[QUOTE=blob100;211505]Thanks for answering.
Others explained what you've said.
The question was about how to call a proposition which wasn't exused and were conjectured?

[/QUOTE]

I don't understand this question.

[QUOTE]

The second question was: if to post my new propositions here even though I'm just me (not a proffesional mathematicain, etc.)?[/QUOTE]

The answer, (once again!) is that do not have the background, knowledge,
or experience to put forth "propositions". You should be asking questions.

[quote=blob100;211505]The question was about how to call a proposition which wasn't exused and were conjectured?
The second question was: if to post my new propositions here even though I'm just me (not a proffesional mathematicain, etc.)?[/quote]As noted by others the word "conjecture" is a specialized term in mathematics. It means a statement which is almost certainly true but for which a proof can't yet be given. Occasionally a conjecture turns out to be a false statement but even in that case there is generally a lot of evidence to suggest that it might be true.

My approach, when presenting a proposition which I think may be true, is to phrase it as a question. For instance:[code]I believe that 2 is the only even prime number.
Everything I've tried so far supports this belief and I've not yet
found a counter-example.

Can anyone provide a proof or a counter-example?"[/code]Now, clearly, this is a silly "conjecture" but it illustrates the procedure.

Please post your propositions here. A number of us are very willing to help you, and other readers of your posts, to learn more mathematics. There's a chance that you will ask a deep question which prompts [B]us[/B] to learn more mathematics. Not a very high chance, admittedly, but high enough for it to be worth doing.

The flip side is that you will have to learn how to take criticism without being offended. In my view, that is a skill very much worth learning and the earlier you start, the greater the benefit it will be to you later.

Paul

[QUOTE=R.D. Silverman;211503]What is the [b]question[/b]????

It is a theorem that lim n-->oo pi(n)/ (n/log(n)) = 1.

It is also a theorem that better approximations to pi(n) exist than
n/log(n). In particular, li(x) = integral from 2 to x of dz/log(z) is a
better approximation (evaluated at n) . We can even give a bound for the
amount of error in the approximation.

It is also known that p(x) - li(x) changes sign infinitely often.

It is also know that p_n > n log(n) for ALL n > 1. (proved in a
deservedly famous paper by Rosser and Schoenfeld) p_n is the n'th prime.
The same paper proved pi(n) > n/log(n) for all n > 17.

This can even be improved to p_n > n(log(n) + loglog(n) - 1)

What do you want to know?[/QUOTE]

Fixed some typos

[quote=xilman;211519]My approach, when presenting a proposition which I think may be true, is to phrase it as a question.[/quote]As Bob has indirectly indicated, the word "proposition" is also a technical term in mathematics. In my quoted post I was using it in the colloquial sense. In a statement about mathematics I should have used "statement" or, perhaps, "observation" or something else which doesn't have quite so precise a technical meaning.

The jargon of any professional field is full of pitfalls like these. Ultimately, about all you can do is learn the jargon and not be too surprised, or offended, if practitioners in the field either misunderstand you or correct your terminology. As far as I can tell, mathematics is no worse and no better than many other fields in this respect.

Paul

[QUOTE=xilman;211531]The jargon of any professional field is full of pitfalls like these. Ultimately, about all you can do is learn the jargon and not be too surprised, or offended, if practitioners in the field either misunderstand you or correct your terminology. As far as I can tell, mathematics is no worse and no better than many other fields in this respect.[/QUOTE]Too true. At a past job of mine, the common 4 letter word for human solid waste was a technical term. And I am not scatting the [COLOR="Sienna"][B]hits[/B][/COLOR] here.

[quote=xilman;211519]As noted by others the word "conjecture" is a specialized term in mathematics. It means a statement which is almost certainly true but for which a proof can't yet be given. Occasionally a conjecture turns out to be a false statement but even in that case there is generally a lot of evidence to suggest that it might be true.

My approach, when presenting a proposition which I think may be true, is to phrase it as a question. For instance:[code]I believe that 2 is the only even prime number.
Everything I've tried so far supports this belief and I've not yet
found a counter-example.

Can anyone provide a proof or a counter-example?"[/code]Now, clearly, this is a silly "conjecture" but it illustrates the procedure.

Please post your propositions here. A number of us are very willing to help you, and other readers of your posts, to learn more mathematics. There's a chance that you will ask a deep question which prompts [B]us[/B] to learn more mathematics. Not a very high chance, admittedly, but high enough for it to be worth doing.

The flip side is that you will have to learn how to take criticism without being offended. In my view, that is a skill very much worth learning and the earlier you start, the greater the benefit it will be to you later.

Paul[/quote]

Thanks Paul,
I'll publish these propositions in a word paper I wrote.

[quote=cmd;211577]there are only two things that scare "u" more than death,
what happened to the dinosaurs to frogs ignored and Spiker
what happens to thinkers "writers" books ...

extinction of the genus ...






( [URL]http://en.wikipedia.org/wiki/William_Shakespeare[/URL] )


note ;) WS-u ... like ... 10metreh

\;+)[/quote]
Did you know that no one painted Shakespeare as he really looked?
That is becuase he was not impressive..

[QUOTE=blob100;211416]I have a problem with understanding "the prime number theorem", and "the twin primes theorem".
The prime number theorem, as I know, means:
For n-->infinity
Pi(n)/(n/ln(n))=1
Right?
This is becuase of the orders of these:
Pi(n) and (n/ln(n)) are equal?
But order (as I know) is not the exaxtly phrase, it is just the dominantic part of it. Yes I agree that at infinity the dominantic part is a much larger infinity than the other parts can be, for example: y=n^2+n, the order is n^2.
for x-->infinity.
But f(x)/g(x)=1
seems not exactly the right thing.
Let me examply:
But x+1/x=1
for x-->infinity.
Is right, right?
Seems still wrong to me.

The second problem is:
The twin primes theorem by Hardy-Littlewood.
I try to play with this conjecture to gain some expirience...
I'm sorry to say that, for everyone who is angry about me, I conjectured some conjectures on this area, and I try to exuse them.
I continued and got some ideas about the area of this conjecture..
I conjectured these without knowing too much about orders and the order of Pi_2(n) (which is still unknown).
Just conjectured by looking on the numbers of twin prime numbers between o to natural "n".
Still sorry for conjecturing, but wanted to say anything about it.
I keep reading and learning..

Thanks tomer.[/QUOTE]

May I suggest the following:

Stop concerning yourself with more advanced topics such as PNT and
distribution of twin primes. You should ignore analytical results until
you thoroughly understand Calculus. And don't run off trying to learn
Calculus either. There are other things you need first.

Here are 5 problems from elementary mathematics. Three involve 1st
semester number theory. Show us that you can do these problems.

(1) Consider a disc. (circle plus its interior). It is intersected by
N lines, each line intersecting at two distinct points (i.e. no tangents)
As a function of N, what is the largest number of regions into which the
disc can be divided? Prove your answer by induction.

(2) Let p be prime, and (a,p) = 1. It is well known that a factor of
a^p - 1, other than (a-1) must be of the form 2kp+1. However, for
Fermat numbers, a factor of 2^2^n+1 must equal k * 2^(n+2) + 1.
Explain why the exponent is (n+2) and not (n+1)

(3) Let p be an odd prime and consider the units of Z/pZ. What is the
product of all of the units?

Definition: A unit of a ring is an element that has a multiplicative inverse.

(4) Let odd N be the product of k distinct prime factors, each dividing exactly.
Suppose x^2 = a mod N has at least one solution. How many total solutions are there?

Hint: Consider the Chinese Remainder Theorem

(5) Consider the two vectors V1 = (x1, y1) and V2 = (x2, y2).

A. Prove that x1 x2 + y1 y2 = |V1| * |v2| * cos (theta) where
theta is the angle between the two vectors.

B. Let V3 be the vector obtained by rotating V1 clockwise by angle mu.
Express this vector in terms of (x1, y1)



Get back to us when you can solve these.

[quote=R.D. Silverman;211607]May I suggest the following:

Stop concerning yourself with more advanced topics such as PNT and
distribution of twin primes. You should ignore analytical results until
you thoroughly understand Calculus. And don't run off trying to learn
Calculus either. There are other things you need first.

Here are 5 problems from elementary mathematics. Three involve 1st
semester number theory. Show us that you can do these problems.

(1) Consider a disc. (circle plus its interior). It is intersected by
N lines, each line intersecting at two distinct points (i.e. no tangents)
As a function of N, what is the largest number of regions into which the
disc can be divided? Prove your answer by induction.

(2) Let p be prime, and (a,p) = 1. It is well known that a factor of
a^p - 1, other than (a-1) must be of the form 2kp+1. However, for
Fermat numbers, a factor of 2^2^n+1 must equal k * 2^(n+2) + 1.
Explain why the exponent is (n+2) and not (n+1)

(3) Let p be an odd prime and consider the units of Z/pZ. What is the
product of all of the units?

Definition: A unit of a ring is an element that has a multiplicative inverse.

(4) Let odd N be the product of k distinct prime factors, each dividing exactly.
Suppose x^2 = a mod N has at least one solution. How many total solutions are there?

Hint: Consider the Chinese Remainder Theorem

(5) Consider the two vectors V1 = (x1, y1) and V2 = (x2, y2).

A. Prove that x1 x2 + y1 y2 = |V1| * |v2| * cos (theta) where
theta is the angle between the two vectors.

B. Let V3 be the vector obtained by rotating V1 clockwise by angle mu.
Express this vector in terms of (x1, y1)



Get back to us when you can solve these.[/quote]
Is (4) an open question? I think so?
I know how many resiue classes are for prime "p".
I think I have some of the begining steps for this problem.

[QUOTE=blob100;211635]Is (4) an open question? I think so?
I know how many resiue classes are for prime "p".
I think I have some of the begining steps for this problem.[/QUOTE]

If by "open", you mean unsolved, then no. This problem
is fully solved. Use the hint.

I think I solved problem 2.
We can show k2^(n+2)+1 as 4k2^n+1.
Where k2^(n+1)+1 can be shown as 2k2^n+1.
We can show that every number of the form 2^(2^n) is of the form a^2,
example: 2^(2^5)=65536^2.
so becuase of 2^(2^n)-1 factors are equivallent to the factors of a^2 which are 4k+1, we can say easily that 2^(2^n)+1's factors are not the same as the factors of 2^(2^n)-1, so we just agree it is of another form (on this situation k2^(n+2)+1).