Clarification of the counterexamples to FLT

[Edgar E. Escultura]

CLARIFICATION OF THE COUNTEREXAMPLES TO FERMAT’S LAST THEOREM
By E. E. Escultura

Although all issues related to the resolution of Fermat’s last theorem have been fully debated worldwide since 1997 and NOTHING had been conceded from my side I have seen at least one post expressing some misunderstanding. Let me, therefore, make the following clarification:

1) The decimal integers N.99… , N = 0, 1, …, are well-defined nonterminating decimals among the new real numbers [8] and are isomorphic to the ordinary integers, i.e., integral parts of the decimals, under the mapping, d* -> 0, N+1 -> N.99… Therefore, the decimal integers are integers [3]. The kernel of this isomorphism is (d*,1) and its image is (0,0.99…). Therefore, (d*)^n = d* since 0^n = 0 and (0.99…)^n = 0.99… since 1^n = 1 for any integer n > 2.

2) From the definition of d* [8], N+1 – d* = N.99… so that N.99… + d* = N+1. Moreover, If N is an integer, then (0.99…)^n = 0.99… and it follows that ((0.99,..)10)^N = (9.99…)10^N, ((0.99,..)10)^N + d* = 10^N, N = 1, 2, … [8].

3) Then the exact solutions of Fermat’s equation are given by the triple (x,y,z) = ((0.99…)10^T,d*,10^T), T = 1, 2, …, that clearly satisfies Fermat’s equation,
x^n + y^n = z^n, (F)

for n = NT > 2. The counterexamples are exact because the decimal integers and the dark number d* involved in the solution are well-defined and are not approximations.

4) Moreover, for k = 1, 2, …, the triple (kx,ky,kz) also satisfies Fermat’s equation. They are the countably infinite counterexamples to FLT that prove the conjecture false [8]. They are exact solutions, not approximation. One counterexample is, of course, sufficient to disprove a conjecture.

The following references include references used in the consolidated paper [8] plus [2] which applies [8]

References

[1] Benacerraf, P. and Putnam, H. (1985) Philosophy of Mathematics, Cambridge University Press, Cambridge, 52 - 61.
[2] Brania, A., and Sambandham, M., Symbolic Dynamics of the Shift Map in R*, Proc. 5th International
Conference on Dynamic Systems and Applications, 5 (2008), 68–72.
[3] Corporate Mathematical Society of Japan , Kiyosi Itô, Encyclopedic dictionary of mathematics (2nd ed.), MIT Press, Cambridge, MA, 1993
[4] Escultura, E. E. (1997) Exact solutions of Fermat's equation (Definitive resolution of Fermat’s last theorem, 5(2), 227 – 2254.
[5] Escultura, E. E. (2002) The mathematics of the new physics, J. Applied Mathematics and Computations, 130(1), 145 – 169.
[6] Escultura, E. E. (2003) The new mathematics and physics, J. Applied Mathematics and Computation, 138(1), 127 – 149.
[7] Escultura, E. E., The new real number system and discrete computation and calculus, 17 (2009), 59 – 84.
[8] Escultura, E. E., Extending the reach of computation, Applied Mathematics Letters, Applied Mathematics Letters 21(10), 2007, 1074-1081.
[9] Escultura, E. E., The mathematics of the grand unified theory, in press, Nonlinear Analysis, Series A:
Theory, Methods and Applications; online at Science Direct website
[10] Escultura, E. E., The generalized integral as dual of Schwarz distribution, in press, Nonlinear Studies.
[11] Escultura, E. E., Revisiting the hybrid real number system, Nonlinear Analysis, Series C: Hybrid Systems, 3(2) May 2009, 101-107.
[12] Escultura, E. E., Lakshmikantham, V., and Leela, S., The Hybrid Grand Unified Theory, Atlantis (Elsevier Science, Ltd.), 2009, Paris.
[13] Counterexamples to Fermat’s last theorem, http://users.tpg.com.au/pidro/
[14] Kline, M., Mathematics: The Loss of Certainty, Cambridge University Press, 1985.

E. E. Escultura
Research Professor
V. Lakshmikantham Institute for Advanced Studies
GVP College of Engineering, JNT University
Madurawada, Vishakhapatnam, AP, India
http://users.tpg.com.au/pidro/

[Vindicator2009]

> [13]  Counterexamples to Fermat’s last theorem,http://users.tpg.com.au/pidro/

> [14]  Kline, M., Mathematics: The Loss of Certainty, Cambridge University Press, 1985.
>
> E. E. Escultura
> Research Professor
> V. Lakshmikantham Institute for Advanced Studies
> GVP College of Engineering, JNT University
> Madurawada, Vishakhapatnam, AP, Indiahttp://users.tpg.com.au/pidro/

So this is what happens when engineers deal with mathematics and
things way over their heads...

You're an idiot.

[Dirk Van de moortel]

Vindicator2009 <Vindica...@live.com> wrote in message
f23e2574-648b-4383...@k19g2000yqc.googlegroups.com

> On Nov 5, 12:21 pm, "Edgar E. Escultura" <escultu...@yahoo.com> wrote:

>> CLARIFICATION OF THE COUNTEREXAMPLES TO FERMAT�S LAST THEOREM
>> By E. E. Escultura

[snip]

>> E. E. Escultura
>> Research Professor
>> V. Lakshmikantham Institute for Advanced Studies
>> GVP College of Engineering, JNT University
>> Madurawada, Vishakhapatnam, AP, Indiahttp://users.tpg.com.au/pidro/
>
>
>
> So this is what happens when engineers deal with mathematics and
> things way over their heads...
>
> You're an idiot.

Worse things happen when they turn their attention to special
relativity. You might enjoy visiting sci.physics.relativity sometime.

Dirk Vdm

[Baugh]

On Nov 5, 11:59 am, Vindicator2009 <Vindicator2...@live.com> wrote:

> On Nov 5, 12:21 pm, "Edgar E.Escultura" <escultu...@yahoo.com> wrote:
>
>
>
> > CLARIFICATION OF THE COUNTEREXAMPLES TO FERMAT’S LAST THEOREM
> > By E. E.Escultura
>
> > Although all issues related to the resolution of Fermat’s last theorem have been fully debated worldwide since 1997 and NOTHING had been conceded from my side I have seen at least one post expressing some misunderstanding. Let me, therefore, make the following clarification:
>
> > 1) The decimal integers N.99… , N = 0, 1, …, are well-defined nonterminating decimals among the new real numbers [8] and are isomorphic to the ordinary integers, i.e., integral parts of the decimals, under the mapping, d* -> 0, N+1 -> N.99… Therefore, the decimal integers are integers [3]. The kernel of this isomorphism is (d*,1) and its image is (0,0.99…). Therefore, (d*)^n = d* since 0^n = 0 and (0.99…)^n = 0.99… since 1^n = 1 for any integer n > 2.  
>
> > 2) From the definition of d* [8], N+1 – d* = N.99… so that N.99… + d* = N+1. Moreover, If N is an integer, then (0.99…)^n = 0.99… and it follows that  ((0.99,..)10)^N = (9.99…)10^N, ((0.99,..)10)^N + d* = 10^N, N = 1, 2, … [8].
>
> > 3) Then the exact solutions of Fermat’s equation are given by the triple (x,y,z) = ((0.99…)10^T,d*,10^T), T = 1, 2, …, that clearly satisfies Fermat’s equation,
> > x^n + y^n = z^n,                                                                                     (F)
>
> > for n = NT > 2. The counterexamples are exact because the decimal integers and the dark number d* involved in the solution are well-defined and are not approximations.
>
> > 4) Moreover, for k = 1, 2, …, the triple (kx,ky,kz) also satisfies Fermat’s equation. They are the countably infinite counterexamples to FLT that prove the conjecture false [8]. They are exact solutions, not approximation. One counterexample is, of course, sufficient to disprove a conjecture.
>
> > The following references include references used in the consolidated paper [8] plus [2] which applies [8]
>
> > References
>
> > [1]    Benacerraf, P. and Putnam, H. (1985) Philosophy of Mathematics, Cambridge University Press, Cambridge, 52 - 61.
> > [2]    Brania, A., and Sambandham, M., Symbolic Dynamics of the Shift Map in R*, Proc. 5th International
> >         Conference on Dynamic Systems and Applications, 5 (2008), 68–72.
> > [3]    Corporate Mathematical Society of Japan , Kiyosi Itô, Encyclopedic dictionary of mathematics (2nd ed.), MIT Press, Cambridge, MA, 1993
> > [4]    Escultura, E. E. (1997) Exact solutions of Fermat's equation (Definitive resolution of Fermat’s last theorem, 5(2), 227 – 2254.
> > [5]    Escultura, E. E. (2002) The mathematics of the new physics, J. Applied Mathematics and Computations, 130(1), 145 – 169.
> > [6]    Escultura, E. E. (2003) The new mathematics and physics, J. Applied Mathematics and Computation, 138(1), 127 – 149.
> > [7]    Escultura, E. E., The new real number system and discrete computation and calculus, 17 (2009), 59 – 84.
> > [8]    Escultura, E. E., Extending the reach of computation, Applied Mathematics Letters, Applied Mathematics Letters 21(10), 2007, 1074-1081.  
> > [9]    Escultura, E. E., The mathematics of the grand unified theory, in press, Nonlinear Analysis, Series A:
> >         Theory, Methods and Applications; online at Science Direct website
> > [10]  Escultura, E. E., The generalized integral as dual of Schwarz distribution, in press, Nonlinear Studies.

> > [11]    Escultura, E. E., Revisiting the hybrid real number system, Nonlinear Analysis, Series C: Hybrid Systems, 3(2) May2009, 101-107.
> > [12]  Escultura, E. E., Lakshmikantham, V., and Leela, S., The Hybrid Grand Unified Theory, Atlantis    (Elsevier Science, Ltd.),2009, Paris.

> > [13]  Counterexamples to Fermat’s last theorem,http://users.tpg.com.au/pidro/
> > [14]  Kline, M., Mathematics: The Loss of Certainty, Cambridge University Press, 1985.
>
> > E. E.Escultura
> > Research Professor
> > V. Lakshmikantham Institute for Advanced Studies
> > GVP College of Engineering, JNT University
> > Madurawada, Vishakhapatnam, AP, Indiahttp://users.tpg.com.au/pidro/
>
> So this is what happens when engineers deal with mathematics and
> things way over their heads...
>
> You're an idiot.

'Ello 'ello, making such an outrageous and sweeping generalization
suggests the commenter above mighn't be much smarter than the deluded
prof.

First of all, there are many competent engineers who were initially
trained in engineering, but master so much math along the way that
they're able to contribute significantly to the field and become math
professor, for instance look up Mark Davis in the Mathematics
Department at Imperial College, London. Be aware that there plenty of
different kinds of engineers out there with different levels of math
mastery, not all are nuts and bolts engineers!

Secondly, Escultura is certainly no engineer! He is in fact supposed
to be a trained mathematician (in this case very poorly trained) with
a PhD degree in maths from UW-Madison in the 70's under the
supervision of L. C. Young. You'll find many graduate engineering
students who grasp math better than this guy.

[spudnik]

what the Hey?...
EEE's result is just the old "trivial" one,
a triple of (1,0,1), a degenerate pythagorean trigon
(if using "two" for the exponent, n).

he used to couch it in the "nonequality
of 1.0000... and 0.9999...," which notion he seems
to have dropped.

lest ye fugeddabowdit,
http://wlym.com/~animations/fermat/Observations20on%20Diophantus.pdf

thus:
well, that was a _Peter_ Michelson. He and
Smolin are some kind of freaked, that they'd worry
about the idea of the index of refraction, varying
for different kinds of Newtonian "photons;" but,
how can a zero-mass point-particle have a frequency, or
a wavelength?

--McSudan Crusades for carbon credits!?!
http://wlym.com/campaigner/8011.pdf

[Edgar E. Escultura]

"So this is what happens when engineers deal with mathematics and
things way over their heads...

You're an idiot."

Name calling based on wrong information not only reveals intellectual inadequacy and emptiness at the top but also racism.

E. E. Escultura
Research Professor

GVP - V. Lakshmikantham Institute for Advanced Studies
and Departments of Mathematics and Physics

[Edgar E. Escultura]

"Escultura is certainly no engineer! He is in fact supposed to be a trained mathematician (in this case very poorly trained) with a PhD degree in maths from UW-Madison in the 70's under the supervision of L. C. Young. You'll find many graduate engineering
students who grasp math better than this guy."

Just as those who cannot do mathematics comment or philosophise about mathematics, those who cannot rebut a comment makes empty claim about the commenter. E. E. Escultura

[Edgar E. Escultura]

"he used to couch it in the "nonequality
of 1.0000... and 0.9999...," which notion he seems
to have dropped."

Read on and there is a summation of the whole debate regarding 1 and 0.99...; 1 and 0.99... are distinct objects like apple and orange and to write spple = orange is simply nonsense. Go beyond SciMath into the universe of blogs and websites and you'll find the definitive resolution of this issue. E. E. Escultura

[Edgar E. Escultura]

Just as those who cannot do mathematics comment or philosophise about mathematics or comment about its history, those who cannot rebutt a comment makes empty claims about the commenter. E. E. Escultura

[Edgar E. Escultura]

Read on and you'll find my summation of the debate on 1 and 0.99... and related issues or go beyond SciMath and you'll find definitive resolution of the issue. At any rate, 1 and 0.99... are distinct objects like apple and orange and to write apple = orange is simply nonsense.
E. E. Escultura

[Justin Benfield]

First of all 0.999...=1, provided of course we are speaking about the real numbers and not some alternate set of numbers. There are many ways to prove this, if you agree that 0.333....=1/3, then 3*(1/3)=(3/1)*(1/3)=(3*1)/(1*3)=3/3=1/1=1 and 3*(1/3)=3*0.333....=0.999.... which implies 0.999...=1. 0.999... and 1 are distinct notations but a quantity has many possible ways of being written. Another way to prove 0.999...=1 is to use a summation, from the definition of decimal notation 0.999...=(9/(10^1))+((9/(10^2))+(9/(10^3))+... which can be written as a summation of (9/(10^n)) as n goes from 1 to infinity, it isn't too difficult to evaluate this sum.

FLT states that x,y,z are positive nonzero integers so the come from the set {1,2,3,4,...}, and n is a positive integer greater than 2. Andrew Wiles successfully proved the theorem in 1994-1995.

[spudnik]

let's not cite Wiles' proof -- too much work
to "get" that. it's also nice to prove
that "one equals dot-nines," but
it was really created by Stevin's "decimals,"
there-shown as the only ambiguity.

the real joke is that EEE fails to give us a "real one,"
1.0000..., ro compare to a real 0.9999... -- alas.

thus:

what the Hey?...
EEE's result is just the old "trivial" one,
a triple of (1,0,1), a degenerate pythagorean trigon
(if using "two" for the exponent, n).

he used to couch it in the "nonequality

of 1.0000... and 0.9999...," which notion he seems
to have dropped.

lest ye fugeddabowdit,

[Pubkeybreaker]

> You're an idiot.- Hide quoted text -

I don't think that he is smart enough to qualify
as an idiot.

[Edgar E. Escultura]

1 and 0.99... are distinct objects in the real world called decimals. As distinct objects they are like apple and orange and to write apple = orange is certainly nonsense. E. E. Escultura

[fishfry]

In article
<357014399.28642.12575...@gallium.mathforum.org>,

I agree with you, 1.0000... and .9999 are distinct decimals.

Do you also deny that they represent the same real number?

[Edgar E. Escultura]

1/3 is a binary operation that maps the pair of decimals (1,3) to the decimal 0.33...; strictly speaking, 1/3 and 0.33... are not equal; rather, 0.33... is the image of 1/3. Thus, the equation, 1/3 = 0.33... is sloppy mathematics. Moreover, one cannot multiply or add nonterminating decimals because either operation needs the last digit on the right. One can only approximate the reult. Therefore, the equation, 3(1/3) = 0.99..., is incorrect because the left side of the equation is only an approximation of the right side.

BTW, this comment is well informed and so I respond in the same manner. E. E. Escultura

[Edgar E. Escultura]

I have seen this name since 1997 but he has not learned a bit since then. See my response to Justin Benfield; that is the same response to your question. E. E. Escultura

[Edgar E. Escultura]

When one cannot refute or contribute to a comment he can only resort to name-calling that reveals intellectual inadequacy and insecurity because the top is empty.
E. E. Escultura

[Edgar E. Escultura]

I can only talk about decimals because at least the terminating decimals are well-defined but the real numbers are not; the field axioms that supposedly define them are inconsistent. Thanks, you are one of the very few who make sense on this thread. I think your name rings a bell from the past. E. E. Escultura

[fishfry]

In article
<531212911.28663.12575...@gallium.mathforum.org>,

"Edgar E. Escultura" <escul...@yahoo.com> wrote:

When you teach freshman calculus, do you cover the geometric series?

Doesn't 3/10 + 3/100 + 3/1000 + ... converge to 1/3 without any
reference to the notion of decimals?

[A]

> [13]  Counterexamples to Fermat’s last theorem,http://users.tpg.com.au/pidro/

> [14]  Kline, M., Mathematics: The Loss of Certainty, Cambridge University Press, 1985.
>
> E. E. Escultura
> Research Professor
> V. Lakshmikantham Institute for Advanced Studies
> GVP College of Engineering, JNT University
> Madurawada, Vishakhapatnam, AP, Indiahttp://users.tpg.com.au/pidro/

The following post in this thread was made by E. E. Escultura but I do
not see it on Google Groups, only on mathforum.org:

> I have already explained the contradiction in i many times and one in this thread is my reply to the anonymous
> guy. I refer you to it. The counterexample to the trichotomy axiom by Brouwer is Benacerraf, P. and Putnam, H.
> (1985) Philosophy of Mathematics, Cambridge University Press, Cambridge, 52 - 61, and my own version is in my
> paper, The new real number system and discrete computation and calculus, 17 (2009), 59 ? 84. Both
> counterexamles prove that the real numbers are not linearly ordered by "<" (natural ordering) and that an irrational
> number is not the limit of a sequence of rational numbers in the standard norm. the Banach-Tarski paradox
> stemming from the axiom of choice (a variant of the completeness axiom of the field axioms of the real number
> system) is discussed in these papers: Bhaskar, T. G., Kovak, D., Lakshmikantham V. (2006) The Hybrid Set
> Theory, Nonlinear Analysis; C-Series, Hybrid Systems and Applications. and, Kline, M. Mathematics: The Loss of
> Certainty, Oxford University Press, New York, 1980.
> Your question makes sense and deserves a serious response. E. E. Escultura

I am not sure why this is (I don't use mathforum.org--are not all
posts there actually made to the Usenet group?) or whether people with
real newsreaders were able to see this post.

I am also having trouble telling who E. E. Escultura is replying to in
each post, since he does not quote the person he replies to. Mr.
Escultura, it would be nice if you would quote the person you reply to
in your posts, so that when you say "you" it is easier to tell who you
are referring to.

In any case, the paper by Heyting on pgs. 52-61 of the book of
Benacerraf and Putnam is about an intuitionistic foundation for
mathematics, and the difficulties in constructing the real numbers
which he discusses there are only difficulties when using
intuitionistic logic (i.e., one is not allowed to use the argument
"the negation of P is not true implies that P is true" in one's
proofs). There are no contradictions to be found in this paper for
anyone who uses the more standard logic in which ~~P implies P.

The Banach-Tarski paradox is likewise not a contradiction but merely a
counterintuitive fact, one which indicates the need for measure theory
(and the need to distinguish between measurable and non-measurable
sets) in order to have a usable theory of integration.

Why are you claiming that these things represent contradictions in the
construction of the real numbers? They do not, unless you either
insist on using intuitionistic logic, or you insist on ignoring or
misusing measure theory.

[Edgar E. Escultura]

When you teach freshman calculus, do you cover the geometric series?

Doesn't 3/10 + 3/100 + 3/1000 + ... converge to 1/3 without any
reference to the notion of decimals?

----

We are just dealing with the basics now. As soon as we have resolved these basic issues we will proceed to calculus and even analysis in general. I have started the rectification of the real number system with the paper, The new real number system and discrete computation and calculus an overview of which is on my website. E. E. Escultura

[Edgar E. Escultura]

First of all 0.999...=1, provided of course we are speaking about the real numbers and not some alternate set of numbers. There are many ways to prove this, if you agree that 0.333....=1/3, then 3*(1/3)=(3/1)*(1/3)=(3*1)/(1*3)=3/3=1/1=1 and 3*(1/3)=3*0.333....=0.999.... which implies 0.999...=1. 0.999... and 1 are distinct notations but a quantity has many possible ways of being written. Another way to prove 0.999...=1 is to use a summation, from the definition of decimal notation 0.999...=(9/(10^1))+((9/(10^2))+(9/(10^3))+... which can be written as a summation of (9/(10^n)) as n goes from 1 to infinity, it isn't too difficult to evaluate this sum.

-------
1) 1 and 0.99... are distinct mamthematical objects, i.e., distinct decimals, like apple and orange and there is something wrong in the statement apple = orange.

2) Since a decimal is determined or well-defined by its digits nonterminating decimals are ambiguous and ill-defined because we do not know all its digits. Therefore, there is something wrong with the equation 1 = 0.99... since the right side is unknown, ill-defined.
Incidentally, we cannot add or multiply a nonterminating decimal because the operation requires the last digit on the right to carry out it out. we can only approximate. Therefore, the equation is never attained. you might write the equation 1 = the limit of 0.99... in the standard norm but that limit is not the decimal 0.99... it's another concept.

FLT states that x,y,z are positive nonzero integers so the come from the set {1,2,3,4,...}, and n is a positive integer greater than 2. Andrew Wiles successfully proved the theorem in 1994-1995.

-----
I have posted elsewhere the two errors in Wile's proof:

1) The integers as real numbers are not presently well-defined because the field axioms which supposedly well-define them are inconsistent

2) Complex analysis which he used in the proof is flawed because the imaginary concept i = the root of the equation i^2 + 1 = 0 among the real numbers does not exist. Therefore, i is a vacuous or ill-defined concept. That is why a contradiction can be extracted from it.

E. E. Escultura

[Edgar E. Escultura]

the real joke is that EEE fails to give us a "real one,"
1.0000..., ro compare to a real 0.9999... -- alas.

----

1 and 0.99... are distinct decimals, distinct objects like apple and orange and to write apple = orange is simply nonsense. E.E.Escultura

[Edgar E. Escultura]

I don't think that he is smart enough to qualify

as an idiot. Brian Q. Hutchings
----

When the top is empty one can only resort to name calling that reveals intellectual inadequacy and racism. I have seen this name a long time ago since 1997 and the guy has not learned a bit; he can only post from the flat of his foot but nothing of substance. He should join the Society of Empty Toppers. E. E. Escultura

[Edgar E. Escultura]

I don't think that he is smart enough to qualify

as an idiot. Pubkeybreaker

When the top is empty one can only resort to name calling that reveals intellectual inadequacy and racism. I have seen this name a long time ago and the guy has not learned a bit; he can only post from the flat of his foot but nothing of substance. He should join the Society of Empty Toppers. E. E. Escultura

[Nunemica]

On Nov 5, 11:49 pm, Justin Benfield <Justin.Benfi...@gmail.com> wrote:
> First of all 0.999...=1, provided of course we are speaking about the real numbers and not some alternate set of numbers.  There are many ways to prove this, if you agree that 0.333....=1/3, then 3*(1/3)=(3/1)*(1/3)=(3*1)/(1*3)=3/3=1/1=1 and 3*(1/3)=3*0.333....=0.999.... which implies 0.999...=1. 0.999...

This is the problem .999 only implies "1" but it is not "1".

If .999 is 1 then 1 must be 1.001

1.001 + .999 = 2

and for 1 to be 1.001 then (zero)0 = 0.001

[Nunemica]

On Nov 9, 5:07 am, Nunemica <tinabarbarar...@gmail.com> wrote:
> On Nov 5, 11:49 pm, Justin Benfield <Justin.Benfi...@gmail.com> wrote:
>
> > First of all 0.999...=1,

Sorry just a slight edit!
>
> If .999...= 1 then 1 = 1.001... also

[Tim Little]

On 2009-11-09, Nunemica <tinabar...@gmail.com> wrote:
> Sorry just a slight edit!
>>
>> If .999...= 1 then 1 = 1.001... also

What is your definition for the notation "1.001..."? Do you mean that
the pattern "001" in the decimal portion repeats?

- Tim

[Edgar E. Escultura]

Pubkeybraker:

You're an idiot.- Hide quoted text -

I don't think that he is smart enough to qualify
as an idiot.

Racists need frustrate surgery to remove sourgrapes and placate their inadequacy. E. E. Escultura

[Nunemica]

On Nov 9, 6:47 pm, Tim Little <t...@little-possums.net> wrote:

> On 2009-11-09, Nunemica <tinabarbarar...@gmail.com> wrote:
>
>
> >> If .999...= 1 then 1 = 1.001... also
>
> What is your definition for the notation "1.001..."? Do you mean that
> the pattern "001" in the decimal portion repeats?
>
> - Tim

Sorry Tim - the statement was ambiguous.

First meaning of '.001':

.001 was meant to express a terminating decimal added to .999
terminating decimal to equal 1.

Second meaning:

In the case of non-terminating decimal .999999999999999999..., the
addition of (infinite leading zeros preceding 1) .
000000000000000001..., would be required to halt the repeating pattern
and produce 1.

The only way .999... is made to equal 1 is by rounding up for
convenience but not mathematically correct. .9999999... is not a
numerical value - it is an operation result which cannot move from the
position it is numerically locked into.

[A]

On Nov 10, 9:12 am, Nunemica <tinabarbarar...@gmail.com> wrote:
> On Nov 9, 6:47 pm, Tim Little <t...@little-possums.net> wrote:
>
> > On 2009-11-09, Nunemica <tinabarbarar...@gmail.com> wrote:
>
> > >> If .999...= 1 then 1 = 1.001... also
>
> > What is your definition for the notation "1.001..."?  Do you mean that
> > the pattern "001" in the decimal portion repeats?
>
> > - Tim
>
> Sorry Tim - the statement was ambiguous.
>
> First meaning of '.001':
>
> .001 was meant to express a terminating decimal added to .999
> terminating decimal to equal 1.
>
> Second meaning:
>
> In the case of non-terminating decimal .999999999999999999..., the
> addition of (infinite leading zeros preceding 1) .
> 000000000000000001..., would be required to halt the repeating pattern
> and produce 1.

What do you think a real number is? What kind of definition of a real
number are you using here?

[Edgar E. Escultura]

I am not in this league by far, but without a doubt we have proven that .999 =1, in a divergent mathematics continuum at 19 inverse,".1 is lost going out and .1 constant is gained in convergence" gain equals loss, 1=.999.Plus the entire mathematics is equalized by the .001 differential (the correct mathematics is.999=1.000), for a reason see the inverse code of number 1-- has your mathematics seen any thing like this?.
-------

When dealing with mathematical objects well-defined by a set of axioms equality makes sense only for the same object unless we qualify that we are referring to the result of an operation (which is a mapping) like,

2 + 2 = 4,

in which case we are not equating 4 to the object on the left but the result of that operation. In the case of 1 and .99..., they are distinct mathematical objects. We may, of course, equate 1 to the the limit of the sum of the series .9 + .09 + ... but the limit of this sum is something else, not the object 0.99... We can also correctly say that .99... is an approximation of 1 or 1 is an approximation of .99... in the standard norm but, an approximation is different from the object being approximated.

I appreciate this kind of comment because it has mathematical content and not an expletive or an insult or name calling or attempt to trivialize someone's post. From my long experience the latter category is the weapon of the racist to put down a commenter. The participation of everyone here including the racist is a good thing and does not reflect in anyway the fine tradition of this forum. In fact, I have a couple of articles online where I pointed to SciMath as the best among all forums in terms of the diversity of ideas and opportunity for expression. I also identified what I consider the worst and listed many excellent ones in between. In my latest post here I even contratulated Drexel University for hosting this fine institution.

Cheers.

E. E. Escultura

As far as racism is concerned, on what basis, we do not know the race of Edgar 1.Edgar, calling some one an idiot is not a big thing in America, The city of Madison that you did your Phd as you know was full of those Idiots, them days-- seen them at State street. Edgar, I come originally from India, there are more damn racists there by far than in America, there is not only racism in India, Color bar exists, Very few African students would study in India, so please cut the racists thing out, the rest is fair game

P. S. I am actually from the Philippines (it is not hard to guess what one's race is) and I am using the term racism scientifically based on its historical root and context. Thus, my use of this term is also my self expression just as the racist has his own right to self expression. I am just making an objective observation that there are participants to which the term applies.

Message was edited by: Vinoo Cameron

[Edgar E. Escultura]

Vinoo Cameron:

Good Phillipino , very fine people, Always found them fine people, many friends. Edgar, I am an anglo Indian my grandfather was born in Glascow Scotland and was in the British military, and My daughter is part Parsi, iranian descent, my other children part Jewish. She is a US attorney, is married to a half African American and half white. So what race is my Grandduaghter. Who cares.

Thanks for the respinte. I'll view your work.

Cheers,

E. E. Escultura

[Edgar E. Escultura]

Hi Vinoo,

I have downloaded your article about inverse 19 and I have noted your interesting observations on the Euclidean plane which we can formalize as the cartesian product space of the real numbers or R^2. I assume you are using the field axioms of the real numbers. To simplify and avoid the inconsistency of the field axioms I offer you the new real number system R* with very simple three axioms:

1) 0, 1 are elements of R* and

2) and 3) the addition and multiplication tables

that first well-define 0 and 1, then the integers, then the terminating decimals and, based on the terminating decimals, well define the nonterminating decimasl.

If you are using the field axioms I would like to look at the analytical proof of your first obsevation based on these axioms. Then you can simplify the proof and avoid the stigma of the field axioms, i.e., their inconsistency, using the results about the new real number system that I posted here or its three axioms. Use my email for your reply: escul...@yahoo.com.

Cheers.

E. E. Escultura

[Edgar E. Escultura]

Vinoo Cameron:

Good Phillipino , very fine people, Always found them fine people, many friends. Edgar, I am an anglo Indian my grandfather was born in Glascow Scotland and was in the British military, and My daughter is part Parsi, iranian descent, my other children part Jewish. She is a US attorney, is married to a half African American and half white. So what race is my Grandduaghter. Who cares.

----------

Operatively, any tinge of color makes a person colored. non-white.

Cheers.

E. E. Escultura

[spudnik]

I am lying about numbertheory, and
the number, 1.0000...;
who gives a floating fart?

thus:
original sources (and "sourcebooks") are really good,
such as the below-linked Ouvre de Fermat for number-
theory, and Bernoulli/L'Hopital's calculus textbook.
(Euclid, not so much, as an encyclopedia, although
he did supply new stuff, they say -- and
Langlands says that Book 7 needs a lot of work; I do have
a nice latter-day textbook on synthetic trigon geometry, but
it's in French, so it's hard work.)

thus:
of course, and the electrons can't go faster
than light *even if*
they might already be orbitting the nucleus
at such a velocity.

thus:
I could see that he got rid of the gamma function, but
it'll be a while before that is clear to me; so,
I asked about a problem he wrote about, before.

m'brain:
L'Ouvre: http://wlym.com/~animations/fermat/index.html

--HW's Cap'n Trade & Warren "choo-choo" Buffet, together again?...
Dubya wouldn't sign the radical free-trade Kyoto Protocol?...
Rep. Waxman's God-am bill, doesn't institute a tarrif, instead!?!