After Reimann

[Moyo]

wtf sorry if i seem rude , but what is the limit of your education and in what feild?

[Moyo]

-

-11-------------------------------121

-7------------------------ 49

-5---10------------25

-3----6-----9

-2----4-----6------10

1-----|2------|3-----|5------|7------|11

[Moyo]

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.


F(p) is the inverse of pi(x)

note 121 which is 11 X 11 is not red and is not in the solution space.

There is more work that needs to be done to get M(2) and then somemore to get P(N)...are you folowing?

NO ITS NOT...

its the triangle with 5 at both ends and 9 in the center...i dont have time to change it...because only those numbers are below F(11) = 11 - 1 = 10 sorry

Okay i changed it now

[Moyo]

Point= the prime counting function and so P(n) has symmetry of a triangle in some way.

We get another theory that we invert and end up with another geometric figure we narrow it down somemore untill, with enough of those ,we get P(n).

[wtf]

It means "how many natural numbers are below a specific prime.

No, of course that's not true. You need to read the Wiki page. https://en.wikipedia.org/wiki/Prime-counting_function. the prime-counting function is the function counting the number of prime numbers less than or equal to some real number x.

E.g if we input the prime 5 we get the natural 4 since there are 4 natural numbers below the prime 5.

No of course that is not true. That's the function f(n) = n - 1.

And if we input the prime 11 we get the natural number 10 since there are 10 natural numbers below the prime 11.

No.

F(p) = p-1

Well that's some new function F, which is defined by F(n) = n - 1.

But you have several different functions floating around. In an earlier post you talked about P(n), p(n), Pi(n), and now F(n). If you can clarify your definitions that will be very helpful.

We have the function P(n) that gives the n-th prime; we have the function pi(x) that gives the number of primes less than or equal to x; we have your function F(n) = n - 1. You seem to not be using all these consistently. It's very confusing.

I reflected the prime counting function.

Reflected? Earlier you said you inverted it. I'll take these to mean the same, but perhaps you mean something else, like reflecting its graph in an axis. What do you mean and why did you change terminology?

The reflection of pi(5)=3 is not pi(3) = 5

Earlier you said "inverse" and that's exactly what the inverse would be; except that the inverse of the prime counting function is a relation, not a function, since the inverse is multi-valued. But I have no idea what you mean by reflection.

, thats why i said (+ and -). In a reflection some thisngs stay the same while the rest changes. The reflection i gave F(p) = p-1 takes into consideration all of that. While pi(n)=..., does not.

Well the inverse of F(n) = n = 1 is the function G(n) = n + 1. Is that what you mean? Your notation and terminology is inconsistent and unclear.

This is all cleard up by seeing that the inverse of pi(x) has naturals/

But the inverse of pi(x), where pi is the prime counting function, is not a function, it's a relation. That's because, for example, pi(5) = 3 and pi(6) = 3. So the inverse relation takes 3 and gives back TWO answers, 5 and 6.

so if we input 11 in F(p) we get 10. and 10 is on the lattice.

10 is on your 2-lattice because 10 = 2*5 is the product of two primes. I agree with that. But what does this have to do with subtracting 1 from a prime?

The value for (a better example) 11 would be a cone with center at 1 (since 1 is the intersection of the axis) and reaching 11 on both axis and an unknown limit in the lattice...probably something like7 X 7 .

A cone? What are you talking about?

Look, can you just clarify your notation? What are P, Pi, p, and F? Nail that down once and for all. And please, read the Wiki page on the prime counting function.

[wtf]

wtf sorry if i seem rude , but what is the limit of your education and in what feild?

In an anonymous discussion forum, one's words speak for themselves. I could claim to be the ghost of Alexander Grothendieck for all that it matters. It's irrelevant.

[wtf]

I don't know what you mean by this. Pi(5) = 3 but that doesn't give any information on what the specific primes are.

Are you sure you are aware of what the prime counting function does? It only gives us the number (count) of primes and not what the specific primes are.

If you don't understand that Pi(5) = 3 you need to go back to the Wiki page and study it till you understand what the prime counting function does. The primes less than or equal to 5 are 2, 3, and 5. There are 3 of them. Please tell me you understand that.

[wtf]

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.

I'm sorry, I see no cones or fulcrums. And frankly including negative integers in a discussion of primes is very confusing. Far better to restrict to the positive integers.

F(p) is the inverse of pi(x)

That's inconsistent with your earlier usage. You said that F(p) = p - 1. But pi(x) is the prime counting function, whose definition you don't seem to have understood from the Wiki page. And in any event, the inverse of pi(x) is not a function, as I've repeatedly explained.

note 121 which is 11 X 11 is not red and is not in the solution space.

There is more work that needs to be done to get M(2) and then somemore to get P(N)...are you folowing?

No, you are being unclear and inconsistent in your notation and terminology.

[Moyo]

Oh never mind...*sigh*

[wtf]

Oh never mind...*sigh*

Instead of sighing, why don't you simply state the correct definition of the prime counting function? That would be a good start. You have perhaps the seed of an interesting idea, but your exposition is unclear.

[Moyo]

Instead of sighing, why don't you simply state the correct definition of the prime counting function?

But i did..here...

Moyo wrote:

wtf wrote:I don't know what you mean by this. Pi(5) = 3 but that doesn't give any information on what the specific primes are.



Are you sure you are aware of what the prime counting function does? It only gives us the number (count) of primes and not what the specific primes are.



If you don't understand that Pi(5) = 3 you need to go back to the Wiki page and study it till you understand what the prime counting function does. The primes less than or equal to 5 are 2, 3, and 5. There are 3 of them. Please tell me you understand that.

Read my nested response which says the exact same thing you said in response . This was me ;

Are you sure you are aware of what the prime counting function does? It only gives us the number (count) of primes and not what the specific primes are.

Your making a strawman.

[Moyo]

Please tell me what the opposite of this is

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.

2 can be expresseed this way F(p) = p -1.

I.e. if you plugin a prime ..the value for the number of naturals below it will always be the value of that prime - 1.

i will stop there and ask if it is clear.

[Moyo]

Not to confuse you more but before you reply the statements 1 and 2 above belong to a symmetry group that contains other statements that have the same symmetry like your version of the opposite of the pi function. There are others, but understand that they all contain the same symmetric information.(imagine each statement at the point of say a triangle)Opposite being the rule for getting from one point to the other)
--or whatever...ignore this if it doesn't make sense...i am trying to preempt your response while going thru this one step at a time.

[wtf]

Please tell me what the opposite of this is

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.

2 can be expresseed this way F(p) = p -1.

I.e. if you plugin a prime ..the value for the number of naturals below it will always be the value of that prime - 1.

i will stop there and ask if it is clear.

Your exposition is extremely confusing to me.

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.

So do you agree that:

a) pi(5) = 3, and pi(6) = 3

b) And therefore, the inverse of pi is a multivalued relation, and not a function.

Yes?

[wtf]

Not to confuse you more but before you reply the statements 1 and 2 above belong to a symmetry group

"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?

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?

How is this "my" version? You think someone else would obtain different results for pi? What do you think is pi(5)? What is pi(6)?

There are others, but understand that they all contain the same symmetric information.(imagine each statement at the point of say a triangle)

What statements?

Opposite being the rule for getting from one point to the other)
--or whatever...ignore this if it doesn't make sense...i am trying to preempt your response while going thru this one step at a time.

If I ignored what you said that didn't make sense, we couldn't have a conversation.

I'm motivated to continue our dialog because in the other thread, your exposition about the equality relationship was also very confusing, but it turned out that you were actually making an excellent point.

I'm thinking that perhaps there is a nugget of interestingness below your muddled and confused exposition in this thread too. "Opposite being the rule for getting from one point to another," is word salad. Words strung together that carry no meaning.