PLUTONIUM ARITHMETIC 1-6-94
Alexander Abian
PLUTONIUM INTEGERS AND ARITHMETIC 1-6-94 (debugging)
A significance of Plutonium Intergers is that although being integers they
are organically related to the real numbers. As a result, Plutonium Arithmetic
could share many properties of the extremely rich structure of the Arithmetic
of the Real numbers.
For instance, Fermat's Last Theorem is to an extreme degree violated in the
Arithmetic of Real numbers. Indeed, given any positive real numbers a, b
and any positive integer n there always exist a real number c such that
(1) a**n + b**n = c**n
showing that FLT is violated almost everywhere in real analysis. As shown below
(1) is basically responsible for the failure of FLT in the Plutonium
Arithmetic (whose main virtue is its organic relation to real numbers and not
the denial of FLT).
Of course, there exist many other arithmetics where FLT is violated.
For example, in the Arithmetic of Ordinal Numbers
(2) 10 **5 + omega ***5 = omega ** 5
in the Arithmetic of Cardinal numbers
(3) aleph sub3 **8 + aleph sub4 **8 = aleph sub4 **8
However, (2) and (3) pertain to transfinite numbers and the failure of FTL
there is almost a natural expectation.
In contrast Plutonium integers are not transfinite and thus failure of FTL
could not be taken there for granted.
As in the development of any new theory a great deal of revision, fine
tuning, and debugging must occur.
Earlier, in my late December 1993 paper,I defined a Plutonium integer as a
configuration REQUIRING A DECIMAL POINT.
That was done for developing later the Plutonium real numbers. But then in
my Early January 1994 paper, I abandoned the REQUIREMENT OF A DECIMAL POINT,
since the subject matter was the Plutonium Integers. This was not a good
strategy because it destroyed the organic link of Plutonium integers to the
real numbers mentioned above, and created undue complications.
I canceled the above Early January posting and am replacing with the
present one.
Without going into further details,I redefine Plutonium integers as
follows, by bringing back the decimal point.
DEFINITION OF A PLUTONIUM INTEGER (P-integer, for short)
A Plutonium integer is a leftward infinite sequence of digits 0, 1, ...,9
preceded on the right by a decimal point . with + or - on the top of the
decimal point.
Thus, each of the following is a Plutonium integer:
...........38383838383897613429765 .+ a positive P-integer
...........10001000100010007865439 .- a negative P-integer
...........00000000000000000000000 .+ P-zero
For simplicity, when a P-integer is preceded by + we drop the + sign.
In the above + and - must be on top of the decimal point . ( unable to
achieve on this computer)
Also, the dots on the left stand for the definite pattern of integers whenever
such a patters is obviously suggested, otherwise they just indicate that a
P-integer is a leftward infinite sequence of integers.
Most basic concepts are the DUAL of a P-integer and a dual of a real number.
DEFINITION OF A DUAL OF A PLUTONIUM INTEGER ( r-Dual of a P-integer)
The DUAL of a P-integer ......abcdefg. (+,-) is the real number obtained by
placing the mirror image of ......abcdefg (+,-) after the decimal point .
Thus,
the Dual of ....215678. is the real number .87651... = 0.87651........
but written just .87651
the Dual of ..........1. is the real number .1...... = 0.1....
but written just .1...
the Dual of .......1560. is the real number .0651.... = 0.0651....
but written just .0651...
The Dual of .....43200.- is the real number -.00234......
Thus, the Dual of P-integer is a real number which should be called the
r-Dual of a P-integer.
Notice that a P-integer has a unique r-Dual.
DEFINITION OF A DUAL OF A REAL NUMBER. (P-dual of a real number r)
In order that a real numbers to have a unique Dual, all real numbers are
(4) written in decimal expansion with NO INFINITE SUCCESSION OF 9's
and every real number WITH ABSOLUTE VALUE LESS THAN ONE IS WRITTEN AS
(5) (+,-) .abcdefgh.........and not as (+ -) 0.abcdefgh........
(6) in the decimal representation of a real number there must be a finite
number of digits appearing on the left side of the decimal point and
the leftmost last digit must be nonzero.
The DUAL of a real number (+,-) abc.defghik.... is the P-integer
obtained by placing the mirror image of (+,-)abcdefghik.... in front of
the decimal point.
Thus,
the Dual of 100.3456........ is the P-integer .... 6543001.
the Dual of .9865001...... is the P-integer .....1005689.
the Dual of -.0003 ....... is the P-integer ........3000.-
the Dual of .5437689.... is the P-integer .....9867345.
the Dual of 5.437689..... is the P-integer .....9867345.
the Dual of 54.437689..... is the P-integer .....9867345.
Thus, the Dual of a real number is a P-integer which should be called the
P-dual of a real number.
Since infinite succession of 9's is not allowed the P-dual of
.9999999999...... is the P-dual of 1.00000000000000000 and
P-dual of 1.00000000.... is .......0000001.
Notice that a real number has a unique P-dual but many distinct reals may
have the same P-dual.
THE PLUTONIUM ARITHMETIC
THE BASIC RULES OF ADDITION AND MULTIPLICATION
ALL THE ARITHMETICAL OPERATIONS IN PLUTONIUM ARITHMETIC ARE PERFORMED BY
PASSING TO THE DUALS AND PERFORMING THE CORRESPONDING PRESCRIBED OPERA-
TIONS AS IN THE USUAL ARITHMETIC OF REAL NUMBERS AND REVERTING
THE RESULTS THUS OBTAINED TO THEIR P-DUALS.
EXAMPLES OF THE ADDITION:
(7) ........0032891009. + .....00859900012.....
first we go to the r-duals of the above P-integers and we add these r-duals
according to the usual arithmetic of the real numbers. Hence,
.9001982300.... + .21000995800... = 1.110208188....
then, according to the BASIC RULE, we revert the result to its P-dual, i.e
...........8818020111.
Hence, in Plutonium Arithmetic, (7) becomes have:
........0032891009. + .....00859900012. = .....008818020111.
Again, let us perform the following addition of the P-integers in the
Plutonium Arithmetic:
.......... 0032763476. + ....0043297654.
passing to the r-duals and performing addition there, we obtain
.6743672300... + .4567923400... = 1.13115957....
and reverting the result into its P-dual, we have that in Plutonium Arith-
metic:
.......... 0032763476. + ....0043297654. = .......00759511311.
EXAMPLES OF MULTIPLICATION
(8) .........003765. * ......0093.
We first go the corresponding r-duals and multiply them according to the
rules of the usual real arithmetic. Hence
.567300........ * .3900... = 2.2124700.....
then we revert the`result to its P-dual, i.,e, ......00742122.
Thus, in Plutonium Arithmetic, (8) becomes
.........003765. * ......0093. = .......00742122.
As expected, exponentiation is treated as repeated multiplication.
EXAMPLES OF EXPONENTIATION.
(9) (.....002.)** 3 = .... 800. and (....001)** 3 = ....100.
Now, in the usual arithmetic of real numbers
(10) .009 ** 1/3 = .02080083823....
Hence, in Plutonium Arithmetic, because of (10), we have;
(11) (..........3283800802.)** 3 = ....900.
Consequently, by (9), (10),(11), in Plutonium Arithmetic, we have:
(12) (...002.)** 3 + (...001.)** 3 = (...3283800802)** 3,,
Clearly, (12) DENIES FERMAT's LAST THEOREM IN THE PLUTONIUM ARITHMETIC.
Infinitely many counter examples to FTL can be given in Plutonium Arithmetic,
Below are two more:
(..0045)** 5 + (..0012)** 5 = (...69045)** 5
and
(...001)** 7 + (...001.)** 7 = (...14011)** 7
As I said in the above, a significance of Plutonium integers and their
Arithmetic is that although being integers they are organically related to the
usual real numbers and thus acquire some of the riches of the extraordinary
rich structure of the real numbers.
What basic Laws the Usual Arithmetic are VIOLATED in Plutonium Arithmetic
is not an issue. No progress in Mathematics (or elsewhere) has ever achieved
without VIOLATING the usual status quo Laws:
In noneucldean geometries the sacrosanct Euclidean parallel Law is violated.
In Nonassociative algebras the sacrosanct laws of associativity is violated
In Relativity the sacrosanct Newtonian addition of velocities is law is
violated.
In the Intuitionistic Logic the sacro sanct Double negation Law of the
Aristotelian Logic (on which the entire classical mathematics, physics, life
itself and the jurisprudence are based) is violated.
In Picasso's painting the sacrosanct Laws of Rembrand's light and shadows
are violated (and you can not buy some Picasso's for many million dollars)
The forefather's of USA violated the British Laws
Stravinsky violated the sacrosanct Laws of musical compositions
Please, O, please do not tell me that all the above are good violations and
violations of Plutonium are bad. WE ALL TRY TO IMPOSE OUR VIEWS UPON THE
OTHERS AND WE ALL CONSIDER OUR VIEWS THE GOOD VIEWS.!!!
For many years Gauss was ashamed to announce that he violated the Euclid's
parallel Law. He felt guilty, ashamed and kept himself in a closet. But when
Lobachevski got a little success announcing his own violation of Euclid,
Gauss came out of the closet and said "O, no, I am the one who First
violated Euclid. So, give me (i.e., give to Gauss) the medal for raping Euclid,
don't give that medal to Lobachevski". Then other rapists came out of the
closets with the priority pretense of raping Euclidean and for
impregnating Mathematics with New, Progressive and brilliant offsprings.
No, progress is achieved without overthrowing some well established
stagnated status quo laws.
PLUTONIUM ARITHMETIC (or some variation with fine-tuning and debugging
of it) will stay here and prosper in the hands of imaginative minds.
Speaking about violating Laws, even in classical Complex Analysis the usual
exponential law (a**b)**c = a **(b*c) is violated.
The process of LIFE is imposing ideas upon each other. And, I love to impose
my ideas upon the others, I love it! It inflates my ego and makes me feel
secure.
I LOVE TO IMPOSE MY IDEAS UPON THE OTHERS. IT INFLATES MY EGO AND MAKES ME
FEEL SECURE !!
P.S. in such a long posting there could be some typos and oversights. The
readers are asked to inform of such things. Thanks.
--
----------------------------------------------------------------------------
TIME HAS INERTIA. EQUIVALENCE OF TIME AND MASS: (1/T)+(1/log M) = 1 (ABIAN).
ALTER EARTH'S ORBIT AND TILT - STOP EPIDEMICS OF CANCER, CHOLERA, AIDS, ETC.
VENUS MUST BE GIVEN A NEAR EARTH-LIKE ORBIT TO BECOME A BORN AGAIN EARTH
Alexander Abian
Sender: ne...@news.iastate.edu (USENET News System)
Organization: Iowa State University, Ames IA
Date: Fri, 7 Jan 1994 16:02:29 GMT
Lines: 342
Alexander Abian
Alexander Abian
Ludwig Plutonium
ab...@iastate.edu (Alexander Abian) writes:
> The process of LIFE is imposing ideas upon each other. And, I love to impose
> my ideas upon the others, I love it! It inflates my ego and makes me feel
> secure.
>
> I LOVE TO IMPOSE MY IDEAS UPON THE OTHERS. IT INFLATES MY EGO AND MAKES ME
> FEEL SECURE !!
Abian, your ideas are great and should be imposed on others. Since
you posted your great ideas 4 times in a row, please impose your ideas
on the 4 color mapping problem. A recent alleged proof of the 4 color
mapping problem was luke-warmly accepted by the mathematics community.
It is called the Appel & Haken alleged proof. However it uses a
reductio ad absurdum argument onto a question of sufficiency. I claim
that mathematical logic cannot accommodate a reductio ad absurdum when
trying to prove sufficiency.
Alexander, please support my claim that reductio ad absurdum when
mixed with sufficiency is unviable. Support the claim that you cannot
mix reductio ad absurdum with sufficiency by showing us many readers a
number of examples. Thank you Abian.
Alexander Abian
...........00000000000000000000000 .+ P-zero
Thus,
but written just .87651
but written just .0651...
r-Dual of a P-integer.
Thus,
THE PLUTONIUM ARITHMETIC
EXAMPLES OF THE ADDITION:
(7) ........0032891009. + .....00859900012.....
...........8818020111.
.......... 0032763476. + ....0043297654.
EXAMPLES OF MULTIPLICATION
(8) .........003765. * ......0093.
EXAMPLES OF EXPONENTIATION.
The process of LIFE is imposing ideas upon each other. And, I love to impose
my ideas upon the others, I love it! It inflates my ego and makes me feel
secure.
I LOVE TO IMPOSE MY IDEAS UPON THE OTHERS. IT INFLATES MY EGO AND MAKES ME
FEEL SECURE !!
Ludwig Plutonium
ab...@iastate.edu (Alexander Abian) writes:
> Speaking about violating Laws, even in classical Complex Analysis the usual
> exponential law (a**b)**c = a **(b*c) is violated.
>
> The process of LIFE is imposing ideas upon each other. And, I love to impose
> my ideas upon the others, I love it! It inflates my ego and makes me feel
> secure.
>
> I LOVE TO IMPOSE MY IDEAS UPON THE OTHERS. IT INFLATES MY EGO AND MAKES ME
> FEEL SECURE !!
Alexander Abian, please support and validate the following two proofs
of the Riemann Hypothesis.
TWO PROOFS OF THE RIEMANN HYPOTHESIS
Discussion: Riemann conjectured that the real component for the
complex numbers at which the zeta function equals zero is 1/2. This
conjecture of Riemann is: the #1, major, most sought-after unsolved
problem in all of mathematics.
An electron has intrinsic spin of +1/2, only the positive value of
+1/2 works for the spin quantum number ms, no other number works. Spin
quantum number has positive values only, but spin states for an
electron or proton can correspond to s' = +1/2 and s'' = -1/2. I assert
our observable universe is the last one electron, the 94th or the 5f6
of a plutonium atom. Then the zeros of the zeta function are the
charges added-up and so protons cancel with electrons, no net charge
remains, because matter comes into existence from spontaneous neutron
materialization and thus there can not exist any net charge since
through radioactivities a neutron transforms into a proton plus
electron. Thus the zeta function is a quantum chart of every neutron,
proton, electron, and atom which came, or will come into existence. The
uncollapsed wave function (figure1, unable to copy) of quantum
mechanics represents numbers of mathematics such as irrational,
transcendental numbers such as e and š. The collapsed wave function
(figure2, unable to copy) is the materialization of an atom or
subatomic particle, where materialization substitutes for existence of
a rational number. The number 2 which is 1+1 represents the Plutonium
Atom Totality itself, and the next term represents perhaps the first
hydrogen atom to exist, and so on for every term in the zeta function.
Figure 1: A logarithmic spiral inside rectangles of whirling squares.
The squares and the rectangles go out to infinity and thus the spiral
goes out to infinity.
Figure 2: Collapsed wavefunction from a logarithmic spiral into
Riemannian space of an ellipse or sphere.
PROOFS: Two proofs of the Riemann Hypothesis follows as (A) and (B).
Proof (A). A geometrical proof follows. It was proved that the Riemann
Hypothesis is equivalent to the following: the Moebius function mu of
x, m(x), and adding-up the values of m(x) for all n less than or equal
to N giving M(N). That M(N) grows no faster than a constant multiple k
of (N^1/2)(N^epsilon) as N goes to infinity (epsilon is arbitrary but
greater than 0). Figure1, by setting-up a logarithmic spiral in a
rectangle of whirling squares where the squares are the sequences:
1,1,2,3,5,8,13,21,34,55,89, . . . 2,2,4,6,10,16,26, . . .
3,3,6,9,15,24,39, . . . then every number appears in at least one of
these sequences because every number will start a sequence. Since all
numbers are represented uniquely by prime factors (the unique prime
factorization theorem or called the fundamental theorem of arithmetic)
and The Prime Number Theorem: the distribution of prime numbers is
governed by a logarithmic function, where (An/n)/(1/Logarithm of n)
tends to 1 as n increases, where An denotes the number of primes below
the positive integer n, and where An/n is called the density of the
primes in the first n positive integers. The density of the primes,
An/n, is approximated by 1/(Ln of n), and as n increases, the
approximation gets better. It is one of the most beautiful things in
all of the known world, that the distribution of prime numbers is
governed by a logarithmic function where these two mathematical
concepts-- one of prime numbers, and the other, logarithms seem
unconnected at first appearance, but in reality they are totally
connected. Geometrically, the logarithmic spiral exhausts every
positive integer, see figure 1. The area of the rectangles containing
the logarithmic spiral is always greater, since the spiral is always
inside the rectangles. Thus the Moebius function k (N^1/2)(N^epsilon)
is satisfied since the area of the logarithmic spiral is less than the
rectangle whose area represents the number N, and whose sides represent
its factors. The area of a logarithmic spiral is represented by
r=(rsub0)(e^(Ej)) , and so depending on where the point of origin for
the spiral is taken rsub0 determines k, and depending on the value of
E, E determines the epsilon value for N, when E=0 then the curve is a
circle. The logarithmic spiral inside rectangles of whirling squares
implies that for any number N then N^1/2 is the limit of the factors
for N, for example, given the number 28, then 28^(1/2)=5.2915. . and so
looking for the factors of 28, it is useless to try beyond 5 because
the factors repeat, 4x7 then repeats as 7x4. But if the Moebius
function was false then there must exist a number M such that M^(1/2)
is not the limit of the factors for M and the spiral is outside of the
square, which is impossible, hence the Moebius function is true.
Therefore the Riemann Hypothesis is proved. Q.E.D.
My second proof (B) of the Riemann Hypothesis uses a reductio ad
absurdum argument. Euler proved that a formula encoding the
multiplication of primes was equal to the zeta function. Euler's
formula in complex variable form is as follows:
(1/(1-(1/(2^c))))x(1/(1-(1/(3^c))))x(1/(1-(1/(5^c))))x(1/(1-(1/(7^c))))x
(1/(1-(1/(11^c))))x . . . , where c is a complex variable, c=u+iv. The
Riemann zeta function is as follows: Re(c) =
1+(1/(2^c))+(1/(3^c))+(1/(4^c))+. . . , where c is a complex variable,
c=u+iv. Euler's formula involves multiplication of terms and the
Riemann zeta function involves addition of terms of a sequence. Taking
Re(c) > 0, suppose the Riemann Hypothesis is false then there is a 0
such that Re(c)=0 and c does NOT equal 1/2 +iy, which implies there is
another 0 which is not on the 1/2 real line. Which means another real
number other than 1/2 works as an exponent resulting in a zero for the
Riemann zeta function, and a zero in the Euler formula. Thus, Riemann
zeta function subtract Euler formula must equal zero. This implies for
any other real number exponent, either rational or irrational numbers,
such as for example the rational exponents: 1/3,1/4,1/5, . . . (Note:
any other exponent y/x , where y and x are Real numbers and where the
Real number of A^(y/x) such that y not equal 1, immediately transforms
to a number A^y(1/x), so that exponents with a 1 in the numerator
entail all of the Real exponents). Then for exponent 1/3 there has to
exist a number M not equal 0 where (M+M+M) - (MXMXM) = 0. Then for
exponent 1/4 there has to exist a number M not equal 0 where (M+M+M+M)
-(MXMXMXM)=0, and so on. Including the infinite number of cases where
the x denominator is irrational are impossible. Only the real number
1/2 works since 2 does not equal 0, and (2+2)^1/2 =(2X2)^1/2, and so
(2+2)^1/2 - (2X2)^1/2= 0. In all of mathematics, 2 is the only number
N where ((N+N)^1/N) - ((NxN)^1/N) = N. Unlike 0, the number 2, its sum
equals its product and where the sum and product is a new number 4. If
RH were false, then another number other than 2 would satisfy the
equation ((N+N)^1/N) - ((NxN)^1/N) = N. False, hence the proof. QED
(Quantum Electrodynamics)
Terry Tao
> TWO PROOFS OF THE RIEMANN HYPOTHESIS
>[RH is equivalent to] That M(N) grows no faster than a constant multiple k
>of (N^1/2)(N^epsilon) as N goes to infinity (epsilon is arbitrary but
>greater than 0).
Quite incredibly, you are absolutely correct so far. But see below about
the Moebius function.
>...and The Prime Number Theorem: the distribution of prime numbers is
>governed by a logarithmic function
True also - for normal, finite integers. Did you know the 10-adics only
has 2 primes? And the Plutonium integers that Abian has posted about have
NO primes whatsoever?
>connected. Geometrically, the logarithmic spiral exhausts every
>positive integer, see figure 1. The area of the rectangles containing
>the logarithmic spiral is always greater, since the spiral is always
>inside the rectangles.
I get the feeling that the rectangles are overlapping in some strange wat
that needs to be taken into account, but not seeing the diagram, I can't be
certain.
>... But if the Moebius
>function was false then there must exist a number M such that M^(1/2)
>is not the limit of the factors for M
Are you sure you know what the Moebius function is? It has nothing to do
with the "limit of factors". \mu(n) is always 0, 1, or -1.
The summand M(x) = \sum_{n=1}^x \mu(n) is also unrelated to the "limit of
factors of x".
>... Euler's
>formula in complex variable form is as follows:
>(1/(1-(1/(2^c))))x(1/(1-(1/(3^c))))x(1/(1-(1/(5^c))))x(1/(1-(1/(7^c))))x
>(1/(1-(1/(11^c))))x . . . , where c is a complex variable, c=u+iv. The
>Riemann zeta function is as follows: Re(c) =
>1+(1/(2^c))+(1/(3^c))+(1/(4^c))+. . . , where c is a complex variable,
>c=u+iv.
These formulas only work when the real part of c is greater than 1. (Just
as the formula 1 + x + x^2 + x^3 + ... = 1/(1-x) only works when -1 < x <
1.) Check any book on analytic number theory. When the real part of c is
less than or equal to 1, the zeta function is defined by analytic
continuation, or an integral formula, or by the functional equation.
This already makes this proof invalid, but let's continue anyway:
>Euler's formula involves multiplication of terms and the
>Riemann zeta function involves addition of terms of a sequence.
Yeah, but different sequences for each formula.
>Taking
>Re(c) > 0, suppose the Riemann Hypothesis is false then there is a 0
>such that Re(c)=0 and c does NOT equal 1/2 +iy, which implies there is
>another 0 which is not on the 1/2 real line. Which means another real
^
complex, not real -|
>number other than 1/2 works as an exponent resulting in a zero for the
>Riemann zeta function, and a zero in the Euler formula. Thus, Riemann
>zeta function subtract Euler formula must equal zero.
>This implies for
>any other real number exponent, either rational or irrational numbers,
>such as for example the rational exponents: 1/3,1/4,1/5, . . . (Note:
>any other exponent y/x , where y and x are Real numbers and where the
>Real number of A^(y/x) such that y not equal 1, immediately transforms
>to a number A^y(1/x), so that exponents with a 1 in the numerator
>entail all of the Real exponents).
This sentence hath no content. This implies WHAT for any other real number
exponent? And why?
>Then for exponent 1/3 there has to
>exist a number M not equal 0 where (M+M+M) - (MXMXM) = 0.
If you're trying to do what I think you're trying to do, each of the M in
that formula is a different M. They all belong to the same sequence,
perhaps. But they're not the same number.
Then again, the sentence before this one made no sense, so all bets are
off.
>(and claims similarly that for every 1/N there is an M for which NM - M^n
= 0)
>... If
>RH were false, then another number other than 2 would satisfy the
>equation ((N+N)^1/N) - ((NxN)^1/N) = N.
^-- perhaps you mean 0, though even
then it doesn't make any sense.
This equation does not follow from the previous. Unless, of course,
each N in that equation refers to a different number.
Incidentally, the 10-adic
N = ....163574218752
satisfies N+N = N*N. (N actually happens to be twice the idempotent that
ends in 6.)
And in Abian-Plutonium arithmetic, there is no number N, apart from 0, for
which the statement
N+N = N*N
is true. For example N = .....000002 does not work, since 0.2 + 0.2 is not
equal to 0.2 * 0.2.
Paradoxically, though, there are infinitely many N in the Abian-Plutonium
arithmetic for which N+N and N*N evaluate to the same number.
Specifically, N = .....00002, ....00020, ...00200, ....02000, etc.
(This of course is an absolutely non-serious violation of any law of
equality you'd care to mention. :-)
--
Terry Tao Math Dept., Princeton University (t...@math.princeton.edu)
"God is dead." - Nietzsche
"Nietzsche is dead." - God
Ludwig Plutonium
GMT POSTING. I HAVE SATISFIED ALL OF TERRY TAO'S COMPLAINTS IN THIS
NEXT POSTING OF MINE ON THE RIEMANN HYPOTHESIS (RH). IN SHORT, TERRY
DOES NOT STICK WITH THE SUBJECT AT HAND BUT WANTS TO MIX IN OUTSIDE
ISSUES. ABIAN, PLEASE SKIP OVER TERRY'S POSTING. ABIAN I ASKED THE
QUESTION ON RH FIRST. RESPECTFULLY REQUEST THAT YOU, ABIAN, ANSWER MY
NEXT POSTING FIRST. RESPECTFULLY REQUEST YOU, ABIAN TO SUPPORT AND
VALIDATE RH.
In article <1994Jan9.1...@Princeton.EDU>
t...@fine.princeton.edu (Terry Tao) writes:
ABIAN, I HAVE MADE SOME TYPOS, AND MINOR ERRORS IN MY 9JAN94, 16:30:33
GMT POSTING. I HAVE SATISFIED ALL OF TERRY TAO'S COMPLAINTS IN THIS
NEXT POSTING OF MINE ON THE RIEMANN HYPOTHESIS (RH). IN SHORT, TERRY
DOES NOT STICK WITH THE SUBJECT AT HAND BUT WANTS TO MIX IN OUTSIDE
ISSUES. ABIAN, PLEASE SKIP OVER TERRY'S POSTING. ABIAN I ASKED THE
QUESTION ON RH FIRST. RESPECTFULLY REQUEST THAT YOU, ABIAN, ANSWER MY
NEXT POSTING FIRST. RESPECTFULLY REQUEST YOU, ABIAN TO SUPPORT AND
VALIDATE RH.
Ludwig Plutonium
version below is what I respectfully request that you ABIAN, please
SUPPORT and VALIDATE the claims.
TWO PROOFS OF THE RIEMANN HYPOTHESIS
Discussion: Riemann conjectured that the real component for the
complex numbers at which the zeta function equals zero is 1/2. This
conjecture of Riemann is: the #1, major, most sought-after unsolved
problem in all of mathematics.
An electron has intrinsic spin of +1/2, only the positive
value of
+1/2 works for the spin quantum number ms, no other number works. Spin
quantum number has positive values only, but spin states for an
electron or proton can correspond to s' = +1/2 and s'' = -1/2. I assert
our observable universe is the last one electron, the 94th or the 5f6
of a plutonium atom. Then the zeros of the zeta function are the
charges added-up and so protons cancel with electrons, no net charge
remains, because matter comes into existence from spontaneous neutron
materialization and thus there can not exist any net charge since
through radioactivities a neutron transforms into a proton plus
electron. Thus the zeta function is a quantum chart of every neutron,
proton, electron, and atom which came, or will come into existence. The
uncollapsed wave function (figure1, unable to copy) of quantum
mechanics represents numbers of mathematics such as irrational,
transcendental numbers such as e and น. The collapsed wave function
entail all of the Real exponents). To make clear of the above, for
example, 2^2/3 is 4^1/3. Then for exponent 1/3 there has to
exist a number M not equal 0 where (M+M+M)^1/M = (MXMXM)^1/M = M. Then
for
exponent 1/4 there has to exist a number M not equal 0 where
(M+M+M+M)^1/M
= (MXMXMXM)^1/M = 0, and so on. Including the infinite number of cases
where
the x denominator is irrational are impossible. Only the real number
1/2 works since 2 does not equal 0, and (2+2)^1/2 = (2X2)^1/2 = 2, and
so
(2+2)^1/2 - (2X2)^1/2 = 0. In all of mathematics, 2 is the only
number
N where ((N+N)^1/N) = ((NxN)^1/N) = N. Unlike 0, the number 2, its sum
equals its product and where the sum and product is a new number 4. If
RH were false, then another number other than 2 would satisfy the
equation ((N+N)^1/N) = ((NxN)^1/N) = N. False, hence the proof. QED
(Quantum Electrodynamics)
Alex.Coventry
being inappropriate when applied to 'questions of sufficiency.'
Because all theorems can be formulated as 'questions of sufficiency,'
it then clearly follows that NO implications using reductio ad
absurdum are permissible. To the best of my knowledge this makes the
rationality/irrationality of the square root of 2 an open question.
Can you find a way to resolve this question without resorting to a
proof by contradiction?
Much obliged,
Alex Coventry.
Erik Max Francis
> Abian,my 9JAN94, 16:30:33 GMT posting contained too many errors. The
> version below is what I respectfully request that you ABIAN, please
> SUPPORT and VALIDATE the claims.
Wow, you're starting to sound just like Abian, too.
Why do I get the haunting impression that Ludwig and Abian are
artificial-intelligence programs that were never designed to interact
with each other?
Feh. (&tSftDotIotE,&tSftDotIotE)
Erik Max Francis, &tSftDotIotE ...!uuwest!alcyone!max m...@alcyone.darkside.com
USMail: 1070 Oakmont Dr. #1 San Jose, CA 95117 ICBM: 37 20 N 121 53 W __
AGCTACTGTACGTACGTTTGCACGTATGCTGTGCACTGCATXCTGACATCGTGACTGATCTGCATGACTTGCA / \
"Omnia quia sunt, lumina sunt." (All things that are, are lights.) \__/
Ludwig Plutonium
cove...@maths.anu.edu.au (Alex.Coventry) writes:
Alex, thanks for your query. We are at the very foundation of
Mathematics ,i.e., Mathematical Logic.
How do you show someone or the math community that they have
misapplied logic? By counterexample within the Natural World, and below
I give two counterexamples.
I ask Alexander Abian to show some other examples that INDIRECT
NONEXISTENCE is an invalid mathematical argument.
The current mathematics community lukewarmly accepts an alleged proof
of the four color mapping which involves a supercomputer. This alleged
proof is a reductio ad absurdum argument. It is an indirect proof
argument applied onto a statement of sufficiency. The four color
mapping problem asks for a proof method of sufficiency. Are four
colors sufficient to color every planar map? The problem is a universal
statement. The logically equivalent statement is an existence
statement. There does not exist a planar map where five colors are
necessary. A reductio ad absurdum argument of the four color mapping
would attempt to prove this problem by stepping-up to a level to five
color mapping. It is curious that the accepted alleged proof using a
supercomputer for verification would attempt a proof by supposing that
if such a planar map existed, it would lead to a contradiction.
The argument, as seen in a depiction, tries to show that it is
impossible to add a fifth region (the one with the question mark) to
the original map in such a way that all the regions share a boundary
with each other.
I contend that a proof of the four color mapping problem is a proof of
sufficiency which can not be mixed with a reductio ad absurdum argument
and I intend to show this clearly with two counterexamples from atoms.
This is one counterexample of the falsity of applying a reductio ad
absurdum method simultaneously onto a sufficiency method. It is
noticed that neutrons, protons, and electrons appear to be sufficient
to make all molecules. When every molecule is checked, it seems that
these three particles are sufficient to make them. Now it is desirable
to demonstrate this fact in the general case that these three particles
are sufficient to make all molecules. A demonstration of the
sufficiency of the 3 particles constituting all molecules is obtained
once I can demonstrate that the 3 particles are sufficient to make all
of the atoms (all of the elements). A demonstration of sufficiency is
obtained by descending below a power of generalization, just as I will
do in the two proofs of the four color mapping problem. I descend from
planar areas to points in a plane (or I could descend to lines in the
plane). But to ascend to a level higher and simultaneously try to show
a contradiction in this higher level is, I contend, impossible. To
demonstrate that 3 particles are sufficient is not possible by
reformulating that no molecule exists which has 4 particles, and if
such a molecule exists than that would lead to a contradiction of
chemistry. It might turn out that a muon along with the other 3
particles is necessary in order to make a particular molecule.
I contend that indirect nonexistence proofs are mathematically
impossible, since a math proof is a 100% guarantee. This is the crux
of the problem of the alleged supercomputer proof of the four color
mapping problem. It is an indirect nonexistence proof which I claim is
mathematically impossible, somewhat like trying to prove a fact by
starting from false premises. Mathematically there are four possible
existence proof methods: 1) direct existence, 2) direct nonexistence,
3) indirect existence, and 4) indirect nonexistence. My indirect proof
method for the infinitude of primes is an example of the indirect
existence. I contend that a proof method of indirect nonexistence is
logically impossible.
Analogously for physics, an indirect existence argument makes
commonsense but an indirect nonexistence is absurd. For example, our
last electron observable plutonium atom universe has ample indirect
evidence for the existence of the plutonium nucleus but yet the quantum
nodes forbid direct observation.
This is my second counterexample for the impossibility of the
indirect nonexistence proof method. It is noticed that 157 neutrons are
sufficient to make every element from 1 to 109. Now demonstrate it. I
propose to step down in level of generalization to nuclei. If I can
demonstrate that 157 neutrons are sufficient to synthesize all nuclei
from 1 to 109 then it is sufficient for all atoms from 1 to 109. Why?
Because nuclei are parts of all atoms and what I can demonstrate for
all known nuclei applies to all known atoms. But a reductio ad
absurdum method onto a sufficiency method would look like this: there
does not exist an atom from 1 to 109 which has more than 157 neutrons
for if there existed such an atom then physics is contradicted. The
flaw of indirect nonexistence is apparent in this counterexample, for
physics is not contradicted if all the atoms of element 108 (or any
other element below 109) had 158 or more neutrons.
ABIAN, PLEASE TRY TO SUPPORT THE CLAIM THAT INDIRECT NONEXISTENCE IS
FALSE LOGIC. PLEASE SHOW OTHER EXAMPLES FROM COMMON DAY EXPERIENCES
THAT DIRECT EXISTENCE, INDIRECT EXISTENCE, DIRECT NONEXISTENCE ARE
LOGICALLY VALID METHODS OF PROOF. BUT THAT INDIRECT NONEXISTENCE IS AN
INVALID METHOD. PLEASE SHOW THIS BY EXAMPLES.
ATOM PLUTONIUM, FISSIONED FOR ME, LET ME SHOW MYSELF IN THEE. CARBON IN
ME, CARBON OF PLUTONIUM, FILL ME WITH LIFE ANEW, THAT I MAY LOVE WHAT
THOU DOST LOVE, AND DO WHAT THOU SUPERDETERMINED ME TO DO. ATOM
MAKE ALL THE PLANETS, PLUS THEIR MOONS A BORN AGAIN EARTH. IN THE
FUTURE THE SOLAR SYSTEM WILL BE ONLY THE SUN AND APPROXIMATELY 500 BORN
AGAIN EARTHS! ATOM
James Kibo Parry
In article <1994Jan7.1...@vaxsar.vassar.edu>,
Alexander Abian <ab...@iastate.edu> wrote:
>
> Please, O, please do not tell me that all the above are good violations and
> violations of Plutonium are bad. WE ALL TRY TO IMPOSE OUR VIEWS UPON THE
> OTHERS AND WE ALL CONSIDER OUR VIEWS THE GOOD VIEWS.!!!
I do not! I try to impose my views upon the world even though I know
them to be bad! EVERYONE MUST PUT BEANS IN THEIR EARS! PLANET EARTH
MUST BE PUT INTO A TATER TWISTER AND GIVEN A BURGER-KING-LIKE FAT CONTENT!
PRESSING YOUR TONGUE TO THE FREEZING COLD DRAINPIPE IS GOOD FOR YOU!
TWO AND TWO MAKE A ZILLION!!!!
> I LOVE TO IMPOSE MY IDEAS UPON THE OTHERS. IT INFLATES MY EGO AND MAKES ME
> FEEL SECURE !!
Yeah, well, MY EGO'S BIGGER THAN YOURS! I have the biggest ego in the
whole world! And not only am I the most egostistical person in all
history--I'm ALSO the MOST HUMBLE!!!
LET US PUT BEANS IN OUR EARS NOW BECAUSE BEING UNHAPPY FEELS GOOD!
-- K.
Archimedes Plutonium
On Thursday, January 6, 1994 at 1:26:21 PM UTC-6, Gerald Edgar wrote:
> Mathematical Cranks
> This is the title of an interesting book by Underwood Dudley, 1992.
> There is an (also interesting) review of it by Ian Stewart in the
> January issue of the American Mathematical Monthly.
> --
> Gerald A. Edgar Internet: ed...@math.ohio-state.edu
> Department of Mathematics Bitnet: EDGAR@OHSTPY
> The Ohio State University telephone: 614-292-0395 (Office)
> Columbus, OH 43210 -292-4975 (Math. Dept.) -292-1479 (Dept. Fax)
I want Terence Tao to do the Cone Oval Slant Cut Experiment of folding a paper cone, dropping a Kerr or Mason lid inside, slanting it at angle and photograph the empty space that is the outline of Oval, never the ellipse. And publish that in a American Mathematical Monthly or another math journal. Include a reference to AP's book on this subject (seen below).
Next, I want Dr. Tao to do a visual cut out of AP's right triangle on a trapezoid when flipped down is part of a calculus integral rectangle, when flipped up on its hinge is the calculus derivative of the slope of the hypotenuse of that right triangle. Dr. Tao publish this in American Mathematical Monthly or some other math journal and include the AP book that references all of this Calculus as seen below.
It is time the world stops propagandizing science education by people who are fools of mathematics, who never engage when it is pointed out they have many mistakes in their presentation of mathematics and end up brainwashing students, not teaching those students.
The Internet, being Freedom of Speech is beyond the control of corrupt gatekeepers of science education and even math professors who cannot tell right from wrong math. And the Internet caused the huge bankruptcy of many a magazine and journal. But there are still too many corrupt math professors and math journals that still keep teaching Propaganda Corrupt Mistaken Math. And it is high time those be cleaned up or cleaned out. For what these journals and bad math professor teachers do, is marr, scar and ruin the education of almost every young person in mathematics they come in contact with. And makes them become a fool that Terry Tao has become in mathematics education.
3rd published book
AP's Proof-Ellipse was never a Conic Section // Math proof series, book 1 Kindle Edition
by Archimedes Plutonium (Author)
Ever since Ancient Greek Times it was thought the slant cut into a cone is the ellipse. That was false. For the slant cut in every cone is a Oval, never an Ellipse. This book is a proof that the slant cut is a oval, never the ellipse. A slant cut into the Cylinder is in fact a ellipse, but never in a cone.
Length: 21 pages
File Size: 1620 KB
Print Length: 21 pages
Publication Date: March 11, 2019
Sold by: Amazon Digital Services LLC
Language: English
ASIN: B07PLSDQWC
Text-to-Speech: Enabled
X-Ray: Not Enabled
Word Wise: Not Enabled
Lending: Enabled
Enhanced Typesetting: Enabled
#8-2, 11th published book
World's First Geometry Proof of Fundamental Theorem of Calculus// Math proof series, book 2 Kindle Edition
by Archimedes Plutonium (Author)
Last revision was 19May2021. This is AP's 11th published book of science.
Preface:
Actually my title is too modest, for the proof that lies within this book makes it the World's First Valid Proof of Fundamental Theorem of Calculus, for in my modesty, I just wanted to emphasis that calculus was geometry and needed a geometry proof. Not being modest, there has never been a valid proof of FTC until AP's 2015 proof. This also implies that only a geometry proof of FTC constitutes a valid proof of FTC.
Calculus needs a geometry proof of Fundamental Theorem of Calculus. But none could ever be obtained in Old Math so long as they had a huge mass of mistakes, errors, fakes and con-artist trickery such as the "limit analysis". To give a Geometry Proof of Fundamental Theorem of Calculus requires math be cleaned-up and cleaned-out of most of math's mistakes and errors. So in a sense, a Geometry FTC proof is a exercise in Consistency of all of Mathematics. In order to prove a FTC geometry proof, requires throwing out the error filled mess of Old Math. Can the Reals be the true numbers of mathematics if the Reals cannot deliver a Geometry proof of FTC? Can the functions that are not polynomial functions allow us to give a Geometry proof of FTC? Can a Coordinate System in 2D have 4 quadrants and still give a Geometry proof of FTC? Can a equation of mathematics with a number that is _not a positive decimal Grid Number_ all alone on the right side of the equation, at all times, allow us to give a Geometry proof of the FTC?
Cover Picture: Is my hand written, one page geometry proof of the Fundamental Theorem of Calculus, the world's first geometry proof of FTC, 2013-2015, by AP.
Length: 137 pages
Product details
ASIN : B07PQTNHMY
Publication date : March 14, 2019
Language : English
File size : 1307 KB
Text-to-Speech : Enabled
Screen Reader : Supported
Enhanced typesetting : Enabled
X-Ray : Not Enabled
Word Wise : Not Enabled
Print length : 137 pages
Lending : Enabled
Amazon Best Sellers Rank: #128,729 Paid in Kindle Store (See Top 100 Paid in Kindle Store)
#2 in 45-Minute Science & Math Short Reads
#134 in Calculus (Books)
#20 in Calculus (Kindle Store)
AP