06/24/2022, 10:29 AM
This is proving to be much more difficult than I thought. But I see the solution. I have attached here a run down of the case \(0 \le s \le 1\) and \(x,y > e\), where we are trying to find the appropriate \(\varphi\) function to solve goodstein. Everything I have prepared in this paper is solid and shown 100%. But it does not produce semi-operators. It solely solves it in limited scenarios. But, this is the solution, and the framework of the proof I want to present. I am almost there for the real line.
The trouble is, I have to introduce complex variables. I have predominantly used real values in this draft. And it holds me back from finding the correct answer. I have working code for a good amount of values, and a lot of garbage code for other values. But a shape of how these objects are looking is starting to appear. I apologize for the rough shape of this paper. I am sending it to everyone here rough, because it is very preliminary. But It uses much of your ideas, even if you don't see how.
This is solely the real line case that I have presented so far. I've come to realize we need to look at the domain \(\Re(y)> e, |\Im(y)| < \pi\). This is just to provide a more efficient proof of existence. It also let's us explain how my code is working. My code fails for a large body of values, but I can explain how it is failing, but I need to use complex dynamics. By this, we can shape out how to correct the error and make the code work and the math sound.
Analytically_interpolating_addition__multiplication_and_exponentiation_FIRST_PART.pdf (Size: 328.2 KB / Downloads: 860)
Any way, just read this to get an update on what I'm getting at! It's still a rough draft! I have absolutely made mistakes! I need to make better references! I need to flesh out some of the proofs! I just thought I'd explain the methodology.
The trouble is, I have to introduce complex variables. I have predominantly used real values in this draft. And it holds me back from finding the correct answer. I have working code for a good amount of values, and a lot of garbage code for other values. But a shape of how these objects are looking is starting to appear. I apologize for the rough shape of this paper. I am sending it to everyone here rough, because it is very preliminary. But It uses much of your ideas, even if you don't see how.
This is solely the real line case that I have presented so far. I've come to realize we need to look at the domain \(\Re(y)> e, |\Im(y)| < \pi\). This is just to provide a more efficient proof of existence. It also let's us explain how my code is working. My code fails for a large body of values, but I can explain how it is failing, but I need to use complex dynamics. By this, we can shape out how to correct the error and make the code work and the math sound.
Analytically_interpolating_addition__multiplication_and_exponentiation_FIRST_PART.pdf (Size: 328.2 KB / Downloads: 860)
Any way, just read this to get an update on what I'm getting at! It's still a rough draft! I have absolutely made mistakes! I need to make better references! I need to flesh out some of the proofs! I just thought I'd explain the methodology.