You say you want to explain your idea better. To that end, I am replying.
Moyo wrote:
This is just a poorly thought out example of finding how the naturals will look like once we see them from the perspective of the prime axi's.
My point was that it can be done.
"It" can be done. What is "it?" This is the heart of your inability to express your idea. You refuse to say what idea you're trying to express. What is "it" that can be done?
Moyo wrote:
F(p) = p-1 so i never reddend all the composites.
I do not understand the significance of F in this context. What good does it do to subract 1 from a prime?
Moyo wrote:
it would make it different from a triangle you are right.
I'm not right and I'm not wrong. You were talking about triangles but your picture reddened a square. I am just an observer trying to point out the inconsistency and lack of clarity in your exposition. You reddened a square. What are you trying to say?
Moyo wrote:
look at the bigger picture
Which is what?
Moyo wrote:
..we can assume P(N) , i.e that we have a formulae for generating the nth prime number.
This is a misunderstanding on your part. There is a function P(n) which inputs n and returns the n-th prime So P(1) = 2, P(2) = 3, P(3) = 5, P(4) = 7, P(5) = 11, and so forth.
P exists as a function. A function need not have a formula; indeed, since there are countably many formulas but uncountably many functions (from the naturals to the naturals), it follows that there must be MANY functions that do not have formulas.
On the other hand, there is a simple algorithm for P, called the Sieve of Erotosthenes, that will always let you determine the n-th prime.
https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes. The sieve is not computationally efficient, however.
So from now on, understand two things:
* There is a function P(n) that inputs n and outputs the n-th prime; and
* There's no simple formula for P. Or at least no simple known formula.
Moyo wrote:
This assumption is shown in that the primes are evenly spaced on the axis.
Ok, we are all agreed that you labeled your axes with the primes. But this is just a disguised form of labeling your axes with the natural numbers 1, 2, 3, 4, ... and then replacing each label n with P(n).
Moyo wrote:
Then see how unevenly the naturals are.
Yes, the primes are unevenly distributed, although they do display regularity as described by the prime number theorem.
https://en.wikipedia.org/wiki/Prime_number_theorem The amazing thing is that the distribution of primes is related to natural logarithms. That's interesting, don't you think?
Moyo wrote:
But you nailed it in your second last post. Forgive me , i dont know how to explain stuff from other peoples perspective, i've always thougt that i should give an explanation like how i would like to receive one.
I think you may perhaps have an interesting idea in here somewhere. I'm trying to work with you to figure out what your idea is.
Moyo wrote:
This is a cardinal issue in my intellectual life. i was just as frustrated as you. I have to regroup caus theres no point in having something you cant explain..#Cantor
Well, you could take some of my points to heart and try to explain why you care about F, or why you reddened a square and called it a triangle.
But let's drill down into the reddened square, which is
6 9
4 6
Note that you chose a square on the main diagonal of the lattice. What is the diagonal of the lattice? It's the sequence of squares of primes: 4, 9, 25, 49, 121, ...
So it's no surprise that you have 4 and 9 on the diagonal of your square.
Now, what are the other two numbers? They are P(1) * P(2) and P(2) * P(1), right? Why should this be a surprise? Any 2x2 square on the main diagonal is exactly of that form.
So I am still wondering: What is about that square that you thought was interesting enough to redden it? What it the point you are trying to make?
Are you trying to observe that if, say, 9 = 3x3 = P(2) x P(2) is on the lattice, then the point to its left must be P(1) x P(2)? But this is obvious, right? The axes are labelled P(1), P(2), P(3), etc.
Just tossing out some ideas. Perhaps you can explain why you reddened the square you did, and what it means to you.