Re: After Reimann
Posted: Sun Oct 18, 2015 8:48 am
wtf sorry if i seem rude , but what is the limit of your education and in what feild?
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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.Moyo wrote: It means "how many natural numbers are below a specific prime.
No of course that is not true. That's the function f(n) = n - 1.Moyo wrote:E.g if we input the prime 5 we get the natural 4 since there are 4 natural numbers below the prime 5.
No.Moyo wrote: And if we input the prime 11 we get the natural number 10 since there are 10 natural numbers below the prime 11.
Well that's some new function F, which is defined by F(n) = n - 1.Moyo wrote: F(p) = p-1
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?Moyo wrote: I reflected the prime counting function.
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.Moyo wrote: The reflection of pi(5)=3 is not pi(3) = 5
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.Moyo wrote: , 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.
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.Moyo wrote: This is all cleard up by seeing that the inverse of pi(x) has naturals/
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?Moyo wrote: so if we input 11 in F(p) we get 10. and 10 is on the lattice.
A cone? What are you talking about?Moyo wrote:
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 .
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.Moyo wrote:wtf sorry if i seem rude , but what is the limit of your education and in what feild?
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.Moyo wrote: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.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.
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.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.
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.Moyo wrote: F(p) is the inverse of pi(x)
No, you are being unclear and inconsistent in your notation and terminology.Moyo wrote: 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?
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 wrote:Oh never mind...*sigh*
But i did..here...wtf wrote:Instead of sighing, why don't you simply state the correct definition of the prime counting function?
Read my nested response which says the exact same thing you said in response . This was me ;wtf wrote: 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.
Your making a strawman.Moyo wrote: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 exposition is extremely confusing to me.Moyo wrote: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.
"Symmetry group" is a technical term in math. https://en.wikipedia.org/wiki/Symmetry_groupMoyo wrote:Not to confuse you more but before you reply the statements 1 and 2 above belong to a symmetry group
"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?Moyo wrote: that contains other statements that have the same symmetry like your version of the opposite of the pi function.
What statements?Moyo wrote: There are others, but understand that they all contain the same symmetric information.(imagine each statement at the point of say a triangle)
If I ignored what you said that didn't make sense, we couldn't have a conversation.Moyo wrote: 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.