Fayez Fok al-Adeh, Leonid Chindelevitch,W. Aschauer,
W. Aschauer, Apr. 17, 2006:
If you want to make a proof, then all the necessary parts of
a proof have to be in the script, so that the logical combination
of these parts is comprehensible, because you cannot expect
that everybody buys the books which you are using.
E.g. the inequation for "t" appears from nowhere.
And beside this the usage of Landau's symbol is wrong as
Mr.Leonid Chindelevitch has very well explained.
Fayez Fok al-Adeh, Apr. 16, 2006:
The book explains how to do calculations whenever equivalnce classes are replaced by representatives of the classes.
W. Aschauer, Apr. 14, 2006:
O.k., you are not able to explain, you only copy the text,
and if there is a question or problem, you lay the responsibility
and blame on the author of the copied text.
Would be good if you learn first basic mathematics before you copy any text, so that you become able to understand a bit of what you read.
Fayez Fok al-Adeh, Apr. 14, 2006:
Ignorance endures unless one review books. Again I refer to my old comment.
W. Aschauer, Apr. 12, 2006:
Tststs, still not able to explain ?!?
You ignore my question about the origin of the inequation of t.
But ignorance is not a mathematical method.
Fayez Fok al-Adeh, Apr. 12, 2006:
Skimming the mentioned book renders the problem a simple mathematical exercise.
W. Aschauer, Apr. 10, 2006:
You still ignore my question about the origin of the inequation of t.
Beside this: A knowledge about mathematics is only knowledge if you are able to use and to explain it. (Otherwise it's only black-coloured text on white paper.) To copy parts of books doesn't make any sense, if these parts have no clear and logical relations. E.g. like the inequation of t.
Fayez Fok al-Adeh, Apr. 9, 2006:
The contradiction arises because of equation(15) What else other than books can be a source
of knowledge?
W. Aschauer, Apr. 9, 2006:
The contradiction is the result of the arbitrary inequation for t.
For this is no logical reason shown.
I am talking about the definition of t and you are answering with books. How nice. Why you don't explain what you are writing? Do you only copy contents of books?
Fayez Fok al-Adeh, Apr. 8, 2006:
Equation(15) leads to a contradiction. This is the main point. Please see the first book in
the list of references mentioned in my paper page - 79, line 31 where you can find a very
similar argumentation using the big order notation which justifies the implications leading
from (11) to (15).
W. Aschauer, Apr. 7, 2006:
What I meant is: t is simply set t < 1/(2(n+1))
and only because of this we have the contradiction.
There is no logical reason for t. If t < 1/(2(n+1)) should be the result of (11),
then it has to be explained - clearly.
Fayez Fok al-Adeh, Apr. 7, 2006:
Equation(15) leads to a contradiction. This the main point.
W. Aschauer, Apr. 7, 2006:
The examination of (14) and (15) shows us,
that we get for n=100 the result
t = 0,009584... > 0,00495... = 1/202 ,
which contradicts the precondition t < 1/202 for n=100.
I ask Mr.Aldeh to check his equations by using numerical examples!
Fayez Fok al-Adeh, Apr. 7, 2006:
I still ask Ms.Aschauer to examine equations(14) and (15)rigorously.
As to Dr.Sfarti: please see the first book in the list of references mentioned in my
paper page - 79, line 31 where you can find a very similar manipulation using the
big order notation.
W. Aschauer, Apr. 6, 2006:
(7) plus (14) is equal to (15) and you have simply
set t < 1/(2(n+1)) in (14), therefore the condition of t
is valid also for (15).
If I set n=100 in (14), (15) or (16) it's equal because (14), (15) and (16) are equivalent because of (7). It's always the same result (of course). For e.g. n=100 is t > 1/(2(n+1)). This makes the following argumentations impossible.
And independent of this, the use of Landau's symbol is wrong, Leonid Chindelevitch had explained it very well.
To (11): n>10 is wrong, it's n>4 . That's not important, but it shows, that you don't check you preconditions.
Adrian Sfarti, Apr. 6, 2006:
Let me make it plainer: you cannot do any algebraic operation with the O
function. You cannot consider the O function like an algebraic element.
In your paper you do so in violation of the definition of the O function.
Fayez Fok al-Adeh, Apr. 5, 2006:
I ask Ms.Aschauer to check the difference
between equations(14) and (15)
W. Aschauer, Apr. 5, 2006:
Ahhh, now I am "disapointed" that you have changed
the content of your script, because the equation
where irrational values were rational is corrected.
But you still haven't read carefully what Mr. Leonid Chindelevitch
had written about how to use the "big-O notation"
(it's nothing else than one of the order symbols of Landau).
Let us set n=100 . Thus we have n+1=101 prime and PI(100)=25. With (14) you get t < 1/202 = 0,00495... . With (15) you get t = 0,009584...
That's a contradiction because t = 0,009584... > 0,00495... = 1/202.
Of course you get such errors because of the wrong use of Landau's symbol.
Fayez Fok al-Adeh, Feb 18, 2006:
There is a famous unsolved problem in Mathematics which relates to the
existence of a prime between any two successive squares. I have already
proved that there always exists a prime between any two successive
squares.
My proof is exact. It has been published in the web journal: General Science Journal on 17 February 2006. The address of the journal is: wbabin.net/aladeh/prime.pdf. Before that I have proved The Riemann Hypothesis. My proof is exact. It has also been published in the same web journal on 18 march 2005. Please circulate this information to all members and students, so that they can find the papers and review them.
Leonid Chindelevitch, Feb. 19, 2006: Email:leonidus@hotmail.com
I am sorry to disappoint you, but your proof is obviously faulty. It is
clear at first glance that you do not understand the meaning of the big-O
notation, which leads you to make erroneous statements. For instance, the
statement "this is because O(1/log(n)) = 1/log(n) = O(1/2*log(n))"
clearly shows that you treat big-O functions without the required
carefulness (i.e. without taking care of the fact that the constant
hidden inside the big-O notation changes when you change the function). I
can recommend you to read the book by Knuth, Orel and Patashnik entitled
"Concrete Mathematics", in which one of the chapters gives a good
explanation of the big-O notation and will hopefully help you
Fayez Fok al-Adeh, Feb 19, 2006:
If we review the first book of the references I mention in my paper, we
find in page 53 the following definition:f(x)=O(g(x)) means that the quotient f(x)/g(x)
is bounded. Apply this definition to the case f(x)=1/log(x) g(x)=1/log(x) and then
for the case f(x)=1/log(x) g(x)=1/2log(x) to arrive at my result. In fact the author
of the book formulates many theorms and proves them using very similar
argumentation. One of the theorms contains just the same argumentation. The big Oh notation
deals with magnitudes,it is not a measure function in the strict mathematical
sense. This means that chaging the constant has nothing to do with the magnitude. The
can not change abruptly. I suggest you read this book.You are wrong.My
proof is exact.
Leonid Chindelevitch, Feb. 20, 2006
I have read all the books that you mention in your reference (although
not completely). Perhaps to make your mistake clear, I should have said
that the main flaw in your argumentation is when you equate big-O
expressions (which indicate only the order of magnitude) with actual
functions (and you do that many times in the paper). I give you a
reasoning along these lines to show you the flaw:
n + 2 = n + O(1) is also a correct statement
Among other major holes in your proof, there is also statement (13); your assumption that (n + 1) is composite in NO WAY implies that Pi((n^2)) = Pi((n+1)^2). For instance, if n = 3, n + 1 = 4 is a composite number, yet Pi (9) = 2*3*5*7 and Pi (16) = 2*3*5*7*11*13, clearly not the same...
I am not going to argue with you if you keep claiming that "your proof is exact", because that would be a waste of time for me. If you are still convinced that your proof is correct, why don't you submit it to a real science journal, so you are recognized as the solver of an open problem in number theory!
Fayez Fok al-Adeh, Feb 20, 2006:
I did not use an erroneous argumentation like the one you introduced.
I did not make any cancellation of equal O(h) magnitudes in all
the equtions in my paper. My equations are correct.
Leonid Chindelevitch, Feb. 20, 2006
OK, since you don't seem to get the point, let me show you exactly
where you made the mistake.
Look carefully at your derivation between equations (4) and (5), and you will see that this is exactly what you are doing. Perhaps the following will help you: you should always think of a statement
Fayez Fok al-Adeh, Feb 20, 2006:
Please note that I did not deduce that the functions are equal, rather that the magnitudes are
the same(O(1/2logn)=O(1/logn)), hence the
functions belong to the same class ((1/2logn)and(1/logn)), they are not equal. The
sum on the left-hand side of (1) is well defined, we can consider an example and calculate it by hand. The
sum is strictly known.
Leonid Chindelevitch, Feb. 21, 2006
I don't know why you keep being so defensive about your proof... I am
not going to waste any more time trying to convince you. Hopefully you'll realize it
yourself one day. This conjecture is an old open problem in number theory, and I seriously
doubt that such a simple approach will ever succeed in establishing its truth.
I hope you can find someone who can explain your mistakes better than me!
Fayez Fok al-Adeh, Feb 21, 2006:
The first book of the references mentioned in my paper interprets equation(1)
as follows: it is an exact equation: you can add the reciprocals of primes less
than or equal to x and get a well defined number. You can arrive at this same well
defined number by adding loglog x to the constant A and adding to them another
number, the order or magnitude of which is O(1/log x), that is it is in the same
class as (1/log x). Many theorems in the book are based on this iterpretation.
W. Aschauer, Feb 24, 2006:
Yes, Mr. al Adeh is still on a run from arguments, which give him an idea of
prudential and well-advised mathematik.
E.g. item (12) is a funny equation: Independent of the condition for the Prime-Function PI(), we have for all natural numbers n > 1 on the left side an irrational number and on the right side a rational number.
Wow :-) :-) :-), I am deeply impressed, because the basis for the whole number-theory is unhinged !!!
Fayez Fok al-Adeh, Feb 25, 2006:
For equation 12 please see the first book in the list of
references mentioned in my paper page - 79, line 31.
W. Aschauer, Feb 26, 2006:
I don't know this book. But I know item (12).
If this item is in the book, then it's not necessary to read this book,
because all what we need is in the script. If it's not in the book, why should I read it ?!
However, if this equation is right, the number-theory is completely
unhinged.
I was not informed about such an event, that now irrational values can
be
rational.
Again: Wow !, I am still deeply impressed !!!