to BEYOND (It hasn't been created yet because I don't understand about OCF)