On Monday, December 19, 2016 at 11:37:39 AM UTC+2, bassam king karzeddin wrote:
> On Saturday, December 17, 2016 at 6:06:40 PM UTC+3, bassam king karzeddin wrote:
> > On Thursday, November 17, 2016 at 4:50:08 PM UTC+3, bassam king karzeddin wrote:
> > > Even this was explained quite many times but never mind to prove it again and again:
> > >
> > > First, the Greek construction of a number by unmarked straightedge and a compass with finite number of steps, with arbitrary shortest distance between two distinct visualized locations on the straight number line defined as a unity, was the base of construction of an existing real number, which implies its true existence, wither it can be measured by rational numbers or not, since the construction of the rational numbers is defined by those definitions also, and was based on the perfection of the ideas behind this elementary principle
> > >
> > > So if we deny or disprove the Greek famous principle, then yes no numbers can be defined on a number line except two numbers by convention as you mentioned earlier, where then the concept of a constructing or measuring a number becomes so meaningless
> > >
> > > So, depending on the validity of the Greek principle, Sqrt(2) is a real existing number, being abstractly and physically a diagonal of a square of defined unity side, thus it is exactly constructed with unique location on a number line that no rational number can occupy, and was originated from the unity “one”, despite being immeasurable by rational.
> > >
> > > Doubling the square in real non zero integers is impossible, (n^2 =/= 2m^2), therefore taking the sqrt of both sides of this eqn. would yield:
> > > Sqrt(2) =/= n/m, where (n/m) is rational number, NO matter if both (n & m) tends to be infinite integers
> > >
> > > So, the rational representation (or the best approximation) of Sqrt(2) is always rational number, no matter if you can fill out the galaxy size of some of its endless digits
> > > And since Sqrt(2) was proved to be irrational number which is impossible to be rational number, hence it is rational representation in any rational number system is fake number that is impossible to exist, trying always and forever to replace the unique location of Sqrt(2) but always unsuccessfully
> > >
> > > Let us see it clearly in our decimal 10base number system representation, as a sequence of endless approximation, for Sqrt(2)
> > >
> > > First Sqrt (2) = 1 = 1/(10)^0
> > > Second = 1.4 = 14/10^1
> > > Third = 1.41 = 141/10^2
> > >
> > > …………. = …………………
> > >
> > > Tenth = 1414213562/10^9
> > >
> > > …….. = ……………
> > >
> > > K’th = n/m, where (m = 10^(k - 1),
> > > and (n) is integer with (k) number of digits
> > >
> > > (k + 1) = n/m, where (m = 10^k), and
> > > (n) is integer with (k + 1) number of digits
> > >
> > > Hence, if we go after exact value, we find this task is impossible to achieve, because we require both of
> > > (m & n) to be infinite integers with infinite sequence of digits, where this is obviously impossible, and also not permissible in mathematics, (then we better admit the truth of real best approximation), or say this is the magnitude of Sqrt(2) in rational number (which is not an exact number)- as John Gabriel continuously describes for immeasurable numbers
> > >
> > > The proof is therefore completed
> > >
> > > Regards
> > > Bassam King Karzeddin
> > > 17Th,Nov., 2016
> >
> >
> >
> > On Thursday, November 17, 2016 at 4:50:08 PM UTC+3, bassam king karzeddin wrote:
> > > Even this was explained quite many times but never mind to prove it again and again:
> > >
> > > First, the Greek construction of a number by unmarked straightedge and a compass with finite number of steps, with arbitrary shortest distance between two distinct visualized locations on the straight number line defined as a unity, was the base of construction of an existing real number, which implies its true existence, wither it can be measured by rational numbers or not, since the construction of the rational numbers is defined by those definitions also, and was based on the perfection of the ideas behind this elementary principle
> > >
> > > So if we deny or disprove the Greek famous principle, then yes no numbers can be defined on a number line except two numbers by convention as you mentioned earlier, where then the concept of a constructing or measuring a number becomes so meaningless
> > >
> > > So, depending on the validity of the Greek principle, Sqrt(2) is a real existing number, being abstractly and physically a diagonal of a square of defined unity side, thus it is exactly constructed with unique location on a number line that no rational number can occupy, and was originated from the unity “one”, despite being immeasurable by rational.
> > >
> > > Doubling the square in real non zero integers is impossible, (n^2 =/= 2m^2), therefore taking the sqrt of both sides of this eqn. would yield:
> > > Sqrt(2) =/= n/m, where (n/m) is rational number, NO matter if both (n & m) tends to be infinite integers
> > >
> > > So, the rational representation (or the best approximation) of Sqrt(2) is always rational number, no matter if you can fill out the galaxy size of some of its endless digits
> > > And since Sqrt(2) was proved to be irrational number which is impossible to be rational number, hence it is rational representation in any rational number system is fake number that is impossible to exist, trying always and forever to replace the unique location of Sqrt(2) but always unsuccessfully
> > >
> > > Let us see it clearly in our decimal 10base number system representation, as a sequence of endless approximation, for Sqrt(2)
> > >
> > > First Sqrt (2) = 1 = 1/(10)^0
> > > Second = 1.4 = 14/10^1
> > > Third = 1.41 = 141/10^2
> > >
> > > …………. = …………………
> > >
> > > Tenth = 1414213562/10^9
> > >
> > > …….. = ……………
> > >
> > > K’th = n/m, where (m = 10^(k - 1),
> > > and (n) is integer with (k) number of digits
> > >
> > > (k + 1) = n/m, where (m = 10^k), and
> > > (n) is integer with (k + 1) number of digits
> > >
> > > Hence, if we go after exact value, we find this task is impossible to achieve, because we require both of
> > > (m & n) to be infinite integers with infinite sequence of digits, where this is obviously impossible, and also not permissible in mathematics, (then we better admit the truth of real best approximation), or say this is the magnitude of Sqrt(2) in rational number (which is not an exact number)- as John Gabriel continuously describes for immeasurable numbers
> > >
> > > The proof is therefore completed
> > >
> > > Regards
> > > Bassam King Karzeddin
> > > 17Th,Nov., 2016
> >
> > How to prove again and again that:
> > ( Sqrt{2} =/= 1.4142135623730950488016887242096980785696718753769… ), With endless sequence of digits or what is known in the current mathematics as infinity
> >
> > I had already explained and proved earlier (around 10 years back in my posts) that any number with infinite sequence of digits is a fake and non existing number except in mind only, and we better redefine them as “unreal numbers”, since we may need them for practical problems and comparison.
> >
> > As was proved rigorously since thousands of years by the Greek, that doubling the square (in integers) is impossible, i.e (2n^2 =/= m^2), where (n & m) are non zero integers representing the whole non zero integers
> >
> > So, we have (2 =/= (m/n) ^2), then take the square roots of both sides, you must get this only:
> >
> > (Sqrt{2} =/= (m/n), no matter however large or (tending to infinity) your both (n & m) are chosen, since by definition the left hand side of this equation is irrational number (being physically existing on a straight line (which is the same as number line) as the diagonal of a square with unity side)
> >
> > And the right hand side is always rational, thus never and forever would they be exactly equals
> >
> > Let us try to understand how the top mathematicians were either deceived innocently by the endless numbers after the decimal notation as being really real numbers or else they were cheating the human minds for their own favor, but I think the first is more likely
> >
> > Now with this evidence proof in numerical analysis, you would certainly understand the whole fiction story of the infinite sequence digit number after the decimal notation are nothing more than indicator or comparison to rational numbers
> >
> > Let us see how did they simply get that integer number (m) to represent the Sqrt{2} in rational decimal.
> >
> > In 10base number system they actually solve this Diophantine equation, and then convincing others that the infinite digital sequence of digits is a real number
> >
> > For simplicity we choose the rational decimal - 10base number system that you are well accustomed to, then they made (n = 10^k), where (k) is positive integer, then (m) is obviously a positive integer with
> > (k + 1) digits, and what the modern mathematician thought wrongly to represent (sqrt{2} exactly you would certainly require that both (n & m) to be with infinite sequence of digits, where then in their tiny concepts thought this would be irrational, but the fact that is irrational is not for this silly reason, the fact is simply because it is impossible to obtain such integers with infinite sequence of digits and not because that we cannot write them or know their repeated patterns, but because this hapless representation is non existing, since it is endlessly to replace another existing number not of their type, which of course impossible, the other type of numbers called constructible numbers (excluding the rational numbers) are the Pythagorean numbers, physically existing on a straight line (which is the same as number line), such as the diagonal of a cube with unity side (Sqrt{3}), or generally (Sqrt{p}), where (p) is a prime number, those are constructible numbers which are only real numbers, they are the rationales and the Pythagorean numbers, the later are not less than rationales, but both of them are
> >
> >
> >
> >
> >
> >
> > Consider the solution of the following Diophantine equation
> >
> > 2*10^{2k} = m^2 + f(m),
> >
> > Where f(m) is integer function of (m ), (no need to know much about it now)
> > So, we choose (k) as increasing natural number (k = 0, 1, 2, 3, … ), and then we solve for (m & f(m))
> >
> > So the triplet solution would be (k, m, f(m)) in integers as the following
> >
> > (0, 1, 1), (1, 14, 4), (2, 141, 119), (3, 1414, 604), (4, 14142, 3836), (5, 141421, 100759),
> > (6, 1414213, 1590631), (7, 14142135, 17641775), (8, 141421356, 67121264),
> > (9, 1414213562, 1055272156), (10, 14142135623, 20674401871),
> >
> > (11, 141421356237, 87541199831), …
> >
> > So, we can see and simply generate as many digits as we require for Sqrt{2}, which are coming from the solution of another solvable Diophantine equation that is described above, also in any number system we desire
> >
> > As generalization (2b^{2k} = m^2 + f(m)), in b-base number system
> >
> > The point here is, how can we neglect the integer f(m) that is significantly comparable to (m) ,which make the endless representation is only fake unreal number, trying hopelessly and forever to replace the original constructible number, but unsuccessfully , since every real number is unique, and with unique representation also, thus all other numbers other than constructible are “unreal numbers”
> >
> > Equivalently, “No real number exist with endless terms”
> >
> > or “Numbers with endless terms are unreal numbers”
> >
> > Some famous numbers examples of my number system:
> >
> > One is real number by definition, and then all real numbers are created from one, (Note: this is not religion, I had explained that before)
> >
> > Sqrt(p) is real existing number , but its RATIONAL endless decimal representation which is unreal number , where (p) is any prime number,
> >
> > Cube root of (p) is unreal number, thus its infinite rational representation is also unreal number
> >
> > (Pi) and (e) are unreal numbers; also their infinite digital representations are unreal number
> >
> >
> > Regards
> > Bassam King Karzeddin
> > 17th, Dec., 2016
> >
> > ©
> On Saturday, December 17, 2016 at 6:06:40 PM UTC+3, bassam king karzeddin wrote:
> > On Thursday, November 17, 2016 at 4:50:08 PM UTC+3, bassam king karzeddin wrote:
> > > Even this was explained quite many times but never mind to prove it again and again:
> > >
> > > First, the Greek construction of a number by unmarked straightedge and a compass with finite number of steps, with arbitrary shortest distance between two distinct visualized locations on the straight number line defined as a unity, was the base of construction of an existing real number, which implies its true existence, wither it can be measured by rational numbers or not, since the construction of the rational numbers is defined by those definitions also, and was based on the perfection of the ideas behind this elementary principle
> > >
> > > So if we deny or disprove the Greek famous principle, then yes no numbers can be defined on a number line except two numbers by convention as you mentioned earlier, where then the concept of a constructing or measuring a number becomes so meaningless
> > >
> > > So, depending on the validity of the Greek principle, Sqrt(2) is a real existing number, being abstractly and physically a diagonal of a square of defined unity side, thus it is exactly constructed with unique location on a number line that no rational number can occupy, and was originated from the unity “one”, despite being immeasurable by rational.
> > >
> > > Doubling the square in real non zero integers is impossible, (n^2 =/= 2m^2), therefore taking the sqrt of both sides of this eqn. would yield:
> > > Sqrt(2) =/= n/m, where (n/m) is rational number, NO matter if both (n & m) tends to be infinite integers
> > >
> > > So, the rational representation (or the best approximation) of Sqrt(2) is always rational number, no matter if you can fill out the galaxy size of some of its endless digits
> > > And since Sqrt(2) was proved to be irrational number which is impossible to be rational number, hence it is rational representation in any rational number system is fake number that is impossible to exist, trying always and forever to replace the unique location of Sqrt(2) but always unsuccessfully
> > >
> > > Let us see it clearly in our decimal 10base number system representation, as a sequence of endless approximation, for Sqrt(2)
> > >
> > > First Sqrt (2) = 1 = 1/(10)^0
> > > Second = 1.4 = 14/10^1
> > > Third = 1.41 = 141/10^2
> > >
> > > …………. = …………………
> > >
> > > Tenth = 1414213562/10^9
> > >
> > > …….. = ……………
> > >
> > > K’th = n/m, where (m = 10^(k - 1),
> > > and (n) is integer with (k) number of digits
> > >
> > > (k + 1) = n/m, where (m = 10^k), and
> > > (n) is integer with (k + 1) number of digits
> > >
> > > Hence, if we go after exact value, we find this task is impossible to achieve, because we require both of
> > > (m & n) to be infinite integers with infinite sequence of digits, where this is obviously impossible, and also not permissible in mathematics, (then we better admit the truth of real best approximation), or say this is the magnitude of Sqrt(2) in rational number (which is not an exact number)- as John Gabriel continuously describes for immeasurable numbers
> > >
> > > The proof is therefore completed
> > >
> > > Regards
> > > Bassam King Karzeddin
> > > 17Th,Nov., 2016
> >
> >
> >
> > On Thursday, November 17, 2016 at 4:50:08 PM UTC+3, bassam king karzeddin wrote:
> > > Even this was explained quite many times but never mind to prove it again and again:
> > >
> > > First, the Greek construction of a number by unmarked straightedge and a compass with finite number of steps, with arbitrary shortest distance between two distinct visualized locations on the straight number line defined as a unity, was the base of construction of an existing real number, which implies its true existence, wither it can be measured by rational numbers or not, since the construction of the rational numbers is defined by those definitions also, and was based on the perfection of the ideas behind this elementary principle
> > >
> > > So if we deny or disprove the Greek famous principle, then yes no numbers can be defined on a number line except two numbers by convention as you mentioned earlier, where then the concept of a constructing or measuring a number becomes so meaningless
> > >
> > > So, depending on the validity of the Greek principle, Sqrt(2) is a real existing number, being abstractly and physically a diagonal of a square of defined unity side, thus it is exactly constructed with unique location on a number line that no rational number can occupy, and was originated from the unity “one”, despite being immeasurable by rational.
> > >
> > > Doubling the square in real non zero integers is impossible, (n^2 =/= 2m^2), therefore taking the sqrt of both sides of this eqn. would yield:
> > > Sqrt(2) =/= n/m, where (n/m) is rational number, NO matter if both (n & m) tends to be infinite integers
> > >
> > > So, the rational representation (or the best approximation) of Sqrt(2) is always rational number, no matter if you can fill out the galaxy size of some of its endless digits
> > > And since Sqrt(2) was proved to be irrational number which is impossible to be rational number, hence it is rational representation in any rational number system is fake number that is impossible to exist, trying always and forever to replace the unique location of Sqrt(2) but always unsuccessfully
> > >
> > > Let us see it clearly in our decimal 10base number system representation, as a sequence of endless approximation, for Sqrt(2)
> > >
> > > First Sqrt (2) = 1 = 1/(10)^0
> > > Second = 1.4 = 14/10^1
> > > Third = 1.41 = 141/10^2
> > >
> > > …………. = …………………
> > >
> > > Tenth = 1414213562/10^9
> > >
> > > …….. = ……………
> > >
> > > K’th = n/m, where (m = 10^(k - 1),
> > > and (n) is integer with (k) number of digits
> > >
> > > (k + 1) = n/m, where (m = 10^k), and
> > > (n) is integer with (k + 1) number of digits
> > >
> > > Hence, if we go after exact value, we find this task is impossible to achieve, because we require both of
> > > (m & n) to be infinite integers with infinite sequence of digits, where this is obviously impossible, and also not permissible in mathematics, (then we better admit the truth of real best approximation), or say this is the magnitude of Sqrt(2) in rational number (which is not an exact number)- as John Gabriel continuously describes for immeasurable numbers
> > >
> > > The proof is therefore completed
> > >
> > > Regards
> > > Bassam King Karzeddin
> > > 17Th,Nov., 2016
> >
> > How to prove again and again that:
> > ( Sqrt{2} =/= 1.4142135623730950488016887242096980785696718753769… ), With endless sequence of digits or what is known in the current mathematics as infinity
> >
> > I had already explained and proved earlier (around 10 years back in my posts) that any number with infinite sequence of digits is a fake and non existing number except in mind only, and we better redefine them as “unreal numbers”, since we may need them for practical problems and comparison.
> >
> > As was proved rigorously since thousands of years by the Greek, that doubling the square (in integers) is impossible, i.e (2n^2 =/= m^2), where (n & m) are non zero integers representing the whole non zero integers
> >
> > So, we have (2 =/= (m/n) ^2), then take the square roots of both sides, you must get this only:
> >
> > (Sqrt{2} =/= (m/n), no matter however large or (tending to infinity) your both (n & m) are chosen, since by definition the left hand side of this equation is irrational number (being physically existing on a straight line (which is the same as number line) as the diagonal of a square with unity side)
> >
> > And the right hand side is always rational, thus never and forever would they be exactly equals
> >
> > Let us try to understand how the top mathematicians were either deceived innocently by the endless numbers after the decimal notation as being really real numbers or else they were cheating the human minds for their own favor, but I think the first is more likely
> >
> > Now with this evidence proof in numerical analysis, you would certainly understand the whole fiction story of the infinite sequence digit number after the decimal notation are nothing more than indicator or comparison to rational numbers
> >
> > Let us see how did they simply get that integer number (m) to represent the Sqrt{2} in rational decimal.
> >
> > In 10base number system they actually solve this Diophantine equation, and then convincing others that the infinite digital sequence of digits is a real number
> >
> > For simplicity we choose the rational decimal - 10base number system that you are well accustomed to, then they made (n = 10^k), where (k) is positive integer, then (m) is obviously a positive integer with
> > (k + 1) digits, and what the modern mathematician thought wrongly to represent (sqrt{2} exactly you would certainly require that both (n & m) to be with infinite sequence of digits, where then in their tiny concepts thought this would be irrational, but the fact that is irrational is not for this silly reason, the fact is simply because it is impossible to obtain such integers with infinite sequence of digits and not because that we cannot write them or know their repeated patterns, but because this hapless representation is non existing, since it is endlessly to replace another existing number not of their type, which of course impossible, the other type of numbers called constructible numbers (excluding the rational numbers) are the Pythagorean numbers, physically existing on a straight line (which is the same as number line), such as the diagonal of a cube with unity side (Sqrt{3}), or generally (Sqrt{p}), where (p) is a prime number, those are constructible numbers which are only real numbers, they are the rationales and the Pythagorean numbers, the later are not less than rationales, but both of them are
> >
> >
> >
> >
> >
> >
> > Consider the solution of the following Diophantine equation
> >
> > 2*10^{2k} = m^2 + f(m),
> >
> > Where f(m) is integer function of (m ), (no need to know much about it now)
> > So, we choose (k) as increasing natural number (k = 0, 1, 2, 3, … ), and then we solve for (m & f(m))
> >
> > So the triplet solution would be (k, m, f(m)) in integers as the following
> >
> > (0, 1, 1), (1, 14, 4), (2, 141, 119), (3, 1414, 604), (4, 14142, 3836), (5, 141421, 100759),
> > (6, 1414213, 1590631), (7, 14142135, 17641775), (8, 141421356, 67121264),
> > (9, 1414213562, 1055272156), (10, 14142135623, 20674401871),
> >
> > (11, 141421356237, 87541199831), …
> >
> > So, we can see and simply generate as many digits as we require for Sqrt{2}, which are coming from the solution of another solvable Diophantine equation that is described above, also in any number system we desire
> >
> > As generalization (2b^{2k} = m^2 + f(m)), in b-base number system
> >
> > The point here is, how can we neglect the integer f(m) that is significantly comparable to (m) ,which make the endless representation is only fake unreal number, trying hopelessly and forever to replace the original constructible number, but unsuccessfully , since every real number is unique, and with unique representation also, thus all other numbers other than constructible are “unreal numbers”
> >
> > Equivalently, “No real number exist with endless terms”
> >
> > or “Numbers with endless terms are unreal numbers”
> >
> > Some famous numbers examples of my number system:
> >
> > One is real number by definition, and then all real numbers are created from one, (Note: this is not religion, I had explained that before)
> >
> > Sqrt(p) is real existing number , but its RATIONAL endless decimal representation which is unreal number , where (p) is any prime number,
> >
> > Cube root of (p) is unreal number, thus its infinite rational representation is also unreal number
> >
> > (Pi) and (e) are unreal numbers; also their infinite digital representations are unreal number
> >
> >
> > Regards
> > Bassam King Karzeddin
> > 17th, Dec., 2016
>
> ©
> This is here NEW theorem that might be concluded from the above absolutely irrefutable true vision provided
>
> Please keep this here for the record, just to discover (by yourself) and may be in the near future how the professional thieves in mathematics would shamelessly steal the ideas of others and develop them as if they were their own real intellect,
>
> Just keep awakened eye on those Wikipedia new pages or new modifications or new published results by Journals or universities or even personal home pages
>
> Of course, as their dirty canny inherited behaviors, they would pretend some references in the old history talking generally about the issue without providing the clear idea as would be provided to you here so explicitly and freely
>
> They would never admit or accept anything new and meaningful submitted and provided freely in the public domain especially by a matures whom they do not know the publishing process or do not have stuffiest time for this since mathematics is not their profession
>
> This is alleged nobility of mathematicians would certainly be found in fabricated fiction stories provided in history of mathematics books, where most often the true hero of the story was realized after his death, even he might be nearly a child
>
> Or may be imposed deliberately upon them as the case of Fermat’s true talent that had been published first by his son, where then they had no choice to ignore it after been published officially and not by their types at first.
>
> And still even after a professional proof provided nearly Quarter a century back by Andrew Wiles & Taylor in 1995 to the Fermat’s conjecture known as Fermat’s last theorem, they were more tortured than ever, since they cannot even understand yet a bit of that alleged proof, wonder!
>
> But strangle, they accept it to unbelievable limit as if the proof was their own, all those behaviors are understood, here Authority is the issue and that is all
>
> Imagine the endless verified or peer reviewed proof was given to them publically, or here in at sci.math for example, then guess what a cranks the proofers would be called by you or by your own categories!?
>
>
> The vast majority of the common typical professional mathematicians are actually mathematickers who keep secretly masturbating and contributing endlessly to their endless mythematics, with their endless gift they had been illegally established as infinity, it is their actual paradise that they would never like to leave, since it gives them endless freedom to keep adding and without any rigorous proof but only by intuitive wrong conclusions many fabricated and fake nonexistent numbers that the whole existing universe cannot contain even one of those assumed fake numbers at infinity
>
> The vast majority had compulsory chosen this profession (MATHEMATICS), because they actually could not obtain admissions in other scientific fields such as medical studies, engineering studies, computer engineering, …,etc, that require obtaining higher score to get a seat, where those who get the admission in those higher fields are actually more mathematical mined than those who were having much less choices
>
> The Psychology issue here is very important and may play more importance in the future
>
> Let us go back to our new theorem, and provide it with so much abbreviation
>
> *Note: this theorem is presented in the current running concepts of mathematics
> As an approximation to a desired degree of accuracy with (n) number of digits after the decimal notation in (10base number system), for the k’th real arithmetical root of a prime number (p)
> *********************************************************************
> Theorem: If (m, n, k, s) are positive real integers, where
>
> (m^k < s*(10)^{kn} < (m + 1)^k)
>
> Then, (m) is the integer sequence of digits that represents the k’th real arithmetical root of (s) with (n) number of digits after the decimal notation
>
> Example:
> What is the third or cubic real arithmetical root of (7) to four digits of accuracy after the decimal notation?
>
> It is too easy problem according to my mentioned theorem above:
> Here, we have (k = 3), (s = 7), (n = 5), then (m) can be obtained from the following equation:
>
> (m^3 < 7*(10)^{15} < (m+1)^3, so easily (m = 191293),
>
> And the real arithmetical cubic root of (7) is approximately (1.91293) to five digits of accuracy after the decimal notation as required
>
> However, honest and keen professionals are welcomed to state it in a professional language, build on it and improve it, but mentioned it is actual origin first
>
> This theorem would play a central role in future mathematics for computations as I may show (once the time for me would be available)
>
> Any constructive comments are welcomed
>
> Copyrighted content ©
>
> Regards
> Bassam King Karzeddin
> 19th, Dec., 2016