After Reimann

What is the basis for reason? And mathematics?

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Moyo
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Re: After Reimann

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wtf wrote:Symmetry group" is a technical term in math. https://en.wikipedia.org/wiki/Symmetry_group

Is that what you mean? Or do you mean something different?
Thats what i mean.
wtf wrote: Moyo wrote:
that contains other statements that have the same symmetry like your version of the opposite of the pi function.



"My" version? Do you agree that pi(5) = pi(6) = 3, and that therefore the inverse of pi is a multi-valued relation and not a function?
Yes. But there are other statements. See below
wtf wrote:Opposite being the rule for getting from one point to another," i
Consider 3 mirrors spaced apart at the points of a triangle at 45 degrees to each other. They all contain a reflection of

each other.
wtf wrote:Are you talking about two different functions? So we have:

1) The prime counting function pi(x) that returns the number of primes less than or equal to a real number x; and

2) The function F(n) = n - 1.

Is that right? You're using two distinct functions in your argument? If so, that's fine. It's just that you go back and forth between them with a lack of clarity.
F(n) is the opposite but not the inverse of pi(x).

I'm considering symmetry to say that.


consider this
Moyo wrote:What is the opposite of 1;

1. the number of primes less than a given natural number.

is it not

2. the number of natural numbers below a given prime number.
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Re: After Reimann

Post by wtf »

Moyo wrote: F(n) is the opposite but not the inverse of pi(x).
What do you mean by that? In what way is F(n) the opposite of pi(x)?

What is the opposite of, say, f(x) = x^2? What is the opposite of f(x) = e^x? What is the "opposite" of a function? How do you define that, and how would I be able to determine that F(n) = n - 1 is the "opposite" of pi(x)?
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Moyo
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Re: After Reimann

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Moyo wrote:Moyo wrote:
What is the opposite of 1;

1. the number of primes less than a given natural number.

is it not

2. the number of natural numbers below a given prime number.
I post this for the third time.
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Re: After Reimann

Post by wtf »

Moyo wrote:
Moyo wrote:Moyo wrote:
What is the opposite of 1;

1. the number of primes less than a given natural number.

is it not

2. the number of natural numbers below a given prime number.
I post this for the third time.
And it's still unclear. What is the "opposite of 1?" Define what you mean by that. If I ask a mathematician, "What is the opposite of 1?" what is the answer, and why?
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Moyo
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Re: After Reimann

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There are two statements there .,..one i called statement 1 and the other statement 2. Is it really me?
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Re: After Reimann

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Moyo wrote:There are two statements there .,..one i called statement 1 and the other statement 2. Is it really me?
It's really you. I want you to explain what is the opposite of what, and why.

I understand this much:

* We have the prime counting function pi(x).

* We have the "subtract 1" function F(n).

* The inverse of pi(x) is a multivalued relation.

* The inverse of F(n) is the function G(n) = n + 1.

* I have no idea what you mean by "opposite" since you have not taken the trouble to define it.
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Re: After Reimann

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wtf wrote:
Moyo wrote:There are two statements there .,..one i called statement 1 and the other statement 2. Is it really me?
It's really you. I want you to explain what is the opposite of what, and why.

I swapped terms in statement 2..i.e. reflected them. Think again of the 3 mirrors at 45 degrees to each other reflecting each other example i gave here ;
Moyo wrote:Consider 3 mirrors spaced apart at the points of a triangle at 45 degrees to each other. They all contain a reflection of

each other.
Symmetry groups recognise these types of reflections. And i mean opposite when i say reflection
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Re: After Reimann

Post by wtf »

I simply can't follow what you're saying. You have a mental picture in mind that you are not communicating, or that I'm failing to understand. I put three mirrors at 45 degree angles to each other. Simply not following. You have something in your mind but it it not being communicated to my mind. I don't know what else to say. I should mention that I did not understand the meaning of the diagram you posted earlier.

What terms did you swap? When you swap the input and the output of a function you get the function's inverse. I have no idea what you mean by opposite. Show me the function whose terms are being swapped.

If you give me F(47) = 46, then "swapping the terms" gives the functional inverse G(46) = 47. You can't just say "swap the terms" without explaining what you mean.
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Re: After Reimann

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wtf wrote:1. the number of primes less than a given natural number.

is it not

2. the number of natural numbers below a given prime number.
Look at how the colours have been swapped; in statement 1 red comes first and blue second , while in two ,blue comes first while red comes last.

Anyway it suffices to show that there is an inverse of pi(x) which would then be expressed using the A=(2,3,5,7....) and B=(2,3,5,7..) and C....axis.

That was you original objection..that we can not express the relationship the naturals have with the primes in this multi dimensional construct.

Primes and naturals are related..so if you arrange primes a certain way (the multi demensional AXBXC... construct) you should be able to show what the naturals will look like under different theorems ..i .e even if we use pi(x)=3 and pi(3) = and 5 so the inverse isnt really a function there is no harm in dealing with relationships.
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Re: After Reimann

Post by wtf »

I have to log off for now so I won't reply for a while. But your last post started to make some sense in some way. Let me think about this, draw some pictures of the prime lattice, apply some symmetry groups ... That would be interesting. You're trying to say that after permuting some subset of the lattice, there's a new relation among the moved elements that relates to the original relation? And that this would give us insight into the primes?

It's an interesting thought. I will think about it. I'll draw some pictures.

More later.
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Re: After Reimann

Post by wtf »

Moyo wrote:Look at the above diagram. The red are in the space for the solution for F(p) where p = 11 ( i only put some of the numbers...it should infact be a cone with 11 at both ends and 1 at the fulcrum.
Ok I looked back at your diagram. I agree you've showed the 2-lattice, which is my name for the 2D lattice whose points are products of 2 primes.

I see that you reddened the square

6 9
4 6

Then you said: "The red are in the space for the solution for F(p) where p = 11"

Now this is inconsistent with what you've said about F(p) in other posts.

You've repeatedly said that F(11) = 10. There's no 10 in what you reddened. You keep saying that F(p) = p - 1, and that therefore F(11) = 10.

Secondly. pi(11) = 5, because the primes less than or equal to 11 are 2, 3, 5, 7, 11. But the numbers in red are composite.

So at best you reddened SOME of the COMPOSITE numbers less than 11. You left out 8 and 10.

So having gone back and drawn the lattice for myself and looked at your own example of what you are trying to do, I do not understand it.

And you have used F(p) inconsistently; first saying that F(p) = p - 1; and here saying that "the red are in the space for the solution of F(p) where p = 11."

There's no way to make sense of both those statements.
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Re: After Reimann

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wtf wrote:I have to log off for now so I won't reply for a while. But your last post started to make some sense in some way. Let me think about this, draw some pictures of the prime lattice, apply some symmetry groups ... That would be interesting. You're trying to say that after permuting some subset of the lattice, there's a new relation among the moved elements that relates to the original relation? And that this would give us insight into the primes?

It's an interesting thought. I will think about it. I'll draw some pictures.

More later.
Yes .oh yes.

I see what is happening. My synaesthesia is getting in the way of my explanations. I'm expecting everone to see what i am saying. THATS why i was exiled from Genius forum.
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Re: After Reimann

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wtf wrote:
Moyo wrote:Look at the above diagram. The red are in the space for the solution for F(p) where p = 11 ( i only put some of the numbers...it should infact be a cone with 11 at both ends and 1 at the fulcrum.
Ok I looked back at your diagram. I agree you've showed the 2-lattice, which is my name for the 2D lattice whose points are products of 2 primes.

I see that you reddened the square

6 9
4 6

Then you said: "The red are in the space for the solution for F(p) where p = 11"

Now this is inconsistent with what you've said about F(p) in other posts.

You've repeatedly said that F(11) = 10. There's no 10 in what you reddened. You keep saying that F(p) = p - 1, and that therefore F(11) = 10.

Secondly. pi(11) = 5, because the primes less than or equal to 11 are 2, 3, 5, 7, 11. But the numbers in red are composite.

So at best you reddened SOME of the COMPOSITE numbers less than 11. You left out 8 and 10.

So having gone back and drawn the lattice for myself and looked at your own example of what you are trying to do, I do not understand it.

And you have used F(p) inconsistently; first saying that F(p) = p - 1; and here saying that "the red are in the space for the solution of F(p) where p = 11."

There's no way to make sense of both those statements.
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.

F(p) = p-1 so i never reddend all the composites. it would make it different from a triangle you are right. look at the bigger picture..we can assume P(N) , i.e that we have a formulae for generating the nth prime number. This assumption is shown in that the primes are evenly spaced on the axis. Then see how unevenly the naturals are. 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.

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
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Re: After Reimann

Post by wtf »

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.
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Re: After Reimann

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wtf wrote: 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 an 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?
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