#539 the proof of the Infinitude of Twin Primes in AP-adics and in the fake system of Natural-Numbers ; new textbook: Mathematical Physics (AP-adic Primer)

[plutonium....@gmail.com]

Tues, Feb 19 2008 9:54 pm was the last time I remember posting to this
book, but since my recent
appearance in a South Dakota newspaper that asks the question: Is
Archimedes Plutonium a genius.
Well, that answer is easy to answer.

I wrote a book correcting about 30 professors of mathematics who each
wrote a book wherein they
gave their own proof of the Euclid Infinitude of Primes and G. H.
Hardy was amoung that group
and there were other prominent mathematicians in that group. And Hardy
is considered a genius
but if Hardy could not deliver a valid Euclid Infinitude of Primes
proof and it took Archimedes Plutonium
to show where those 30 professors of math made a big mistake. And if
we consider Hardy
a genius, then we have to say that Archimedes Plutonium must be a
genius.

What Archimedes Plutonium did to correct Euclid Infinitude of Primes
proof is show that in the
indirect method of reductio ad absurdum, that you have to fall back on
an earlier step in the proof
which is the definition of prime and by doing so, this referring back
to the earlier step, forces the
prover to have to say that the new number formed of multiply the lot
and add 1, is necessarily and
irrefutably a new prime. The mistake that Hardy and 30 math professors
make is they mix the
direct method with the indirect method and end up with a confused
invalid proof argument.

Now I bring that up not because I want to arrogantly fluant that I am
a genius and easily verified
by having corrected mathematics of its Euclid Infinitude of Primes
Proof, but also because, in
writing this post, I have discovered some new information on the
Infinitude of Twin Primes and
why the Natural Numbers as "finite integers" is a fake set of numbers.
As fake as the idea that
fire breathing dragons exist.

The real Counting Numbers are not finite specimens. The real Counting
Numbers are each a
infinitely long string. The number 1 is not 1 but is really an
infinite string ....000000001. We ignore
all those zeroes to the left, not because they are meaningless but
because we are not advanced
in mind and intelligence to realize every number is "infinite". And
for mathematics of the past, they
thought a rule that only finite strings could be numbers and could be
well-defined were simply deluded
people.

The number ....99999999 although infinite is a Natural Number the same
as the numbers 1,2,3 etc.

I called this set of all numbers ....000000, then ....000001,
then .....0000002, all the way up to and
including .....999999999 the AP-adics but they are also the Counting
Numbers and the Natural-Numbers.

So what we teach in mathematics at present and in the past, those
numbers which we called the
Counting Numbers or Natural Numbers as "finite integers" were a bag of
lies. They were useful, mighty
useful, but because they were a bag of tricks and lies, they started
to cause the buildup of a huge
mountain of unsolved problems in mathematics and to name a few--
Riemann Hypothesis, Fermat's
Last Theorem, and one which I am going to talk about now-- Infinitude
of Twin Primes Conjecture.

Euclid in his famous proof of the Infinitude of Primes did a elegant
proof and as become a gem of
mathematics and the intellectual heritage of the world. This proof is
often called one of the top ten
mathematical gems.

TWIN PRIMES INFINITUDE CONJECTURE: there are some primes called twin
primes since they are
separated by a metric of 2, such as 3 and 5 and such as 11 and 13. But
are there an infinitude of these
Twin Primes?

If mathematics with its definition of Natural Numbers as "finite
integers" was not a lie and a sack of
ill-defined contraptions, the question is, why so easy of a proof for
all the primes-- 2,3,5,7, 11, 13,....
Why so easy of a proof, yet when you ask for the infinitude of twin
primes, why nearly impossible
to find a proof?

Now let us stand back for a moment and review all of mathematics and
its proofs. Whenever in mathematics
you have a "true and well defined area" and if you provide a proof of
something such as infinitude of
some objects, if that area is really well defined, then by logic, a
subclass of that infinitude of objects
should be easier to prove than the original infinitude of that object.

In the AP-adics, we use and endorse the Euclid Infinitude of Primes
proof. We simply recognize
that we have the primes not as 2, 3, 5, 7, .... but as ....
000002, .....00003, ....000005, etc

But we also have these strange looking primes ......13121110987654321

So in AP-adics we endorse the Euclid Infinitude of Primes Proof, and
now is requested to prove the
Infinitude of Twin Primes. Simple for us since all we do is take the
Twin Primes of 11 and 13 and
we construct a proof that Twin Primes are infinite as such:

.....131211109876543211 with ....131211109876543213
now the next pair of twin primes is that we eliminate the "2" that
precedes the 11 and 13 as such:
.....13121110987654311 with .....13121110987654313
now we continue to eliminate the "3" before the 11 and the 13 to
construct our next pair of twin primes
and we do this construction knowing it is endless and thus the Twin
Primes are Infinite.

So in mathematics, when you have a true set of numbers that are well
defined and not a phony bag
of lies, once you have proven the "overarching theorem of infinitude
of primes" the infinitude of a lesser
class of primes should be as easy as the AP-adics proof of the
Infinitude of Twin Primes.

But with the phony bag of lies that Natural Numbers are "finite
integers" it is impossible to prove
Infinitude of Twin Primes. Yes impossible, and let me show why it is
impossible by using the above
construction.

In order to prove Infinitude of Twin Primes as the phony set of
"finite integers" all that one needs to
do is show that just one single pair in each category above is a Twin
Prime Pair.

In the above I show two categories of these two:
.....131211109876543211 with ....131211109876543213
.....13121110987654311 with .....13121110987654313

Now, Infinitude of Twin Primes proof in the old finite integer scheme
requires a simply thing. It only
requires that we find a set of twin primes in each category.

This is the first category:
.....131211109876543211 with ....131211109876543213

So we ask, is 211 and 213 twin primes in "finite integers" if not,
then we ask is 3211 and 3213
twin primes in "finite integers".

Simple and easy. To prove Infinitude of Twin Primes in "finite
integers" requires us to simply find
a pair of twin primes in each category of the AP-adics.

Mind you, the AP-adics proved Twin Primes are infinite in "infinite
integers", but why in the world
cannot the "finite integers" come forth with a proof?

The answer is obvious. Noone in mathematics can ever prove Infinitude
of Twin Primes simply because
they are a phony and liaring set of ill-defined numbers. There is no
"finite integer" for all numbers extend
infinitely long.

The reason the AP-adics can swallow up and validate Euclids method of
proving Infinitude of Primes
and then turn around and in 5 minutes prove the Infinitude of Twin
Primes is because Natural Numbers
are all "infinite integers". They are not a bag of phony lies of Loch
Ness or Bigfoot or fire breathing dragons.

Now some may pop their stupid heads up and say that Twin Primes is a
Godel undecidable conjecture.
These are only more stupid people who would propose that, because
Godel's undecidable proof was
based on another falsehood found in mathematics of the Cantor
Diagonal, but that is too long of a story
here.

The basic facts are these: It is reasonable to expect that if you can
build a car engine, you can build
smaller engines to run smaller things like lawnmowers. If you can
prove the infinitude of regular primes,
then mathematics should easily prove a smaller subclass of primes
whether they are infinite or not.
Since mathematics proves infinitude of regular primes via Euclid
method and since AP-adics easily
proves infinitude of twin primes, would tell a commonsense person that
the trouble with this picture
is that modern mathematics is under a false and delusion that "finite
integers" holds any reality.

Now recently in a newspaper article on Archimedes Plutonium in the
South Dakota newspaper which
showed me on the front cover and had a full page story on me has Jesse
Hughes commenting about
me saying this:
--- quoting a biased Argus Leader story over Archimedes Plutonium ---
Jesse Hughes, an
adjunct professor of philosophy at Bennett College and Salem State
College in Arlington, Mass., in an e-mail.

Hughes, a long-time contributor to many of the same Usenet newsgroup
that Plutonium frequents, called Plutonium's theory "mind-bogglingly
silly," and dubbed him the "reigning king of Usenet cranks."

--- end quoting ---

All I have to say about Jesse Hughes is where did he ever correct
Hardy and thirty other
math professors who could not do a valid Euclid Infinitude of Primes
proof? Show me any
post by Hughes where he puts forth some new ideas of mathematics and
where he corrects
the Euclid Infinitude of Primes proof.

I would dare say that Hughes, in all of his life as a philosophy
professor was unable to even
deliver a valid proof of Euclid Infinitude of Primes, and people like
this become so sour and bitter
towards other people who do have new ideas that Hughes lashes out at
them and calls them
"cranks".

Archimedes Plutonium
www.iw.net/~a_plutonium
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies

[plutonium....@gmail.com]

[Active Member]

#539 "Archimedes Plutonium" anagram -

"Demonic Mailer, Shut Up!"

<plutonium....@gmail.com> wrote in message
news:4ba8362b-c053-4d03...@k30g2000hse.googlegroups.com...
> Tues, Feb 19 2008 9:54 pm was the last time I remember anything

[Jan Burse]

Could you please explain your argument in a simpler
example. Nothing with primes and numbers so on.

But much simpler. For example Clavius Law respective
Consequentia mirabilis:

Assume the universe is empty,
then the universe has size zero,
but then zero belongs to the universe,
hence the universe is not empty,
.:. therefore the universe is not empty.

Accepted or not?

Bye

[plutonium....@gmail.com]

I had asked that this poem be included in the recent Argus Leader done
on Archimedes Plutonium,
but that story tried to depict me more as eccentric as wearing
mosquito jacket while working in
the garden (Argus Leader calls it a beekeeper-suit) or falsely saying
that I wore "homemade cape"
when it was simply my coat slung around my neck. I asked them to
include this poem because
it is far better for the reading public to read something that makes
them "ponder and think" rather
than to read a newspaper story crafted to make the reader believe AP
is some eccentric.

Physics Poem

All things are made up of atoms
as Democritus told us in the Atomic theory
The Universe itself is a thing, for it is not nothing
So the Universe must be a big atom, or dare we
say Democritus forgot an exception to his theory

The above, Jan, is really a syllogism

All things are made up of atoms is the Atomic Theory of Physics.

The Universe is a thing for it is not empty.

Hence, the Universe must be a single big atom, or we have to amend the
Democritus
Atomic theory to include the exception.

Now I know Jan was refering to something else, but this is more
important.

[Jan Burse]

plutonium....@gmail.com schrieb:
>
> Physics Poem

>
> Now I know Jan was refering to something else, but this is more
> important.

Near hit or near miss, I cant tell.
Awaiting a deaper answer.

Bye

[Jan Burse]

Jan Burse schrieb:

> Awaiting a deaper answer.
>
Oops, should read:
Deeper, not diaper.

Bye

[plutonium....@gmail.com]

Jan Burse wrote:
> Could you please explain your argument in a simpler
> example. Nothing with primes and numbers so on.
>

I already gave the analogy of car motors. If you cannot understand
that,
forget it.

> But much simpler. For example Clavius Law respective
> Consequentia mirabilis:
>
> Assume the universe is empty,
> then the universe has size zero,
> but then zero belongs to the universe,
> hence the universe is not empty,
> .:. therefore the universe is not empty.
>

To recognize that the first line is quantity, the second line
is geometry, and so hopelessly unconnectable lines do not allow for
any conclusions.

But let me see if I can squeeze the Atom Totality Syllogism in there.

Assume the Universe is not an atom
then the Universe must not be composed of matter interspersed by empty
space, for that is an atom
but then, as we look at the Night Sky we observe matter in galaxies
and stars interspersed in empty space
hence the Universe is an atom

I should be able to improve on the above.

Basically the inside of an atom mirror images what we see in the Night
Sky of matter interspersed in
empty space, for most of the volume of an atom is empty space and most
of the volume of the Night
Sky is empty space.

[mal...@gmail.com]

I have had a lot of fun reading all this stuff. I have also read
http://groups.google.com.by/group/sci.logic/msg/a6235d5653d6af68

I think that what Hardy had in mind is that since natural numbers are
well ordered, to prove the infinitude of primes you just need to prove
that the subset of all prime numbers greater than any given prime is
not empty. This and the reductio ad absurdum proof are both based on
the construction of the number 'product of primes plus one', so it is
normal to somehow 'confuse' them, being each of them correct in their
own.

Mathematicians do not normally write formal proofs but instead they
sort of describe them; they tell us how we should be able to write a
formal proof. This being understood, it is normal that whenever we
talk about things we know and understand well we make mistakes in our
discourse which, from a pragmatic point of view, can perfectly be
ignored without any damage. So giving any importance to that kind of
mistakes doesn't make anyone any sort of genius.

By the way, why should these strange looking ......13121110987654321
be a prime?

Cheers.

[Jan Burse]

plutonium....@gmail.com schrieb:

> Jan Burse wrote:
>> Could you please explain your argument in a simpler
>> example. Nothing with primes and numbers so on.
>>

You mean:

> It is reasonable to expect that if you can
> build a car engine, you can build
> smaller engines to run smaller things like
> lawnmowers.

I meant simpler but still math. So car engines
falls out of the picture.

Bye

[plutonium....@gmail.com]

Alright, I well attempt to explain this in math in as simple way as
possible.

We want to know if a concept is well-defined or ill-defined. The
concept in question is
"finite integer" as compared to "infinite integer". The mathematics
community believes
"finite integer" is well-defined for they start mathematics with the
Peano Axioms which
is the axiom system of "finite integers".

So, here is a Test Procedure to tell us whether a concept of "finite
integer" is really well-defined
or whether it is phony baloney.

METHOD OF TESTING OF WELL-DEFINED in MATHEMATICS:

In infinite-integers such as AP-adics we can define primes and we ask
a question of whether
the primes in AP-adics are infinite or finite. We can prove in AP-
adics using Euclid's method of
proof that the primes in AP-adics are infinite. Now we look at other
sets of primes in AP-adics
and ask to prove if they are infinite or finite sets. We ask if Twin
Primes or primes of other forms
such as Mersenne primes or primes of form 2k +1 or 2k-1 or primes or
many other forms of primes.

Here is the crux of the test. How easy is it to prove primes of forms
are infinite in AP-adics. It is
very easy. Almost as fast as someone asks-- is this form of primes
infinite or finite in AP-adics,
that I can almost give a proof as fast as the person voices what form
of primes he wants to know
whether finite or infinite.

The picture for "Finite Integers" is very much different. Yes, the
Euclid Infinitude of Regular Primes
is an easy proof, but the moment you ask whether Twin Primes is
infinite or Mersenne Primes are
infinite, noone can find proofs.

Here is another example. For the proof that there are Pythagorean
triples is an easy proof to solve
for exponent 2. But now more general we want to prove Fermat's Last
Theorem, and for more general
even yet, we want to prove the Beal Conjecture.

So that in the case of infinitude of primes proofs we scaled down to
subsets of primes and wanted to
know if those subsets were infinite in primes. In the case of
Pythagorean Triples we scaled upwards
asking for proofs of more general than the Pythagorean triple of
exponent 2.

Whether we scale up or scale down in our quest for proofs, we have to
ask a question. When we
are working with "infinite integers" we easily prove all subsets of
primes as to whether they are infinite
or finite and we easily prove all generalizations of Pythagorean
Triples whether it is Fermat's
Last Theorem or the step more general of Beals.

But when we ask the same feat of "finite integers" we can only prove
infinitude of primes and only
prove Pythagorean Theorem.

What this should tell a commonsense person, is that the very
definition of "finite integer" is to blame.
That the definition is so lousy and so inconsistent that it cannot
provide what I call "Scaling Proofs"

If in mathematics, someone finds concepts and well-defines those
concepts, then they have a breeze
of finding proofs in both scaling up and scaling down.

Take the example of the Riemann Hypothesis where there are scaling
down, (not sure if there are
scaling up) but the Moebius function is a scaling down of the Riemann
Hypothesis. Now in "infinite
integers" we have proofs of the Riemann Hypothesis, it is a breeze,
and we have proofs of scaled down
theorems related to RH.

So, here is the test, the test of whether a concept in mathematics is
dirty and ill-defined and a fake,
is whether it can find a proof such as Euclid Infinitude of Primes,
but then is stuck, stuck with Twin Primes
and stuck with Mersenne primes and stuck with primes of form 2k+1 and
2k-1 and stuck with thousands
of other forms of primes. Now, looking at "infinite integers" and they
easily prove every one of these
forms and not stuck with any.

So if a concept in mathematics is pure and clean and true, it is not
going to provide a proof of regular
primes and then be stuck with not able to prove any generalizations of
regular primes or any subset
form of primes.

If a concept cannot have easy and fast proofs when scaled up or scaled
down from a theorem-- Euclid's
Infinitude of Primes or Pythagorean Theorem is indication that the
concept is so dirty and lousy and
fake.

[plutonium....@gmail.com]

In the previous post I described a new test procedure in mathematics
to tell us whether we have given birth
to a worthy mathematical entity, or whether we have defined a fire
breathing dragon that does not exist,
except in our imagination.

The test is summarized as able to find proofs in scaling up and
scaling down of a theorem, and the ease or
difficulty in finding proofs of scale. So that if a definition or
concept in mathematics seems to have a
huge pile of unproven conjectures, then it is commonsense to think
that what is wrong is not the lack of
geniuses in mathematics who can find proofs, but rather the problem is
that the definition or concept
was phony baloney. When we see an area of mathematics that has a huge
logjam pileup of unsolved
problems such as Number theory, we do not need another Wiles or Godel
who offer deluded alleged
proofs. What we need are many mathematicians to stand back of the
scene and say, "let us reexamine
the definition and concept of "finite integer". Mathematics really has
only one logjam, one huge pile
of unsolved problems and they are in Number theory.

If you examine Geometry, the other half of mathematics, you do see
unsolved problems, but no huge
logjam pileup.

A wise and astute mathematician who stands back and reflects on the
over all condition of all of mathematics
cannot fail to see that Geometry is relatively clean and unfestered
with logjam pileups. And cannot fail
to see the abysmal pit of Number theory.

So why should that be? Well, a commonsense person would then point a
finger at the definition and
concept of "finite integer"

If we tossed out "finite integer" in all of mathematics and replaced
it with "infinite integer" then the overall
condition of mathematics would have few outstanding unsolved
conjectures. And the unsolved problems
of Number theory would be about the same number as the unsolved
problems in Geometry. In other words
no imbalance in all of mathematics.

Now let me try to give a specific example and the best I can do at
this moment is the concept and
definition of "regular polyhedra" in geometry. There are no
outstanding unsolved problems that I know
of in geometry involving regular polyhedra. Ask a question as a
conjecture in regular polyhedra and almost
instantly a proof can be summoned. What this means is that the
concepts and definitions surrounding
regular polyhedra in geometry are pristine pure, clean and true. And
any conjecture involving scaling up or
scaling down of he concept of regular polyhedra is easily solved.

The picture for "finite integers" in Number theory is the contrast
opposite of "regular polyhedra" in
Geometry.

Mathematics as a science is the laziest of the sciences to be able to
correct itself "system wide". I mean
if the science of mathematics has a buildup of fakeries, it is slow to
realize the cancer in mathematics
and the reason mathematics is so vulnerable to a cancer buildup of
fakes, is because mathematics
unlike physics does not have that impartial judge of "experiment
results". In mathematics, what is deemed
to be true is merely a country-club-group of old men. In physics what
is deemed to be true are a long
list of experiments that any generation of physicists can re-do or re-
perform. Physics is not tied to
the opinion of some old aged men in physics as to whether something is
true or phony baloney. Math
on the other hand is not allied with experiments. In math, some old
geriatric professor's opinion counts
more than anything else. This is why Physics had a revolution in
replacing Newtonian Mechanics with
Quantum Mechanics in the early 1900s, because the tidal wave of
experiments had to throw Newtonian
Mechanics out the window. In contrast, the subject of mathematics has
never had a modern day
revolution but instead has built a larger mountain of fakes in the
20th century. Whereas Physics
can clean up its house every 100 years, a subject like mathematics
bound more to opinions of old aged
men than experiments would have a tough time of cleaning up its house
in every 1,000 years.

[plutonium....@gmail.com]

malc...@gmail.com wrote:

>
> I have had a lot of fun reading all this stuff. I have also read
> http://groups.google.com.by/group/sci.logic/msg/a6235d5653d6af68
>
> I think that what Hardy had in mind is that since natural numbers are
> well ordered, to prove the infinitude of primes you just need to prove
> that the subset of all prime numbers greater than any given prime is
> not empty. This and the reductio ad absurdum proof are both based on
> the construction of the number 'product of primes plus one', so it is
> normal to somehow 'confuse' them, being each of them correct in their
> own.
>
> Mathematicians do not normally write formal proofs but instead they
> sort of describe them; they tell us how we should be able to write a
> formal proof. This being understood, it is normal that whenever we
> talk about things we know and understand well we make mistakes in our
> discourse which, from a pragmatic point of view, can perfectly be
> ignored without any damage. So giving any importance to that kind of
> mistakes doesn't make anyone any sort of genius.
>
> By the way, why should these strange looking ......13121110987654321
> be a prime?
>
> Cheers.

You have a touch of what I call the Jesse Hughes syndrome as
illustrated in the
Argus Leader news story of Archimedes Plutonium. This is a syndrome of
where
you hate someone and the hatred then never allows you to acknowledge
the
achievements of the person you hate. You belittle, you ignore, you
dismiss,
you attack the person, and no matter how high of a achievement, how
important
the achievement, you simply can never acknowledge it.

And I believe that such a condition are the signs that the person is
no longer fit to
be in education or the science.

Imagine a professor on campus who hates a sports person, and who in
the weekend
won the game for the hometeam. And the professor failing to
acknowledge the achievements
of the sports person.

Perhaps the prime reason we have "educators" is for the moment in
which they can congratulate
those who have achieved something academically or physically. And when
we see educators
full of hatred who cannot for a single moment acknowledge the
achievement of others, is time,
I believe for them to be pushed out of education since they do more
harm than what little good.

I have discovered there is a LOGICAL flaw in most renditions of the
Euclid Infinitude of Primes Proof.
I have written a book and published it on the Internet showing where
many textbooks on math
give an invalid proof of Infinitude of Primes. Hardy's book A
Mathematicians Apology is one amoung
30 that fails to give a valid proof of Infinitude of Primes.

It is a "big mistake". And not as Malcolm wants to dream is a minor
mistake. For Malcolm is acting
more like Jesse Hughes, in his hatred of Archimedes Plutonium, that
you deny me of my achievement.

If you taught a group of Grade School Children how to add and these
children learn it for the first time
and then you quized them with a sum such as this:

Add this column:
3
5
10
9
____

And 30 Grade school children handed in their answer and 28 of them
summed to 18
while two of the children summed to 27.

Then both Malcolm and Jesse Hughes should congratulate those two who
had the correct
answer of 27. And even if they hated the guts of those two, should
still congratulate them.

Likewise.

What I should as a fundamental mistake of logic reasoning performed by
a group of 30
math professors which included Montgomery in a Number theory textbook
and include
Hardy in A Mathematicians Apology and included Conway and many other
math professors
is akin to adding the above list and coming up with 18.

The mistake that Hardy makes as well as thirty other professors of
mathematics is that
they commit themselves to a Reductio Ad Absurdum proof, but fail to
apply the "definition
of prime" that forces them to recognize that the new number has to be
prime also. That if
3 and 5 were the only primes that exist, then 16 is also a prime
number in this universe of
all primes. That is the mistake made by nearly everyone who has
written a Euclid Infinitude of
Primes proof in a book.

It is a big mistake, just as the Grade Schoolers added 10 as if it
were a 1 and arrived at 18
instead of the correct answer of 27.

So for Malcolm and Jesse Hughes to continue to belittle and ignore and
lambast my accomplishements
to never accept my achievements, reflects more on your hatemongering.

If any handful of pipsqueck professors of mathematics had corrected
Hardy and a group of 30
professors of their tainted and invalid attempt of Euclid Infinitude
of Primes, they would have been
touted around the world as the new genius. But because it was
Archimedes Plutonium who
accomplished this, the world only rises up to spew more hatred and
suppression of the man
who discovered the Atom Totality theory.

Archimedes Plutonium

[Alexander Nogonnaworkherenomore]

#543 "Archimedes Plutonium" anagram -

"Posh, numerical tedium!"

<plutonium....@gmail.com> wrote in message
news:b1dd67a9-4e37-495d...@m3g2000hsc.googlegroups.com...

> In the previous post I blithered uncontrollably, finishing up
> by filling my shorts with shockingly foul liquishit.

[Jan Burse]

plutonium....@gmail.com schrieb:
>
> If a concept cannot have *easy and fast* proofs when scaled up or

> scaled down from a theorem-- Euclid's Infinitude of Primes or
> Pythagorean Theorem is indication that the concept is so
> dirty and lousy and fake.
>

Not so fast.
No pain, no gain.

It is well known, that omega induction is not always
sufficient for the proofs, and that transfinite
induction is sometimes needed.

Guess why?

[mal...@gmail.com]

> where dots of the electron-dot-cloud are galaxies- Ocultar texto de la cita -
>
> - Mostrar texto de la cita -

Just to put things in order:

I do not hate anyone. I just noted that in normal speech such kind of
mistakes are common and that it is also normal not to pay much
attention on them. Certainly one would expect any competent person in
any field to be able to grasp this kind of mistakes instantly.
However, as you have come to realize, this simply doesn't happen.

I think that the matter on how horrible the mistake is, is a bit
subjective. For me it is a curiosity, and I believe that it is due to
a confusion of two very similar proofs. I do not think any of those
mathematicians, Hardy included, would not have corrected their proofs
as soon as anyone would have made them note that.

I am sorry that you have felt my discussion as an attack.

The question about the primeness of the strange looking ......
13121110987654321 was serious. Is there anything similar to the
fundamental theorem of arithmetic for your AP-adics?

Cheers.

[plutonium....@gmail.com]

malc...@gmail.com wrote:

>
> Just to put things in order:
>
> I do not hate anyone. I just noted that in normal speech such kind of
> mistakes are common and that it is also normal not to pay much
> attention on them. Certainly one would expect any competent person in
> any field to be able to grasp this kind of mistakes instantly.
> However, as you have come to realize, this simply doesn't happen.
>

When G.H. Hardy writes the Euclid Infinitude of Primes Proof in a book
"A Mathematicians Apology"
and makes the logical mistakes and when Niven, Zuckerman, Montgomery,
in a textbook
AN INTRODUCTION TO THE THEORY OF NUMBERS makes the logical mistakes.

--- quoting from my book Correctiong Euclid's Infinitude of Primes
Proof ---
(#3) --- quoting WHAT IS MATHEMATICS? Richard Courant and Herbert
Robbins
1941 page 22 ---
The proof of the infinitude of the class of primes as given by Euclid
remains a model of mathematical reasoning. It proceeds by the
"indirect
method". We start with the tentative assumption that the theorem is
false. This means that there would be only a finite number of primes,
perhaps very many -- a billion or so -- or, expressed in a general and
non-committal way, n. Using the subscript notation we may denote these
primes by p1, p2, ...,pn. Any other number will be composite, and must
be divisible by at least one of the primes p1,p2,...,pn. We now
produce
a contradiction by constructing a number A which differs from every
one
of the primes p1, p2, ..., pn because it is larger than any of them,
and which nevertheless is not divisible by any of them. This number is
A = (p1xp2x...xpn) +1, i.e. 1 plus the product of what we supposed to
be all the primes. A is larger than any of the p's as a divisor. Since
our initial assumption that there is only a finite number of primes
leads to this contradiction, the assumption is seen to be absurd, and
hence its contrary must be true. This proves the theorem.
--- end quoting WHAT IS MATHEMATICS? Courant and Robbins ---

One thing that Courant and Robbins do that is really good is clearly
state what they thought Euclid method was.
But then their proof pretty much dissolves away or
collapses. For they did not fetch a new prime to ever warrant them
saying
they reached a contradiction. They say that A is different and A is
absurd,
but why were they never able to say that A is necessarily a new prime.
Like the other authors listed before, if Courant and Robbins had had
to
provide
both a indirect and direct method proof, perhaps they would have
delivered
a clear and valid result instead of this incomplete attempt.
--- end quoting ---

I would say those books are serious books and if they cannot give a
waterproof proof of
Euclid IP without huge error, then Malcolm is a hatemonger that trys
to diminish and belittle
the accomplishments of Archimedes Plutonium.

In my example of the Grade Schoolers Analogy:

Add this column:
3
5
10
9
____

And if thirty Grade school children handed in their answer and twenty-
eight of them

summed to 18
while two of the children summed to 27.

Then Malcolm is going to say that all thirty had it correct and that
their mistakes were
minor language mistakes.

This is where people in academics and education no longer belong in
those fields, where
they continue to make excuses and continue to not recognize
achievement.

When we ask the question of 30 professors of mathematics about their
published "alleged"
proof of Euclid Infinitude of Primes (of course Hardy and Courant and
Polya are dead) but
of those 30 professors who are living who made the mistakes. If you
ask them this question:

If the Universe of "all the primes" were merely the set of 3 and 5,
then (3x5) + 1 = 16
then the 16 is
necessarily a new prime in that universe, and the reason for the
contradiction is because
of the starting off definition of prime. If you ask those of the
thirty who got it wrong, whether
they can agree and understand that 16 is a new prime number, then they
are admitting to
their big mistake.

Likewise, if we were to question the two Grade Schoolers why they
added 10 as 10 and not as
1 and they are able to tell you that 10 is the number after 9 while
the twenty eight kids with the
wrong answer see 10 as 1 and 0.

> I think that the matter on how horrible the mistake is, is a bit
> subjective. For me it is a curiosity, and I believe that it is due to
> a confusion of two very similar proofs. I do not think any of those
> mathematicians, Hardy included, would not have corrected their proofs
> as soon as anyone would have made them note that.
>

A mistake is a mistake. If you answer that 3 + 5 + 10 + 9 = 18, then
do not
cover up your mistake. Likewise, if you claim to be giving a valid
Euclid Infinitude of Primes
Proof such as Niven, Zuckerman, Montgomery or Courant and Robbins or
Polya or Hardy,
then do not try to be making excuses for your big mistake. Come forth
and admit the
mistake is big.

> I am sorry that you have felt my discussion as an attack.
>

You suffer the same disease of hatred that Jesse Hughes suffers. You
see someone you
hate, and then you make all sorts of excuses. You cannot admit that
Archimedes Plutonium corrected a
big mistake made by mathematics professors in delivering a valid proof
of Infinitude of Primes.

The moment that a person such as you, cannot admit to the
accomplishments and
achievements by others then you should depart education and science.

> The question about the primeness of the strange looking ......
> 13121110987654321 was serious. Is there anything similar to the
> fundamental theorem of arithmetic for your AP-adics?
>
> Cheers.

I wrote a very long book recently called AP-adics primer, where your
question is answered. That
answer is too long to get started here. The above is a prime number
for it is Champernowne's (spelling)
number attached to the primes 11 and 13 or any other pair of primes.
In that book I argue that
this set of numbers 1,2,3,.... the Counting Numbers are fictional.
Again, too long to start a discussion
here.

Archimedes Plutonium

[Tonico]

****************************************************************

Nonsense Archie.

First, you have no accomplishment other than the ones your rather wild
and pretty pitiful imagination causes you to believe.

Second, the only huge error is that you believe you can do meaningful
physics and maths instead of making an ass of yourself.

Third: aren't you ashamed of yourself?? I honestly hope you haven't
spawned kids: they'll be laughed and scoffed at badly at school.

Fourth: knock it off, fruitcake!

Regards
Tonio

[Larry Hammick]

Tonico, I blush to admit that it was I myself who inadvertantly put this bee
in Archie's bonnet. I remarked here at sci.math that there are several
differences between Euclid's proof of IX.20
http://aleph0.clarku.edu/~djoyce/java/elements/bookIX/propIX20.html
and the modern version, although the basic ideas are same and the proof is
still attributed to Euclid. In particular,

-- Euclid dares not speak of "infinitely many" primes (or any other actual
infinite) as we do.

-- Euclid works on what we would call an arbitrary finite non-empty family
of primes. He does not argue by contradiction and hypothesize that they are
/all/ the primes, and he does not assume that they are distinct.

Anyhow, here's a proof of IX.20 discovered by Filip Saidak in 2005 AD!
Define inductively a sequence (x(n), y(n)) of ordered pairs by
x(1) = 2
y(1) = 3
and for n >= 2 :
x(n+1) = x(n)y(n)
y(n+1) = x(n)y(n) + 1
By induction, x and y stay positive. Also x(n) and y(n) are relatively prime
by definition. So y(n) has a prime factor which x(n) lacks, and that factor,
along with all the factors of x(n), appears in x(n+1). So by induction x(n)
has at least n distinct prime factors, for arbitrary n.

LH

[Bill Dubuque]

"Larry Hammick" <larryh...@telus.net> wrote:
>
> Anyhow, here's a proof of IX.20 discovered by Filip Saidak in 2005 AD!
> Define inductively a sequence (x(n), y(n)) of ordered pairs by

> x(1) = 2, > y(1) = 3

> and for n >= 2 :
> x(n+1) = x(n)y(n)
> y(n+1) = x(n)y(n) + 1
> By induction, x and y stay positive. Also x(n) and y(n) are relatively prime
> by definition. So y(n) has a prime factor which x(n) lacks, and that factor,
> along with all the factors of x(n), appears in x(n+1). So by induction x(n)
> has at least n distinct prime factors, for arbitrary n.

SIMPLER NN + N has more prime factors than N

"Saidak's proof" is certainly not new.

--Bill Dubuque

[plutonium....@gmail.com]

Hi Malcolm, I am thinking that from reading your synopsis, that you do
not see it as a big mistake because
your synopsis is wrong:

Here is your synopsis:

malc...@gmail.com wrote:

> I think that what Hardy had in mind is that since natural numbers are
> well ordered, to prove the infinitude of primes you just need to prove
> that the subset of all prime numbers greater than any given prime is
> not empty. This and the reductio ad absurdum proof are both based on
> the construction of the number 'product of primes plus one', so it is
> normal to somehow 'confuse' them, being each of them correct in their
> own.

> Mathematicians do not normally write formal proofs but instead they
> sort of describe them; they tell us how we should be able to write a
> formal proof. This being understood, it is normal that whenever we
> talk about things we know and understand well we make mistakes in our
> discourse which, from a pragmatic point of view, can perfectly be
> ignored without any damage. So giving any importance to that kind of
> mistakes doesn't make anyone any sort of genius.

Malcolm, I do not see it as you described above. So I am asking not
for
some childish request on my part, but as an instructive quest. I am
asking
that you provide a Euclid Infinitude of Primes Proof reductio ad
absurdum
from you, purely from your mind and not something that you read and
try to
verbalize in your own words.

And if you feel good, even a Direct proof of Euclid Infinitude of
Primes; and if
not feeling good, well okay, no big deal.

So if you would care to offer up from your mind a Euclid IP reductio
ad absurdum
then I will check it out, and hopefully convince you that what I have
done is a big
accomplishment of correcting the Euclid IP proof.

Again, if you do not feel up to it, well, that is that.

Also, Jesse Hughes is probably reading and watching. If he feels up to
writing a Euclid IP
both in direct and indirect, or just one of them, I would be happy to
check it out, because I
seriously doubt that Jesse could even do a Euclid IP from his mind
without reading it and
parroting from some book.

[plutonium....@gmail.com]

Larry Hammick wrote:
(snipped)

> in Archie's bonnet. I remarked here at sci.math that there are several
> differences between Euclid's proof of IX.20
> http://aleph0.clarku.edu/~djoyce/java/elements/bookIX/propIX20.html
> and the modern version, although the basic ideas are same and the proof is
> still attributed to Euclid. In particular,
>

Not true. Apparently you arrived at the sci.math in 2002.

I had started discussing the flaw of Euclid's IP in 1993-1994 sci.math

witness:

Sun, 20FEB1994, 21:05:13 GMT sci.math
INCONSISTENT PEANO AXIOMS AND MATH PROFESSORS
Lines: 36
Sender: k...@spdcc.com (Karl Heuer)

k...@ursa-major.spdcc.com (Karl Heuer) writes:

In article (5JChA8g2...@jojo.escape.de>

det...@jojo.escape.de (Detlef Bosau) writes:
>Ludwig.Pluton...@dartmouth.edu meinte am 18.02.94
>>det...@jojo.escape.de (Detlef Bosau) writes:
>>>Wrong. Your two numbers are not necessarily prime
>>NO, YOU ARE WRONG. Those numbers are necessarily prime, due to
>>UPFAT, all the primes that exist in the finite set leave a remainder
>>of 1.
>I'll give you a lesson of elementary arithmetics. . .

I really shouldn't bother to get involved in this discussion again,
but
Ludwig is right. In logical terms, his key statement is "if P is a
finite set containing all the primes, then prod(P)+1 is prime." This
is
a true statement.

Let's step through your alleged counterexample:

>consider your set of primes to be: {2,3,5,7,11,13}, as I assert 13 to be
>the largest prime. [. . .] Now, you made the assertion, that
> > > > (2x3x5x11x13) + 1 [=30031] must be prime.

Yes, it's true that if 13 is the largest prime, then 30031 is prime.
Do
you disagree with that assertion?

>As you stated before, there exists an unique prime decomposition of
>30031. This is 59x509. It could be easily shown, that 59 and 509
>both are prime.

If 13 is the largest prime, then 59x509 is not a factorization of
30031.

--- end quoting Karl Heuer's post of 1994 ---

And earlier than 1993-4, I had sent a journal article to Notre Dame,
some
logic journal where I discussed the flaw of Euclid's IP circa
1991-1993

So, Larry, how is it that you influenced me in 1991 with your posts of
2002?

If you cannot even get your dates right, you expect to get the logic
of a math proof right?

[plutonium....@gmail.com]

Not as neat or tidy or all-inclusive as the new Euclid Infinitude of
Primes
Proof that includes all the Natural Numbers. When Euclid or Saidak did
their proofs
of the Infinitude of Primes they were not aware of all the Natural
Numbers such as
....999999 or ....666666777777. Where Natural Numbers = AP-adics.

So what is the easiest of all proofs that primes are infinite? And I
believe this proof is
the fastest, easiest.

We simply construct an Infinitude of Primes:
(1) 11 and 13 are prime
(2) the number ....1413121110987654321 is also prime as Champernownes
number (spelling)
(3) construct an infinite set of primes by simply attaching the "11"
and "13" on the far right
yielding ....141312111098765432111 and ....141312111098765432113 now
for the next
pair of twin primes we attach a 2 giving ....1413121110987654321211
and ....1413121110987654321213
now the next pair of twin primes we attach a 3 giving ....
14131211109876543213211 and ....14131211109876543213213
now for the next pair of twin primes we attach a 4 to the previous 3
and 2 and we keep doing this infinitely.
Now I not only proved the primes are infinite but that Twin-primes are
infinite. So this is the first
proof of Euclid Infinitude of Primes and Twin-primes in one proof.

Now I like to challenge Mr. Bill Dubuque to a case of "logical flow"
of proof coupled with brevity.
Brevity that Ian Stewart showed when he called it "multiply the lot
add 1". I
challenge Bill to give a Euclid Infinitude of Primes proof of Direct
Method and then Indirect Method.
Two proofs simultaneously, one of direct and the other indirect for
contrast. In the past,
mathematicians were never required to give both simultaneously. Maybe
if they had been required
that such a high percentage of failures 28/30 = 93% failure to render
a valid proof argument.

Are you up for a challenge Bill?

[mal...@gmail.com]

Hi,

You say my synopsis is wrong as a whole? Please, explain.

It also seems you want me to provide a proof... Ok, here it goes.

We say a natural number is prime iff it is greater than 1 and doesn't
have any divisor other than 1 and itself.
By the fundamental theorem of arithmetic, every number greater than 1
has a prime divisor.

Let us suppose that the subset of all prime numbers is finite.
Then the product of all primes plus one, since it doesn't belong to
the subset of all prime numbers (it is greater than any of them) is
not a prime, but it has a prime divisor, since it is greater than 1.
But in fact, it doesn't have any divisor from the list of all primes.
Contradiction.

I keep on believing that the key idea in this proof is the
construction of the number "the product of all primes plus one", and
not the strict application of the rules of logic, which are supposed
to work when applied correctly.

For some other proofs of the infinitude of primes I recommend:

Number Theory. An Introduction via the Distribution of Primes
Benjamin Fine
Gerhard Rosenberger
Birkhäuser

Cheers.

[Larry Hammick]

<plutonium....@gmail.com> wrote in message
news:e6c0d43e-e82d-44aa...@b1g2000hsg.googlegroups.com...

>
> Larry Hammick wrote:
> (snipped)
>> in Archie's bonnet. I remarked here at sci.math that there are several
>> differences between Euclid's proof of IX.20
>> http://aleph0.clarku.edu/~djoyce/java/elements/bookIX/propIX20.html
>> and the modern version, although the basic ideas are same and the proof
>> is
>> still attributed to Euclid. In particular,
>>
>
> Not true. Apparently you arrived at the sci.math in 2002.

Sounds about right.

>
> I had started discussing the flaw of Euclid's IP in 1993-1994 sci.math
>
> witness:
>
> Sun, 20FEB1994, 21:05:13 GMT sci.math
> INCONSISTENT PEANO AXIOMS AND MATH PROFESSORS
> Lines: 36
> Sender: k...@spdcc.com (Karl Heuer)

Okay, but were you looking at Euclid himself, or at Hardy and the numerous
other writers who speak of "the set of all primes" and "Euclid's proof"?
Anyhow, it's a trivial quibble.

[plutonium....@gmail.com]

malc...@gmail.com wrote:

>
> Hi,
>
> You say my synopsis is wrong as a whole? Please, explain.
>

Thanks for participating, because I think we can unravel much more
when
we actually do a Euclid IP rather than we commenting on the sidelines
on Euclid IP. As
an old pragmatist that I am and pragmatist saying-- The learning is in
the doing, and not the peripheral commenting.

> It also seems you want me to provide a proof... Ok, here it goes.
>
> We say a natural number is prime iff it is greater than 1 and doesn't
> have any divisor other than 1 and itself.
> By the fundamental theorem of arithmetic, every number greater than 1
> has a prime divisor.
>
> Let us suppose that the subset of all prime numbers is finite.
> Then the product of all primes plus one, since it doesn't belong to
> the subset of all prime numbers (it is greater than any of them) is
> not a prime, but it has a prime divisor, since it is greater than 1.
> But in fact, it doesn't have any divisor from the list of all primes.
> Contradiction.
>

There is a problem with this statement in your above.

"Let us suppose that the subset of all prime numbers is finite."

I doubt it is a mathematical statement but the assemblage of
contradictions in terms. Like saying "Let us suppose infinity is
finite."

Malcolm, can you write your above and parallel each statement with a
numbers example.

Here is one for my proof of Euclid IP.

(1) Definition of Prime number
(2) Suppose the set of all primes is Finite
(2*) Suppose 3 and 5 were all the primes that exist
(3) Multiply the lot and add 1
(3*) (3x5) +1 = 16
(4) This new number is necessarily a new prime since we revert to our
definition in (1)
and all the primes divided into this new number leave a remainder of 1
(4*) 3 and 5 are all the primes that exist and when divided into 16
leave a remainder
of 1 and by the definition of prime from (1), that 16 is indeed a new
prime
(5) Contradiction
(6) Set of all primes is infinite

The essence of the correction of math professors such as Conway,
Courant, Hardy, Niven,
Montgomery, Zuckerman, is that they could not understand that 16 is
prime in the Indirect
Method. No matter what the number "multiply the lot and add 1" is, no
matter what it is, whether
it is 16 or (3x5x7) +1 = 106, that 106 is a new prime when the
universe of all primes is 3,5,7.

This is my correction of the math communities horrible habit of not

giving a valid Euclid Infinitude

of Primes proof, as they seem unable to understand the logic and they
mix the direct with the indirect.

Malcolm, you see how I parallel the statements with a numbers example.

Your above is not a proof because you can never run a numbers example
parallel to your statements
for some of your statements are not even mathematical.

> I keep on believing that the key idea in this proof is the
> construction of the number "the product of all primes plus one", and
> not the strict application of the rules of logic, which are supposed
> to work when applied correctly.
>

The crux of the proof is the synchronized working arrangement between
two elements in the proof-- the definition of prime at the start and
the "multiply the
lot and add 1" Yours above Malcolm does not even use the definition of
prime.

I am hoping that Bill Dubuque offers up his version so that I can dive
into
the internal logic of the direct versus the indirect. There is much
mathematics
in the what I call "Meta-Euclid Infinitude of Primes Proof" The
analysis of the
logical underpinning of the direct and indirect.

> For some other proofs of the infinitude of primes I recommend:
>
> Number Theory. An Introduction via the Distribution of Primes
> Benjamin Fine
> Gerhard Rosenberger

> Birkh�user
>
> Cheers.

Thanks, will look them up next time in a library and see if they
managed to give a valid
Euclid IP proof. The statistics for math professors is not running
good since only 2 out of
30 have managed to give a valid Euclid IP.

Archimedes Plutonium

[plutonium....@gmail.com]

Larry, I doubt you can even give a valid Euclid IP both direct and
indirect without major flaws.

You want to give it a try?

[plutonium....@gmail.com]

The title of this post is not capricious in "all sorts of forms" There
are the two listed forms but there are many
other forms of primes such as k^2 +1 and k^2 -1 and then there are
forms such as k!+1 and k!-1.

So there are very many forms of primes, and if my memory is correct,
someone thought they proved
a certain form of primes is a finite set. I say they must review their
alleged proof because they
started with the assumption that Natural Numbers are finite integers
when in fact the true blue
Natural Numbers are the AP-adics or infinite integers.

A number such as this is a prime number 100000.......00000003 which is
an infinite integer whose
front-view is "1" and whose endview is "3". Another prime number
is ....1413121110987654321.
So in earlier times, mathematicians never realized that the set of
primes is so much larger than their
deluded picture of primes. They were playing cards with over half the
deck missing.

In a previous post I gave a proof of the infinitude of Twin Primes by
grafting 11 and 13 unto the backbone
of the above Champernownes number .....1413121110987654321. So I
constructed a infinite string of
Twin Primes.

Now, can I construct an infinite string of primes of form 2k+1? It is
a little more challenging than Twin
Primes construction.

It goes like this. I start with the prime number of .......
1111100001111000111001101. Now it is
similar to the pattern of Champernownes number only its digits are 1
and 0. It is prime because these
numbers are "Irrational Counting Numbers". Now I have to give a
precise definition of Irrational Natural
Numbers. We have definition of Composite Natural Number and Prime
Natural Number but now
we must provide definitions of Irrational Natural Numbers and Rational
Natural Numbers. I am not going
to do that here for this is already long enough.

Now this number .......1111100001111000111001101 in the form 2k+1
is .......2222200002222000222002203
which is also prime. Now the next prime I construct is to scoot down
leftwards and eliminate the first
"1" as this number .......111110000111100011100110 which is not prime
itself but when I do the
2k+1 it becomes .......222220000222200022200221 Now I infinitely scoot
down the line and produce a
new prime of form 2k+1. Thus the set of all primes of form 2k+1 is an
infinite set. Likewise for primes
of form 2k-1 and likewise for all other forms.

Even the form that some mathematicians of the past were thought to be
a finite set, because of their
alleged proof, is not questioned since they started their work with
the deluded belief that Natural Numbers
are finite integers.

[plutonium....@gmail.com]

I wrote earlier today:

> > It also seems you want me to provide a proof... Ok, here it goes.
> >
> > We say a natural number is prime iff it is greater than 1 and doesn't
> > have any divisor other than 1 and itself.
> > By the fundamental theorem of arithmetic, every number greater than 1
> > has a prime divisor.
> >
> > Let us suppose that the subset of all prime numbers is finite.
> > Then the product of all primes plus one, since it doesn't belong to
> > the subset of all prime numbers (it is greater than any of them) is
> > not a prime, but it has a prime divisor, since it is greater than 1.
> > But in fact, it doesn't have any divisor from the list of all primes.
> > Contradiction.
> >

Malcolm, I now realize what you were trying to do above. You were
trying to
do a Direct Euclid IP. It should have looked like this, with number
examples
for steps.

Earlier today I gave the Indirect methof of Euclid IP and here it is:

>
> Here is one for my proof of Euclid IP.
>
> (1) Definition of Prime number
> (2) Suppose the set of all primes is Finite
> (2*) Suppose 3 and 5 were all the primes that exist
> (3) Multiply the lot and add 1
> (3*) (3x5) +1 = 16
> (4) This new number is necessarily a new prime since we revert to our
> definition in (1)
> and all the primes divided into this new number leave a remainder of 1
> (4*) 3 and 5 are all the primes that exist and when divided into 16
> leave a remainder
> of 1 and by the definition of prime from (1), that 16 is indeed a new
> prime
> (5) Contradiction
> (6) Set of all primes is infinite
>

Malcolm, here is the direct method that you were attempting to do:
Euclid IP (direct method)

(1) Definition of Prime number

(2) Set of primes is this set {2,3,5,7,11,13,....} and we are out to
prove whether it is finite or infinite
(3) Given any subset of primes, that subset has a cardinality
(3*) a subset of primes such as {3,5} had cardinality of 2 since it
has two members
(4) The proof involves the increase in set cardinality of given any
subset of primes
and since we can increase the cardinality by one more prime, means the
set of
all primes is infinite
(4*) the crux of the proof is that like numbers, given any set of
numbers, add one to
the largest and you automatically increase the set cardinality and
thus an infinite set
(5) Every particular subset of primes, we multiply the lot and add 1.
(5*) The subset {3,5} gives (3x5)+1 = 16
(6) This new number "multiply the lot and add 1" can either be prime
itself or have
a prime factor because of (1) definition of prime
(6*) (3x5)+1 = 16 so this subset of cardinality 2, we have either 16
is prime or has
a prime factor. Obviously 16 is not prime and the prime factor is 2.
(7) Thus, given any finite set of primes we can augment that set with
a new prime
of either "multiply the lot add 1" or a prime factor of "multiply the
lot add 1"
(7*) 16 is not prime but 2 is prime and not in the subset {3,5}
(8) Since any finite subset of primes has the ability of augmentation
of a new prime
not in the list, means the set of all primes is an infinite set

There Malcolm, you were striving for the Direct Method, but you made
several mistakes. You
included a Suppose reductio ad absurdum, when you should have never
done so. There is no
"suppose" and a contradiction involved in the Direct method.

What is the difference between Direct and Indirect? Both rely on the
definition as first step.
Both require the use of "multiply the lot and add 1". The major
difference is that in the Indirect,
the new number formed by "multiply the lot and add 1" is necessarily
prime, and it can not have
a prime factor. Most math professors get it wrong and deliver an
invalid proof because in the back of
their minds they remember that 30031 has factors of 59x509 for the
subset where 13 is the
largest prime, but in the indirect method the number 30031 is a new
prime since
the set of all primes is {2,3,5,7,11,13}. The definition coerces you
to conclude 30031 is a new prime
not on the list of all primes and this new prime number 30031 is the
contradiction and discharge of the
proof. This is the mistake Niven, Zuckerman, Montgomery made in their
textbook, and the mistake that
Courant and Conway and Wikipedia and 30 other math professors make.

The mistake is a lack of Logical Continuity, just as if we were to
electrically wire a new house and
if the lines are not connected correctly there will be no flow of
electricity.

So the moment you do a Indirect Euclid IP and mention a search for a
"prime factor", you lost the proof
and have fallen off the mountain.

[drmw...@gmail.com]

Seldom has one human being (Archimedes Balonium) written so much and
said so little of value.

There is nothing wrong with the standard proof of the infinitude of
prime. It is a clear proof by contradiction. One assumes one has them
all and then constructs a new number that may or may not actually be
prime, but even if composite, its divisors are not among the assumed
finite set of all primes.

Newbies should not be taken in by this nonsense.

Dr. Michael W. Ecker
Associate Professor of Mathematics
Pennsylvania State University
Wilkes-Barre Campus
Lehman, PA 18627

[plutonium....@gmail.com]

drmwec...@gmail.com wrote:
> Seldom has one human being (Archimedes Balonium) written so much and
> said so little of value.
>

I offered the Atom Totality theory and the Fusion Barrier Principle
and scores of other
new ideas. By comparison Ecker has given the world nothing as far as
new ideas of
any importance.

> There is nothing wrong with the standard proof of the infinitude of
> prime. It is a clear proof by contradiction. One assumes one has them
> all and then constructs a new number that may or may not actually be
> prime, but even if composite, its divisors are not among the assumed
> finite set of all primes.

How silly and stupid of you, for you then imply that the direct and
indirect
are identical proofs. Even a High School student can see that you are
wrong
on that score.

>
> Newbies should not be taken in by this nonsense.
>
> Dr. Michael W. Ecker
> Associate Professor of Mathematics
> Pennsylvania State University
> Wilkes-Barre Campus
> Lehman, PA 18627

Hatred by envy is one of the worst hatreds in the world.

When someone is in education and then deny those that have achieved
something
of Corrective value and of newness, then they no longer belong in
education. Why they
deny others of the successes they achieve is probably due to their own
careers as
being lackluster and their bitterness then lashes out at people who
accomplish
something.

Ecker does not deserve to have a degree in mathematics when he cannot
even understand
a valid Euclid Infinitude of Primes proof. Of the list of 30 or more
math professors who
I cited in my book "Correcting the Euclid Infinitude of Primes Proof,
some of them did
do a valid Euclid IP. Those that did not, are not in agreement with
Ecker. They recognize
the mistake and fault of their rendition. There was a team of authors
who I cited in my
book with a invalid Euclid IP and because of my insistence, they
corrected or at least
attempted to correct in a revised edition.

Even Wikipedia had a invalid Euclid IP and then changed it because of
my prodding.

In the above, it is apparent that Ecker is unable to do a valid Euclid
IP proof in direct and
indirect method.

In the old days before the Internet, these sour professors would
simply stew on campus
and not really be a menace to those in the sciences, but in our modern
day life, these sour
and bitter professors can magnify their bitterness in Internet
hatemongering.

When any teacher in education gets to the point where they cannot
recognize the achievement
or accomplishements of others in their respective science field, they
are more of a harm to the
science and the students and should be removed of education. If you
cannot congratulate someone
who achieved some work, then get you gone.

[Bill Dubuque]

mal...@gmail.com wrote:
>
> I keep on believing that the key idea [in Euclid's proof that there
> are infinitely many primes] is the construction of the number

> "the product of all primes plus one"

Actually the "reason" such proofs work is because the ring of integers
has relatively few units. Thus, by way of the Pigeonhole Principle,
one can avoid them and generate an infinite sequence of pairwise-coprime
nonunits. For the details see the generalizations given in the theorems
below from my prior post [0].

sttsc...@tesco.net wrote:
>
> Is there any analog A to N, where the usual rules of arithmetic
> apply, every non-unit is divisible by some prime, A is infinite
> and yet the number of primes or irreducibles are finite ?

Yes, vacuously, let A = Q or any infinite field. Less trivially
force all but finitely many primes to become units, e.g. grow
Z to a subring of Q by adjoining 1/p for almost all primes p.
For example, all primes but 2 become units in the subring of Q
of all rational numbers expressible in the form m/n with n odd.
All primes but 2,3 are units in subring of form m/n, (n,6) = 1.
Such enlarged domains remain Euclidean -> PID -> UFD... since
the localization construction always preserves such structure.

Thus generalizing Euclid's theorem to other rings will require
some hypotheses other than Euclidean, PID, UFD, etc, that are
preserved by localizations. In general 1 + pqr... can fail to
produce a new prime (or irreducible) because it may be a unit.
But we can also try 1 + d pqr... for any d in D. If all those
are units then D has a lot of units. Therefore we can eliminate
such failure by hypothesizing D has relatively few units, e.g.

THEOREM Suppose that D is an infinite integral domain where all
nonunits have an irreducible factor. If D has finitely many units
then D has infinitely many irreducibles (= primes if D is a UFD).

PROOF Via contradiction. Let m = product of all irreducibles.
Since D is infinite so is 1 + m D [ 1+md = 1+md' <=> d = d']
so it must contain a nonzero nonunit [ since only finite #units ]
with irreducible factor p | 1 + m d; but p|m => p|1 =><= QED

It is easy to generalize this theorem even further, for example:

THEOREM If a commutative ring R has a smaller cardinality subset U
containing all divisors of 0 and 1, then ~U, the complement of U,
contains an infinite number of pair-coprime nonunits (hence also an
infinite number of irreds if every r in ~U has an irred factor).

PROOF Enlarge any finite set P < ~U of pair-coprime nonunits as
follows. Let m be the product of all p in P (m = 1 if P empty).
Elements of S = 1 + m R are coprime to each p in P since p|m
Hence S is disjoint from P since coprime nonunits cannot be equal.
Now enlarge P by adjoining any s in S /\ ~U, which is nonempty
since S is too big to lie inside U by the cardinality hypothesis.
In fact #S = #R > #U because r -> 1 + m r injects R into S,
that is 1+mr = 1+mr' => mr = mr' => r = r' via m cancellable,
being a product of non-zero-divisor (so cancellable) p in P. QED

COROLLARY Elements of a finite commutative ring R divide 0 or 1.
In particular a finite integral domain is a field.

PROOF Let U = { all divisors of 0 and 1 }. Necessarily U = R
else #U < #R => ~U is infinite by Theorem, contra R finite. QED

What a surprisingly sweet little application of Euclid's theorem!
Compare the above proof with the classic pigeonhole based proof
http://planetmath.org/encyclopedia/AFiniteIntegralDomainIsAField.html

Other ring theoretic generalizations of Euclid's theorem can be
expressed in terms of the nilradical (intersection of all prime
ideals) and related notions such as G-domains [1]. If there are
only a finite number of prime ideals then the nilradical is
clearly nonzero: take a product of elements from each prime.
But for a wide class of domains, Krull domains (including UFDs,
Dedekind domains, etc) it is easy to show that the nilradical
is nonzero iff D has the structure in the example above, i.e.
a PID with finitely many primes. So, for example, any non-PID
in this class has infinitely many prime ideals; e.g. this
leads to Larry Washington's proof of Euclid's theorem via any
non-UFD number ring (if Z had a finite #primes then so would
every number ring, so every number ring would be a PID so UFD)
Closely related are various topological generalizations of
Euclid's theorem, e.g. work by Golomb, Gotchev, Porubsky.

These are the sort of results that a curious student can easily
discover independently when pondering generalizations of Euclid's
theorem (indeed I found them as a teenager). They make excellent
exercises for beginning number theory students. If I can dig up
my original notes I will post further results. I hope readers
will contribute some of their favorites (there are many other
variants of proofs of Euclid's theorem listed in Ribenboim's
Book of Prime Number Records, but not those I presented above).

--Bill Dubuque

[0] http://google.com/groups?selm=y8zbr8kv5vl.fsf_-_%40nestle.csail.mit.edu
[1] http://google.com/groups?selm=y8z7jjzdivj.fsf%40nestle.csail.mit.edu

[plutonium....@gmail.com]

Bill Dubuque wrote:
> mal...@gmail.com wrote:
> >
> > I keep on believing that the key idea [in Euclid's proof that there
> > are infinitely many primes] is the construction of the number
> > "the product of all primes plus one"
>
> Actually the "reason" such proofs work is because the ring of integers
> has relatively few units. Thus, by way of the Pigeonhole Principle,

Not true, because Bill is under the assumption Natural-Numbers =
Finite
Integers, which is an ill-defined set. Things are different in Natural-
Numbers
= Infinite Integers.

The reason that "multiply the lot add 1" works is that it is merely
another form
of primes such as 2k+1 or 2k-1. One form that does not work is 2k for
2 is the
only even prime number. Twin Primes are of the form k,k+2 such as 3,5
but there
are primes of form k,k+2,k+4 such as 3,5,7.

Now Bill with his old fake math of Natural-Numbers = Finite Integers
would
be unable to launch into the question of whether there is a infinitude
of primes
such as 3,5,7, but when you do mathematics with the true-blue counting
numbers
the Infinite Integers there is a simple constructive proof of the
infinitude of Triplet Primes.
An infinitude of Natural Numbers whose last digit is 9, 1, and 3 and
then those whose last digit
is 7, 9, and 1. Obviously no number whose last digit is 5 is prime. So
what Bill
thinks is the underpinning of these infinitude proofs with some
Pigeonhole Principle is far
off the mark. The underpinning is that almost any form for primes is
an infinite set, not all sets
but most.

>
> These are the sort of results that a curious student can easily
> discover independently when pondering generalizations of Euclid's
> theorem (indeed I found them as a teenager). They make excellent

So you are doing Ring theory as a teenager? But when reading Hardy's
book, unable to spot a mistake in his Euclid Infinitude of Primes
proof?

To me, a mathematics proof is like the electrical system wiring of an
entire
house. The lights and appliances work because everything is connected
and there are no shorts or grounds. But many proofs of mathematics
have so
many holes and gaps, that no electricity works for them. Many proofs
in mathematics
would be like a electrician coming to wire a house and throwing down
some wire
and then leaving.

> exercises for beginning number theory students. If I can dig up
> my original notes I will post further results. I hope readers
> will contribute some of their favorites (there are many other
> variants of proofs of Euclid's theorem listed in Ribenboim's
> Book of Prime Number Records, but not those I presented above).
>
> --Bill Dubuque

I challenge Bill to write a Euclid Infinitude of Primes proof both
direct and indirect. I challenge him
because I want to discuss Metamathematics
of the differences in the pattern of Direct versus Indirect. I cannot
discuss that if the person has no
reference to a mathematics proof that has a Direct and Indirect. Most
mathematicians believe that
if they provide a proof of a subject, that they can switch to a
indirect or direct, freely. So if they get hold
of one, they believe they can turn around and provide the other
method. I do not share that opinion, because
I know that in geometry proofs, the indirect method is virtually
nonexistent and that only one method of
proving occurrs-- some form of direct method.

The method of proofs-- direct or indirect, I feel comes more from
physics than it comes from mathematics
or logic and is meta-mathematics. This subject of an analysis of
direct versus indirect method is
seldom discussed and there is a paucity of anyone researching this
subject.

So the Euclid Infinitude of Primes is a pretty example of a proof that
has both Direct and Indirect and
allows for analysis of these two methods. I believe they are
Complimentarity methods, and that means
if a proof is of one, then it may or may not have the other.
Complimentarity is independence of one another.

So again, I challenge Bill, if not too scared, to write a Euclid IP in
direct and indirect. Then we can
analyze the Metamathematics of the two methods.

The way I see it, the direct method versus indirect method is like the
physics of electron versus
positron, where both have things in common -- same mass, but have
things opposite -- charge.
Both are independent of one another. And I hope to dispel this widely
perceived false notion
in the math community that once a proof is found, whether direct or
indirect, that they thence can
transform the proof into the other method.

Maybe Bill is too scared to do a Euclid IP both direct and indirect.
Maybe he is more of a politician and
dodging a challenge rather than simply offering his rendition. Maybe I
scare people, for fear of any
shortcoming.

Archimedes Plutonium

[plutonium....@gmail.com]

Archimedes Plutonium wrote:
>
> The reason that "multiply the lot add 1" works is that it is merely
> another form
> of primes such as 2k+1 or 2k-1. One form that does not work is 2k for
> 2 is the
> only even prime number. Twin Primes are of the form k,k+2 such as 3,5
> but there
> are primes of form k,k+2,k+4 such as 3,5,7.
>

The idea here is that most forms of primes are infinite.

Now that raises an interesting question about some alleged forms under
Natural-Numbers = finite integers are shown to be finite. I believe I
remember
this in connection with Whitehead over a discussion of the Riemann
Hypothesis
where he imagines that RH is false because of some forms of prime
slowly and
gradually end up as finite. I do not remember what form of primes it
was.

The reason I bring this issue up, is because, under Natural-Numbers =
infinite
integers, I suspect those forms that were thought to and proven as
finite, are, now,
once again truly infinite sets of primes.

I also remember trying to graph that sequence of primes to try to get
a sense of
how they stopped, never to continue. But in infinite integers I want
to reraise that issue
for I have the sneaky suspicion that such a form was really infinite
after all.

Now is the Riemann Hypothesis true or false? I cannot remember clearly
what conclusions
I had last drawn on RH, and my problem stemming from too many irons in
the fire. I believe
I ended up last time concluding RH was false. But I like to reenter
that analysis the next time
by comparing RH with e^(i x 2pi) = 1. Can we relate strictly RH with
Euler's identity? If we can
do so, then the failure of Euler's Identity is the fact that we have e
and pi belong to a different geometry
than does i. And realizing that, we realize that the Euler Identity is
nothing more than
n^0 = 1 and where i has the value of 0 in NonEuclidean geomety
accounting for the Euler
Identity.

[plutonium....@gmail.com]

Well, people of the future can actually eyewitness the aging process
of Mr. Archimedes Plutonium.
I would never have made such a mistake of above in my 40s or younger
decades, but here as I
am now 58 years of age, I am slipping in memory. It was Littlewood, so
how could I have ever
suggested it was Whitehead? Memory is going to start to fail on all of
us, and for me, it is obvious
that at 58, that process has begun. So it is a good thing that I am in
the midst of writing all these books
before my memory gets so bad that it impinges on my organizing of all
my past thoughts.

I believe we can prove the Riemann Hypothesis is false by a
paralleling of primes of form where they
are primes and an infinite set, but which they are so spread far apart
that we only find the first such
prime of that form that we would believe they are like the Riemann
Hypothesis that all the nontrivial
zeros are on the 1/2 Real line.

Now in the Infinite Integers = Natural-Numbers, the primes are as
dense as the Natural Numbers get into
....3333333 or say .......6767676767 as they are dense in the interval
of 0 to 10.
In fact the prime numbers ......141312111098765432109 and ......
141312111098765432111 and
......141312111098765432113 and ......141312111098765432117
and ......141312111098765432119
has five primes in a interval of equal length to 0-10 where there are
only four primes 2,3,5,7 in 0-10.

Now Littlewood said there was really no evidence to believe the
Riemann Hypothesis is true and that
there is stronger evidence to believe it is false and he used an
example of a funtion, which I was unable
to locate.

Now the Mersenne Primes are primes of form 2^k-1 where the k is prime
also. If my memory is correct
we have found only 45 such Mersenne primes.

Now, does the search for Mersenne primes remind us of the Riemann
Hypothesis? Yes indeed in that
we believe those primes are well behaved that the nontrivial zeroes
remain on the 1/2 Real line.

And since 2^k-1 has only 45 Mersenne primes, what about primes of the
form (2^k-1)^2^k-1?
In other words, what about primes of the form of Mersenne primes
raised to the power of Mersenne
primes? Does this not parallel the Riemann Hypothesis? Of course it
does, for you could travel
what seems like an eternity and never come upon such a prime, yet they
are infinite.

Likewise, the first nontrivial zero of the Riemann Hypothesis starts
at such a huge distance from
0 that we are lulled into believing RH is true when in fact it is
false.

So a parallel way of proving RH is false, is the proving that Mersenne
Primes raised to the power
of Mersenne Primes is an infinite set of primes. This is
straightforward proof in AP-adics by
using the Champernownes number as rootstock and grafting onto the
rightwards end a prime
such as .....11110001110011013.

And to prove Riemann Hypothesis is false is easily done via geometry.
The Natural Numbers lie
on a curved surface of elliptic geometry, not Euclidean geometry where
the 1/2 Real line is thought
to be a straight line. The Natural Numbers bend and curve around in
Space and come back to a zero
point. So the Riemann Hypothesis crumbles apart as nonsense as to how
the primes of the Natural
Numbers are located on a spherical surface.

[plutonium....@gmail.com]

Archimedes Plutonium wrote:
>
> I believe we can prove the Riemann Hypothesis is false by a
> paralleling of primes of form where they
> are primes and an infinite set, but which they are so spread far apart
> that we only find the first such
> prime of that form that we would believe they are like the Riemann
> Hypothesis that all the nontrivial
> zeros are on the 1/2 Real line.
>

I believe the above is an alternative equivalent statement of the
Riemann Hypothesis. What it implies is
that if the Riemann Hypothesis were true, then we come to a point of a
"Prime form" wherein those
primes are no longer an infinite set and any prime forms beyond this
prime form are also finite sets.

There are only 45 known Mersenne Primes, and the proof that Mersenne
Primes are finite or infinite has
eluded mathematicians. I have recently given a method of proving
Mersenne Primes are infinite sets
in Natural-Numbers = Infinite Integers. This same method would easily
prove that Mersenne Primes
raised to the power of Mersenne Primes FORMS is also a form that is an
infinite set of primes.

So, if the Riemann Hypothesis is true, then we arrive at a FORM of
primes in Natural-Numbers = Finite
Integers for which those primes are a finite set and cannot be
infinite set and also, all forms beyond that
initial Riemann Hypothesis-Form are finite prime sets. So if the
Riemann Hypothesis is true, then
near the Mersenne Prime Form is a finite set and not infinite and all
higher forms beyond the Mersenne-Form
are also finite sets. So if the Riemann Hypothesis is true, means that
somewhere out there, perhaps
the Mersenne primes or a form slightly higher than Mersenne Primes do
all those forms have only
a finite set of primes and no more prime sets that are infinite in
cardinality.

So I think that I have linked the truth or falsity of the Riemann
Hypothesis with the FORM of primes and
their set cardinality.

If the Riemann Hypothesis is false, then, no matter how extended the
Form of prime-- say we have
Mersenne primes raised to the power of Mersenne primes or say we have
2 raised to successive powers subtract
1. No matter how attenuated or thin it is for a Prime Form, that Form

is an infinite set of primes.

So if you believe the RH is true, then there is a Form in which the
primes of that Form are finite and all higher
forms are finite. But if you believe RH is false, then no matter how
extended of a Form of primes, they are
still infinite set of primes that make up that form.

And the geometry equivalent is that the Riemann Hypothesis is lines of
latitude and those lines are formed
by an infinite set of numbers. The lines of latitude is infinite set
of latitude lines and the points on the
latitude lines are all infinite sets.

[John Jones]

plutonium....@gmail.com wrote:
> Tues, Feb 19 2008 9:54 pm was the last time I remember posting to this
> book, but since my recent
> appearance in a South Dakota newspaper that asks the question: Is
> Archimedes Plutonium a genius.
> Well, that answer is easy to answer.
>
> I wrote a book correcting about 30 professors of mathematics who each
> wrote a book wherein they
> gave their own proof of the Euclid Infinitude of Primes and G. H.
> Hardy was amoung that group
> and there were other prominent mathematicians in that group. And Hardy
> is considered a genius
> but if Hardy could not deliver a valid Euclid Infinitude of Primes
> proof and it took Archimedes Plutonium
> to show where those 30 professors of math made a big mistake. And if
> we consider Hardy
> a genius, then we have to say that Archimedes Plutonium must be a
> genius.
>
> What Archimedes Plutonium did to correct Euclid Infinitude of Primes
> proof is show that in the
> indirect method of reductio ad absurdum, that you have to fall back on
> an earlier step in the proof
> which is the definition of prime and by doing so, this referring back
> to the earlier step, forces the
> prover to have to say that the new number formed of multiply the lot
> and add 1, is necessarily and
> irrefutably a new prime. The mistake that Hardy and 30 math professors
> make is they mix the
> direct method with the indirect method and end up with a confused
> invalid proof argument.
>
> Now I bring that up not because I want to arrogantly fluant that I am
> a genius and easily verified
> by having corrected mathematics of its Euclid Infinitude of Primes
> Proof, but also because, in
> writing this post, I have discovered some new information on the
> Infinitude of Twin Primes and
> why the Natural Numbers as "finite integers" is a fake set of numbers.
> As fake as the idea that
> fire breathing dragons exist.
>
> The real Counting Numbers are not finite specimens. The real Counting
> Numbers are each a
> infinitely long string. The number 1 is not 1 but is really an
> infinite string ....000000001. We ignore
> all those zeroes to the left, not because they are meaningless but
> because we are not advanced
> in mind and intelligence to realize every number is "infinite". And
> for mathematics of the past, they
> thought a rule that only finite strings could be numbers and could be
> well-defined were simply deluded
> people.
>
> The number ....99999999 although infinite is a Natural Number the same
> as the numbers 1,2,3 etc.
>
> I called this set of all numbers ....000000, then ....000001,
> then .....0000002, all the way up to and
> including .....999999999 the AP-adics but they are also the Counting
> Numbers and the Natural-Numbers.
>
> So what we teach in mathematics at present and in the past, those
> numbers which we called the
> Counting Numbers or Natural Numbers as "finite integers" were a bag of
> lies. They were useful, mighty
> useful, but because they were a bag of tricks and lies, they started
> to cause the buildup of a huge
> mountain of unsolved problems in mathematics and to name a few--
> Riemann Hypothesis, Fermat's
> Last Theorem, and one which I am going to talk about now-- Infinitude
> of Twin Primes Conjecture.
>
> Euclid in his famous proof of the Infinitude of Primes did a elegant
> proof and as become a gem of
> mathematics and the intellectual heritage of the world. This proof is
> often called one of the top ten
> mathematical gems.
>
> TWIN PRIMES INFINITUDE CONJECTURE: there are some primes called twin
> primes since they are
> separated by a metric of 2, such as 3 and 5 and such as 11 and 13. But
> are there an infinitude of these
> Twin Primes?
>
> If mathematics with its definition of Natural Numbers as "finite
> integers" was not a lie and a sack of
> ill-defined contraptions, the question is, why so easy of a proof for
> all the primes-- 2,3,5,7, 11, 13,....
> Why so easy of a proof, yet when you ask for the infinitude of twin
> primes, why nearly impossible
> to find a proof?
>
> Now let us stand back for a moment and review all of mathematics and
> its proofs. Whenever in mathematics
> you have a "true and well defined area" and if you provide a proof of
> something such as infinitude of
> some objects, if that area is really well defined, then by logic, a
> subclass of that infinitude of objects
> should be easier to prove than the original infinitude of that object.
>
> In the AP-adics, we use and endorse the Euclid Infinitude of Primes
> proof. We simply recognize
> that we have the primes not as 2, 3, 5, 7, .... but as ....
> 000002, .....00003, ....000005, etc
>
> But we also have these strange looking primes ......13121110987654321
>
> So in AP-adics we endorse the Euclid Infinitude of Primes Proof, and
> now is requested to prove the
> Infinitude of Twin Primes. Simple for us since all we do is take the
> Twin Primes of 11 and 13 and
> we construct a proof that Twin Primes are infinite as such:
>
> .....131211109876543211 with ....131211109876543213
> now the next pair of twin primes is that we eliminate the "2" that
> precedes the 11 and 13 as such:
> .....13121110987654311 with .....13121110987654313
> now we continue to eliminate the "3" before the 11 and the 13 to
> construct our next pair of twin primes
> and we do this construction knowing it is endless and thus the Twin
> Primes are Infinite.
>
> So in mathematics, when you have a true set of numbers that are well
> defined and not a phony bag
> of lies, once you have proven the "overarching theorem of infinitude
> of primes" the infinitude of a lesser
> class of primes should be as easy as the AP-adics proof of the
> Infinitude of Twin Primes.
>
> But with the phony bag of lies that Natural Numbers are "finite
> integers" it is impossible to prove
> Infinitude of Twin Primes. Yes impossible, and let me show why it is
> impossible by using the above
> construction.
>
> In order to prove Infinitude of Twin Primes as the phony set of
> "finite integers" all that one needs to
> do is show that just one single pair in each category above is a Twin
> Prime Pair.
>
> In the above I show two categories of these two:
> .....131211109876543211 with ....131211109876543213
> .....13121110987654311 with .....13121110987654313
>
> Now, Infinitude of Twin Primes proof in the old finite integer scheme
> requires a simply thing. It only
> requires that we find a set of twin primes in each category.
>
> This is the first category:
> .....131211109876543211 with ....131211109876543213
>
> So we ask, is 211 and 213 twin primes in "finite integers" if not,
> then we ask is 3211 and 3213
> twin primes in "finite integers".
>
> Simple and easy. To prove Infinitude of Twin Primes in "finite
> integers" requires us to simply find
> a pair of twin primes in each category of the AP-adics.
>
> Mind you, the AP-adics proved Twin Primes are infinite in "infinite
> integers", but why in the world
> cannot the "finite integers" come forth with a proof?
>
> The answer is obvious. Noone in mathematics can ever prove Infinitude
> of Twin Primes simply because
> they are a phony and liaring set of ill-defined numbers. There is no
> "finite integer" for all numbers extend
> infinitely long.
>
> The reason the AP-adics can swallow up and validate Euclids method of
> proving Infinitude of Primes
> and then turn around and in 5 minutes prove the Infinitude of Twin
> Primes is because Natural Numbers
> are all "infinite integers". They are not a bag of phony lies of Loch
> Ness or Bigfoot or fire breathing dragons.
>
> Now some may pop their stupid heads up and say that Twin Primes is a
> Godel undecidable conjecture.
> These are only more stupid people who would propose that, because
> Godel's undecidable proof was
> based on another falsehood found in mathematics of the Cantor
> Diagonal, but that is too long of a story
> here.
>
> The basic facts are these: It is reasonable to expect that if you can
> build a car engine, you can build
> smaller engines to run smaller things like lawnmowers. If you can
> prove the infinitude of regular primes,
> then mathematics should easily prove a smaller subclass of primes
> whether they are infinite or not.
> Since mathematics proves infinitude of regular primes via Euclid
> method and since AP-adics easily
> proves infinitude of twin primes, would tell a commonsense person that
> the trouble with this picture
> is that modern mathematics is under a false and delusion that "finite
> integers" holds any reality.
>
> Now recently in a newspaper article on Archimedes Plutonium in the
> South Dakota newspaper which
> showed me on the front cover and had a full page story on me has Jesse
> Hughes commenting about
> me saying this:
> --- quoting a biased Argus Leader story over Archimedes Plutonium ---
> Jesse Hughes, an
> adjunct professor of philosophy at Bennett College and Salem State
> College in Arlington, Mass., in an e-mail.
>
> Hughes, a long-time contributor to many of the same Usenet newsgroup
> that Plutonium frequents, called Plutonium's theory "mind-bogglingly
> silly," and dubbed him the "reigning king of Usenet cranks."
>
> --- end quoting ---
>
> All I have to say about Jesse Hughes is where did he ever correct
> Hardy and thirty other
> math professors who could not do a valid Euclid Infinitude of Primes
> proof? Show me any
> post by Hughes where he puts forth some new ideas of mathematics and
> where he corrects
> the Euclid Infinitude of Primes proof.
>
> I would dare say that Hughes, in all of his life as a philosophy
> professor was unable to even
> deliver a valid proof of Euclid Infinitude of Primes, and people like
> this become so sour and bitter
> towards other people who do have new ideas that Hughes lashes out at
> them and calls them
> "cranks".

>
> Archimedes Plutonium
> www.iw.net/~a_plutonium
> whole entire Universe is just one big atom
> where dots of the electron-dot-cloud are galaxies

I adjusted your title. It was too long.

[David R Tribble]

Plutonium Archimedes wrote:
> the number ....1413121110987654321 is also prime as Champernownes
> number (spelling)

It looks to me like it's a multiple of ...1111000111001101, or perhaps
3, or 11. Can you prove it is prime?

[plutonium....@gmail.com]

The proof is simple. It is irrational. Champernownes type numbers are
irrational numbers.
They do have a pattern, but they do not repeat. All Composite Natural
Numbers repeat or
end in a "even digit"or end in "5" , except of course the prime ....
0000002. All nonrepeating Natural Numbers which end in 1,3,7, or 9
are prime Natural Numbers, and
some prime Natural Numbers repeat such as .....00000003. But if you
have a Natural Number
that does _not repeat_ and end in those four listed odd endings
(except of course the prime 2), then it is prime Natural Number.

I do not have time at this moment to define all of these things and
will do it in the 2nd edition of the
AP-adics Primer. I should retitle that book as AP-Adics = Natural
Numbers.

So I answered your question. Now I need some help from you. I need to
find out of a case example
of where a Form of primes such as 2k +1 or 2^k -1 (examples of prime
form). A case in which I believe
Littlewood used to explain how the Riemann Hypothesis can be false. It
may have been an example
of a different author explaining why Littlewood was skeptical of the
RH validity. Anyway, I do remember
the example where it appeared as though there were many primes that
obeyed the "Form" until the
numbers became very much larger and then all of a sudden, no more
primes existed to fulfill that form
requirement. So David, does this ring a bell? Do you know of a "prime
Form" for which there are plenty of
primes initially, but as the n grows the Form cannot supply a new
prime and thus the primes of that form
are Finite. Maybe the Littlewood example was not primes but something
else, maybe a convergence or
divergence of a sequence. I am relatively certain it dealt with the
Riemann Hypothesis.

[David R Tribble]

David R Tribble wrote:
>> the number ....1413121110987654321 is also prime as Champernownes
>> number (spelling)
>>
>> It looks to me like it's a multiple of ...1111000111001101, or perhaps
>> 3, or 11. Can you prove it is prime?
>

Plutonium Archimedes wrote:
> The proof is simple. It is irrational. Champernownes type numbers are
> irrational numbers.

How can a natural integer be irrational?

> They do have a pattern, but they do not repeat. All Composite Natural
> Numbers repeat or
> end in a "even digit"or end in "5" , except of course the prime ....
> 0000002. All nonrepeating Natural Numbers which end in 1,3,7, or 9
> are prime Natural Numbers, and
> some prime Natural Numbers repeat such as .....00000003. But if you
> have a Natural Number
> that does _not repeat_ and end in those four listed odd endings
> (except of course the prime 2), then it is prime Natural Number.

So that means that ...39000039000390039039 and
...27000027000270027027 are primes, even though they
both look like they are divisible by 3?

[plutonium....@gmail.com]

David R Tribble wrote:

>
> So that means that ...39000039000390039039 and
> ...27000027000270027027 are primes, even though they
> both look like they are divisible by 3?

Good perception. As I wrote in that same post, I am going to iron out
the definitions
in the 2nd edition. Both of your above are "nonrepeating" as well
as ....1413121110987654321.
However, both of those are composite divisible by 3. There is another
aspect to be Irrational
involving the frontview digits and endview digits which I did not even
mention. I do not want to say more now as my head
is full of other things more important at this moment. This Natural
Number is Irrational
135790000000......00000001 and prime. My definition of Irrational
Natural Number is going to have
to involve not only "nonrepeating" but both endview and frontview. Now
why Irrational Reals
do not bother with frontview and endview is another matter and which I
have not straightened
out in my mind. For I hate to have to say that no-one ever really
thought about a Irrational Real such
as 0.133333.......333337 They never focused on the frontview and
endview of a Real Number. So it
maybe simply overlooked or it maybe some fundamental ingrained feature
of the difference between
Reals and Natural-Numbers.

Also, apparently Irrationals in Reals is silent about whether the
addition or subraction of two Irrational
Reals is another irrational, but clear about multiplication and
division. Whereas in Irrational Natural
Numbers the reverse is true where addition and subtraction is workable
but where multiplication and
division is silent. This stems, I suspect from the definition of
operators in Reals versus Natural Numbers.

[plutonium....@gmail.com]

plutonium.archime...@gmail.com wrote:
> David R Tribble wrote:
>
> >
> > So that means that ...39000039000390039039 and
> > ...27000027000270027027 are primes, even though they
> > both look like they are divisible by 3?
>
> Good perception. As I wrote in that same post, I am going to iron out
> the definitions
> in the 2nd edition. Both of your above are "nonrepeating" as well
> as ....1413121110987654321.
> However, both of those are composite divisible by 3. There is another
> aspect to be Irrational

The world's largest three prime numbers are 9999....9999997 then
9999....999993
and then 99999....9999991

In Sept of 2007 I started to define the roots operation on AP-adics

--- quoting some of old post ---
Newsgroups: sci.math, sci.physics, sci.edu
From: a_plutonium <a_pluton...@hotmail.com>
Date: Tue, 25 Sep 2007 20:40:23 -0700
Local: Tues, Sep 25 2007 10:40 pm
Subject: #17 (sic) Chapter, Roots Operation in Infinite Integers/P-
adics; new textbook; "Mathematical-Physics (p-adic primer) for
students of age 6 onwards"

Looks like I am going to have to define Roots operation such as the
square root for P-adics.

So what is the square root of ......999999999999 ?

We do this operation in the same manner we define all operations for
p-
adics. We keep everything
similar to the operations of Reals and we run sequences to get the
answer.

So the square root of .......99999999 goes like this:

square root of 9

then

square root of 99

then

square root of 999

then

square root of 9999

then

square root of 99999

and on and on until we have the digit place we are satisfied with.

sqrt of 9 = 3
sqrt of 99 = 9.9
sqrt of 999 = 31.6
sqrt of 9999 = 99.9
sqrt of 99999 = 316.2
sqrt of 999999 = 999.9
sqrt of 9999999 = 3162.2

So the square root of the p-adic or Infinite Integer of ......99999999

is two answers. One answer is ......999999
and the second answer involves a string with digits of 316 which can
be represented
as such

.........316.....r where the r is the radix point.

--- end quoting some of old post ---

When I write the 2nd edition I will have to clarify the operations

Notice that for the square root of 9999.....999999 there are two
answers

When David Tribble says that .....39000039000390039039 is
not a prime since it is divisible by 3 is true, however when we divide
by
3 what is the frontview?

Is the frontview 00....... or is the frontview 39.......

So is the division by 3 of that number 00......013 or is the division
1300......013

So many of the answers of operations in AP-adics have dual answers.

Now when I did this book in Sept 2007, I was doing the operations
definitions for the first
time in the world so alot of things were revised in that 1st edition
from beginning to end
but alot more revision is set on its way when I do the 2nd edition.

In the first edition, I cannot remember who it was that barraged me on
the fact that 999....99997
is evenly divisible by 13 and probably was Dik Winter who then went to
show that 999....99993 was
not prime and that 9999....999991 was not prime.

But hold on a minute. That was back in Sept of 2007 when I was
introducing this to the world
for the first time and as expected would have alot of errors that I
would have to work out in the future.

Well, Tribble and Winter are correct, but I am also correct in that
these AP-adics have a duality
of two answers.

997 is prime
9997 is not prime 13x769

So, when Tribble says ....0039039 is not prime is true, but what is
the frontview? Is it a 00 or is it
a 39, but either way it is composite.

So when Winter says 9999.....999997 is not prime is only half true in
that is 9999....999997 like the
9997 or is it like the 997. So how many "9" is there in the
9999.....99997? Is there the number of
"9" so that it is prime or not prime?

The square root operation above illustrates this duality of answers.
Is the square root the number
that looks like this ....99999999r, or is it the number that looks
like this .....316....r

For some numbers such as .....33333 divided by 3 has one answer, but
for many operations in
AP-adics there are dual answers.

So the number 99999......99999997 depending on its length, for if it
has a length of 9s then it is
prime but if it has a length otherwise it is not a prime.

This is a major problem and I may or may not be able to get rid of the
duality. If I define the length
of 9999....999999 so that 9999.....999997 is prime, that is what I am
thinking. I think I can manage
to get away with that in consideration that the next number beyond
99999.....999999 is imaginary
and it may have some "telling power" over the length of
9999....999999. Keep in mind, that this
entire program is spurred from the intrinsic numbers that make up
Elliptic geometry and Hyperbolic
geometry.

[plutonium....@gmail.com]

Archimedes Plutonium wrote:
>
> So the number 99999......99999997 depending on its length, for if it
> has a length of 9s then it is
> prime but if it has a length otherwise it is not a prime.
>
> This is a major problem and I may or may not be able to get rid of the
> duality. If I define the length
> of 9999....999999 so that 9999.....999997 is prime, that is what I am
> thinking. I think I can manage
> to get away with that in consideration that the next number beyond
> 99999.....999999 is imaginary
> and it may have some "telling power" over the length of
> 9999....999999. Keep in mind, that this
> entire program is spurred from the intrinsic numbers that make up
> Elliptic geometry and Hyperbolic
> geometry.
>

I am hoping that the successor number to 9999....99999 in AP-adics has
some influence as to the length of 99999.....999999 and thus fix
whether 9999....99997
is prime or not prime. And perhaps fix the length of the strings. It
maybe a variable
fix since Elliptic geometry comes in variety of shapes-- spheres
ellipses, elongated
ellipses.

When I wrote the 1st edition, this successor number to 9999....99999
was an imaginary
number such as pi or 2pi.

Towards the end of the 1st edition I began to use the Pseudosphere,
which made a vast difference
in my program. So I have alot of revision to do.

The key and major idea in the entire program is that geometry is the
guiding force. The Natural-Numbers
are the intrinsic numbers on a sphere surface. So the notion or
definition of "prime" is a minor notion
compared to the big picture. So I have to watch myself to not fall
into some trap of chasing the
definition of prime to where I give it too much importance. All
numbers are important and to focus on
3 since it is prime and to think less of 4 because it is composite, is
not mathematics but psychology.

[plutonium....@gmail.com]

So now, back in Sept of 2007 when Dik Winter complained that
99999.....999997 was composite
since he could find some divisors, but where neither Winter nor
Plutonium fixed the length of the string
of nines in 99999.....99999997. So if I fix that length so that
99999....999997 is prime, what does
it do for the other AP-adics? Does it make 99999.....999993 and
99999.....9999991 also prime?

I believe some sort of answers can be fetched from the Reals of the
Reals such as
0.9999999......99997 where the Real 0.99999.....999999 is
0.00000.....0000001 away
from 1.0. The Real 0.99999......99999 is not prime since 3 divides
into it

Can I say anything about the primeness of the Real 0.9999....99997? I
can say if the
length of the nines is a certain length then it is prime, if not that
length it can be
composite.

So, is there anything in mathematics that compels or impels me to fix
the length
of the Real 0.99999.....99997 to be prime? Nothing I can think of.

That leaves the fixing to the AP-adics = Counting Numbers of
99999....999999
Do I fix the length of the nines in 99999.....9999999 so that
9999.....9999997 is
prime? And will that fixing cause 99999.....9999993 and
99999.....999991 to be
prime also?

Is there anything telling or suggestive of the successor of
99999.....99999 as
to the length of the nines? I believe the successor is 2pi. Does 2pi
have some
influence or power as to the length of nines in 99999......999999?

I believe the answer is affirmative in that the pseudosphere is
hyperbolic geometry and
is tied to the sphere of elliptic geometry. And the fixing of the
length of nines in
99999......999999 is the connection of the pseudosphere to the sphere.

So if we fix 999999....99999 length so that 99999....99997 is prime,
then the Real
number of 0.99999.....9999999 is also fixed so that the Real number
0.99999....99997
is prime in a definition of primeness in Reals.

[Archimedes Plutonium]

Well in my geometry program of clearing and clarifying the Natural
Numbers as numbers on the surface of a Elliptic Geometry, there
are two poles, South and North Pole which are assigned the imaginary
number pi and 2pi respectively. The number pi is transcendental in that
the number is incompletely formed or is growing to be mature and fully
formed, and that is what it means to be a transcendental number. We can
write out a fully grown number such as 1/3 which is 0.33333.....333333
but pi cannot be written out fully because at some digit place value
it ceases to have a value for it has not yet grown to have a digit in
the place value.

Now as to the question of whether 999999......999997 as a Counting
Number is prime or whether the Real Number 0.99999.....99997 is
Real-prime depends on the definition of multiplication and division
but also depends on the length of the nines in both of those strings.

That length is determined by the length of pi to its last grown digit
place value. It is infinite to be sure, but it is a length for which
it determines whether the number 99999.....9999997 of the Counting
Numbers is prime or not prime and whether the Real 0.99999....99997
is Real-prime or not.

I have to wait for some other data, other constraints in mathematics
before I say that the structure of mathematics is such that it
behooves us to say that the length of nines in 99999.....999999 is such
that 9999....999997 is prime. We have a situation similar to this
with regards to n^0 as equal to 1 and another situation in regards to
saying that 1 is not prime but unit. So these other situations do not
force us to say they are what they are, but that imply they are such due
to the overall structure of mathematics. So just as I can say n^0 = 1
or that 1 is not prime but unit because it fits best with the rest of
mathematics, so also am I looking for reasons to say that the length
of nines in 99999.....99997 makes it a prime number.

[bRAINS]

> where dots of the electron-dot-cloud are galaxies- Hide quoted text -
>
> - Show quoted text -

Hey chaps, lets just say 'prime numbers' is good.

Good for what!!! ?

Beat this kiddies.....
http://www.justservices.com/9ukp.html

Bob Hope, little hope and NO hope!

You lot have NO chance!

brAinS

[Archimedes Plutonium]

Actually I kind of think I was correct all along and my reply to
Dik Winter back in Sept-Oct 2007 indicates that 9999....99997 was
prime, according to my definition.

I think we have to distinguish between being prime and have divisors
of infinite integers.

The string 9999.....999999 is clearly composite because 9 divides it.

However, the string 9999....99997 is it composite or prime because of
7? Does it depend on the length of nines digits as what I responded to
that argument in 2007.

--- quoting a 2007 post ---
Newsgroups: sci.math, sci.physics, sci.edu
From: Archimedes Plutonium <a_pluton...@hotmail.com>
Date: Mon, 22 Oct 2007 12:53:24 -0500
Local: Mon, Oct 22 2007 12:53 pm
Subject: #175 the Prime Distribution Theorem of mathemaics is only
locally true and AP-adics ; new textbook: "Mathematical-Physics (p-adic

primer) for students of age 6 onwards"

Dik T. Winter wrote:
> In article <1192865353.837264.308...@e34g2000pro.googlegroups.com>
a_plutonium <a_pluton...@hotmail.com> writes:
> ...
> > The P-adics as defined in this book are infinite leftward strings of
> > all possible
> > digit arrangement and whose operations are the same as for Reals as
> > a Cauchy sequence to the final answer.

> What is 7 * 142657...1428571?

> > Dividing 3 into 88888......88888871 in the new P-adics which I call
> > Decimal P-adics not 10-adics is this:

> > 3 into 8 is 2 with 2 remainder. Carry the 2 and we have 28.
> > Then 3 into 28 is 9 with 1 remainder. Carry the 1 and we have 18.
> > Then 3 into 18 is 6 and we repeat the block of 296 where we have
> > 296296296 and 3 does not divide 71 evenly so the entire
> > number is prime.

> No, by that method you will see that the number is divisible by 71.

> > .....999997

> Is divisible by 7. Using your method:
> 7 into 9 is 1 with 2 remaining
> 7 into 29 is 4 with 1 remaining
> 7 into 19 is 2 with 5 remaining
> 7 into 59 is 8 with 3 remaining
> 7 into 39 is 5 with 4 remaining
> 7 into 49 is 7 with nothing remaining.
> We repeat the block of 142857 where we have 142857142857 and 7 dies
> divide 7 evenly, so the entire number is divisible by 7. Note that
> using this method the number is also divisible by 97, 997, 9997, etc.

Good try but not true.

The definition as setup in what I am going to rename as AP-adics so as
to not confuse with P-adics (as Wikipedia teaches me to call them
something different).

Anyway the definition of multiplication and division uses a radix if
there is a remainder. And the final answer is a Cauchy Sequence over all
the piecewise divisions. So if the radix disappears and never again
shows up then the number is composite, but if the radix continually
shows up, even though one or two piecewise divisions is even, means the
final answer is composite.

7 into 97 is 13.8
7 into 997 is 142.4
7 into 9997 is 1428.1
7 into 99997 is 14285.2
7 into 999997 is 142856.7
7 into 9999997 is 1428571
7 into 99999997 is 14285713.9
and the fractional radix repeats in a block

So the Cauchy sequence of the above never eliminates the radix, does it,
so it is Prime not composite.

Just because you can find one smooth even division every periodically in
the sequence does not make it overall Composite. To be overall Composite
then the Cauchy Sequence stops yielding a radix answer.

By the way, I was doing some checking and quantity of Primes in the
...999 series matches the quantity of primes in the ....00000 series.
Mathematicians have never explored the fact that the number of primes at
the end of the Counting Numbers is the same quantity as the beginning
where you have 25 Primes in the first 100 counting numbers and you have
25 Primes in the last 100 Counting Numbers where ....999997 is the
world's largest prime. But the same quantity exists in ....11111 series
as well as .....22222 series as well as ....33333 series etc.
I have not checked whether the series such as .....454545 would have
25 Primes in their first 100 Counting Numbers but suspect that is true.

What this tells us is that the Prime Distribution Theorem in mathematics
is only locally true for a Series of Primes out to a large number but
not true overall for Mathematics. For the Primes are distributed in the
Counting Numbers as a layered structure that repeats itself such as a
onion layering.

--- end quoting old post ---

So I think the way I am going to tackle this problem is via the
definition. Make the definition of multiplication and division so
well defined that it eliminates the above tussle as to whether
999...9997 is prime or composite. We did not have this problem with
Finite Integers because the zeroes that preceded all those numbers
were ignored because vacuous-- for we never had to worry about how
many zeroes preceded. But as to whether say ....5555557 is prime or
composite we have to worry about how many fives precede the 7.

In the case of where Dik found divisors is a sort of hinting of p-adics
where nothing is prime.

But the way I set up the definition of multiply divide add subtract,
makes 9999....99997 a prime.

[plutonium....@gmail.com]

Note: the post below was sent from an ISP a day ago, and seems to have
problems getting onto
the newsboard in a timely manner. One of the problems is probably
these news forums like "Math
Forum" that include posts, but in their processing of a post can delay
the post from ever reaching
the reader board. So this can create a situation of censorship and not
allow a free flow of conversation
since every post is delayed. Or it may be Google delaying. My original
#563 is delayed untimely.

--- begin post that is delayed ---

Actually I kind of think I was correct all along and my reply to
Dik Winter back in Sept-Oct 2007 indicates that 9999....99997 was
prime, according to my definition.

I think we have to distinguish between being prime and have divisors
of infinite integers.

The string 9999.....999999 is clearly composite because 9 divides it.

However, the string 9999....99997 is it composite or prime because of
7? Does it depend on the length of nines digits as what I responded to
that argument in 2007.

--- quoting a 2007 post ---
Newsgroups: sci.math, sci.physics, sci.edu

From: Archimedes Plutonium <a_pluton...@hotmail.com>
Date: Mon, 22 Oct 2007 12:53:24 -0500
Local: Mon, Oct 22 2007 12:53 pm
Subject: #175 the Prime Distribution Theorem of mathemaics is only
locally true and AP-adics ; new textbook: "Mathematical-Physics (p-

adic primer) for students of age 6 onwards"

Dik T. Winter wrote:

> > .....999997

Archimedes Plutonium

[Archimedes Plutonium]

Ideally the sci newsgroups should be like email where two persons,
online, can have a conversation in real-time, immediately, as if
they were on a telephone having the same conversation. There is
almost no delay in time with a telephone and the Internet sci.
newsgroups can match this conversation.

But for example #562 post and #563 post of mine, the delay is not
in seconds but in days. Delay when I hit the send key to where it shows
up in Google is in days, whereas previously the Google delay was in
seconds.

When the delay from send to seeing on the newsboard is in seconds, then
conversations can take place on the newsgroup as if it were real live
conversations.

This is a feature of the Internet that Google should always try to maintain.

Just today I started to open a YouTube video on quantum mechanics, but
realized that all of YouTube is really too primitive. Why does anyone
think it is worth my time to spend 2 hours waiting for a 5 minute video
on something? The day YouTube eliminates this downloading time, is the
day that YouTube makes sense to use.

My own ISP delivers all my posts in seconds. This sort of tells me the
trouble is with Google in this "one day or more delay of seeing posts".

It is understandable that Google can have new features to install and
causing shortterm interruptions, but when Google has these sort of
interruptions every other week.

If my ISP can keep a stable unchanging platform that deals in seconds of
time delays, then Google ought to be able to do the same.

[Jan Burse]

Archimedes Plutonium schrieb:

Stop Whining

http://www.sonofthesouth.net/uncle-sam/stop-whining.htm

[Cletis Perkins]

Why does Archimedes Plutonium post from Google?
Because he has been kicked off EVERY OTHER
newsgroup provider for being a spamming ass,
and is now reduced to posting from the only
"bullet-proof" host Google, what never cancels
anyone's account no how, even if they are
a big poop head.

"Archimedes Plutonium" <a_plu...@hotmail.com> wrote in message
news:4873B59E...@hotmail.com...
>

[Bill Dubuque]

plutonium....@gmail.com writes:
>
> Where Natural Numbers = AP-adics ..

Archie, before I can comment you need to answer the following
questions about your ring of AP-adics, henceforth called AP.

1) Is the hypothesized ring AP a (totally) ordered ring, i.e.
does AP have a subset P of "positives", closed under + and *,
with every elt either positive (in P), negative (in -P) or 0 ?

2) Are the positive elements P well-ordered, i.e. does every
nonempty subset of P have a least element?

Lurkers please refrain from commenting until AP responds.

--Bill Dubuque

[plutonium....@gmail.com]

Bill Dubuque wrote:
> plutonium....@gmail.com writes:
> >
> > Where Natural Numbers = AP-adics ..
>
> Archie, before I can comment you need to answer the following
> questions about your ring of AP-adics, henceforth called AP.

Well, Bill, the reason I wanted you to give a Euclid Infinitude of
Primes proof, both
direct and indirect, two proofs of contrast, is to dive into the
question of the
direct method compared to indirect method. Euclid IP offers us a proof
where
we can talk in depth over the differences of one method versus the
other method.
In 1993 when I was discussing the Fermat's Last Theorem and there were
three graduate
students at Princeton who were actively debating every issue I raised
as to why FLT
had counterexamples (hence FLT was false). One of those three
Princeton graduates
made a remark to me, whether Terry or Kin or Will, saying that once
you have a indirect proof
of something in mathematics, you immediately have the direct proof of
the same thing.

In other words, it is a common belief, perhaps, you Bill Dubuque,
shares this belief with
that Princeton graduate student, that whenever we have a proof in
math, either direct or
indirect method, we easily and simply can fetch the other method.

I do not buy that.

I believe these proof methods of direct and indirect are
Complimentarity, meaning that they
are fundamentally different and where most often is the case, that if
you prove something
in math with the direct method, there is no possible indirect method
for that same proof. Or
the case of where you have a indirect method proof, but no possible
direct method due to
the elements in the proof argument.

So, the reason I would like for you to give your own version of Euclid
Infinitude of Primes proof
one in the direct method, the other in the indirect method, is to
point out the Complimentarity nature
of mathematics of its proof method.

There is really an utter lack of knowledge in the literature of
mathematics concerning the underpinnings
of Direct versus Indirect, and the Euclid IP offers us a diving
platform to get at the inner workings of these
two methods.

>
> 1) Is the hypothesized ring AP a (totally) ordered ring, i.e.
> does AP have a subset P of "positives", closed under + and *,
> with every elt either positive (in P), negative (in -P) or 0 ?
>

Well, Bill, as I told Dik Winter, what kind of algebraic structure
does "All Possible Digit Arrangements
of Rightward Infinite Strings" have? These are the Reals. Now the
Reals have an Algebraic structure,
ring-- field etc. But the Reals are of the very same infinity as the
AP-adics since those are All Possible
Digit Arrangements to the Leftward Infinite. Both are equinumerous
since they differ only in direction.

Here is something that you believe in Bill, but which is false. You
believe that between any two Reals
exists another Real. This is given some fancy name, but is utterly
unsound.

In All Possible Digit Arrangements there is the AP-adic of
00000....00000 and 00000....000001
commonly known as 0 and 1, yet in All Possible Digit Arrangements
there cannot exist a number between
those two numbers.

Likewise for Reals, in All Possible Digit Arrangements there is the
Real Number 0.0000....0000
and the Real Number 0.0000....000001.

Now I know that FrontView is a new concept for mathematicians to mull
over and I discovered it only
recently to be able to use it as a tool. This tool destroys the Real
Number concept that between
any two Reals is another Real.

Well, what Real Number exists between 0 and 0.00000.....000001 ??
There is none.

In fact, mathematicians of the past could have asked themselves a very
important question that would
have told them that Between Any Two Reals may not necessarily give you
a new Real.

Ask themselves this question. Are the Real Numbers larger than the set
of All Possible Digit Arrangements
of infinite rightward strings, or are the Reals the same set as All
Possible Digit Arrangements?

I think you Bill is a commonsense practical man and would say that the
Reals are the same as the
All Possible Digit Arrangement.

I forgotten what fancy name was given to this idea in mathematics
"between any two Reals
exists another Real". Well that idea was one of the worst and phonyest
ideas to come along
in all of mathematics.

So, to answer your question, Bill, about the AP-adics, you see, I have
altered much of what
you previously thought was true of the Reals and their algebraic
structure of a closed Field.

I defined multiply, add, divide and subtract on AP-adics.

So the question of Ring or Field or Algebra on AP-adics is simply the
question of
what does All Possible Digit Arrangements, whether rightwards for
Reals or leftwards for
AP-adics as infinite strings. What does All Possible Digit
Arrangements yield?

I am no expert on Galois Algebra but I would estimate that All
Possible Digit Arrangements
yields a Closed Field for both Reals and for AP-adics. Closed because,
it is commonsense
that All Possible really means All Possible. And because infinite
rightwards yields 3D Euclid
geometry, even though it has tiny holes between every number, it is
still a smooth geometry.
And AP-adics forms both Elliptic and Hyperbolic geometries. So,
because of All Possible
and because both number sets form geometries-- they are closed
algebraic fields.

Now we may have to redefine Galois Algebras before the dust settles.

> 2) Are the positive elements P well-ordered, i.e. does every
> nonempty subset of P have a least element?
>

Well that is easy to answer. When Reals are All Possible Digit
Arrangements and ditto
for AP-adics, (only difference is that one is rightward infinite and
other is leftward infinite).
That given any subset of Reals or of AP-adics, because they are All
Possible Digit Arrangements
means that you have a least element.

> Lurkers please refrain from commenting until AP responds.
>
> --Bill Dubuque

Too much fanfare, Bill. All I wanted was you to give your direct and
indirect Euclid IP so that I can
discuss why Indirect-Direct is Complimentarity of Physics onto
mathematics. Like the three graduates
of Princeton with their vague and unsound notion of the difference
between Direct and Indirect.

You see, Physics is dominate over mathematics, and that Elliptic +
Hyperbolic = Euclidean
is another Complimentarity relationship of physics dominance over
mathematics, just as
Direct method versus Indirect method is another physics dominance over
mathematics.

Much of what Bill Dubuque knows of Galois Algebra needs to be revised
and parts thrown out as
pure fabrication. One part is the "between any two Reals is a new
Real" is simply a lie of modern
day mathematics.

Last call, Bill, please provide your own Euclid Infinitude of Primes
proof, direct and indirect, using

"multiply the lot and add 1"

Archimedes Plutonium

[plutonium....@gmail.com]

plutonium.archime...@gmail.com wrote:
> Bill Dubuque wrote:
> > plutonium....@gmail.com writes:

Now Bill will not like my answer that I gave earlier. Nor did Dik
Winter like any of my comments
on Galois theory as it pertains to AP-adics.

One of the problems here is that noone has really elaborated on why
Galois theory even works
in the first place and why it is a tool.

But the program of AP-adics never really uses Galois theory and
suggests that Galois theory needs
a modern day cleaning-up, revision and even some trashcanning of
trashy parts.

Most mathematicians would have started tackling AP-adics with Galois
theory, but I started them
with purely Geometry. Geometry is going to be around longer than any
Galois theory and geometry
has no chance of withering and dying away as does Galois theory. This
is one of the great avenues
of misguidance by mathematicians of the last century for they went
overboard on the importance of
Galois theory.

So I did this AP-adics program purely on the need to have these
numbers as points intrinsic to
Elliptic and Hyperbolic geometry. Only geometry as guide and careless
if anything agreed or disagreed
with Galois theory.

What makes Galois theory work? Or a better question is what is the
basic underpinning of Galois theory?
And this subject is seldom talked about by mathematicians, even those
that spend most of their time
on Galois theory.

What makes it work is that it is based on the concept of All Possible
Digit Arrangements. Galois theory
in essence is Probability theory in reverse. What I mean by that, is
that Probability theory is based on
knowing a "universe space of possibilities" and once you know that
space, they it is routine to figure out
the probability of a particular event as event/space.

So in essence Galois theory is Probability theory in reverse. And what
makes Probability theory work
is All Possible Digit Arrangements for that is a fancy title for
"universe space of possibilities".

Now what few people who worked in Galois theory failed to recognize is
that all of Galois theory is dependent
on "All Possible Digit Arrangements". So, when mathematicians were
working to find out if the Reals
are a ordered field or some sort of commutative ring or some other
algebraic structure, they thought
that their work consisted of defining operations to make it all agree
with those algebraic structures. When
in fact, all they really needed to do was to see if the collection of
numbers is a "all possible digit arrangement"

Now here is a finite set of all possible digit arrangements:
.00 up to .99. That set are two place value of Reals between zero and
1.0. But it is all possible digit
arrangements of two place value to the right of the decimal point. It
forms an algebraic structure, not because
some mathematicians can spend hours defining and redefining operations
to satisfy some algebraic structure,
but it is a algebraic structure because it is all possible digit
arrangements for two place value right of decimal
point.

And also, the Integers of two place value is 00, 01, on up to 99. So
that set is all possible digit arrangement
for two place value on integers. It also is a algebraic structure, the
same as the Real example. It is a
structure not because someone spent long hours making the operations
fit, but because from the beginning
it was "all possible digit arrangements for two place value"

So my answer to Bill, is that I developed the AP-adics purely from
geometry, and care less about whether
anything obeyed some algebraic structure.

But I know the AP-adics have a algebraic structure that is probably a
Ordered Field, simply because
the Reals are an ordered-field and both sets are "all possible digit
arrangements".

So here is a question for Bill. What Algebraic structure is the above
Reals of all possible digit arrangement
for two place value, and same question for integers of all possible
digit arrangement of two place value.

Now if I remember correctly the all possible digit arrangement of two
place value of two digits of
00, 01, 10, 11 is a Field. Now would all possible digit arrangements
of three place value of two digits
be the same structure as the two place value?

As I said so many times to Dik Winter, geometry is more important,
more vital, more guiding than
is Galois theory, and Galois theory is highly overrated.

[Bill Dubuque]

plutonium....@gmail.com wrote:
>Bill Dubuque <w...@nestle.csail.mit.edu> wrote:

>>plutonium....@gmail.com wrote:
>>>
>>> Where Natural Numbers = AP-adics ..
>>
>> Archie, before I can comment you need to answer the following
>> questions about your ring of AP-adics, henceforth called AP.
>>

>> 1) Is the hypothesized ring AP a (totally) ordered ring, i.e.
>> does AP have a subset P of "positives", closed under + and *,
>> with every elt either positive (in P), negative (in -P) or 0 ?
>>

>> 2) Are the positive elements P well-ordered, i.e. does every
>> nonempty subset of P have a least element?
>>

>> Lurkers please refrain from commenting until AP responds.
>

> Well, Bill, the reason I wanted you to give a Euclid Infinitude of

> Primes proof, both Integers, which is an ill-defined set [...]

I didn't see an answer to my questions. Could you please plainly
answer either true or false to the above questions. It would help
if you could do so concisely, e.g. something like:

1) is ____

2) is ____

--Bill Dubuque

[plutonium....@gmail.com]

Bill Dubuque wrote:

Bill Dubuque wrote:

>
> Archie, before I can comment you need to answer the following
> questions about your ring of AP-adics, henceforth called AP.
>
> 1) Is the hypothesized ring AP a (totally) ordered ring, i.e.
> does AP have a subset P of "positives", closed under + and *,
> with every elt either positive (in P), negative (in -P) or 0 ?
>
> 2) Are the positive elements P well-ordered, i.e. does every
> nonempty subset of P have a least element?
>

> I didn't see an answer to my questions. Could you please plainly
> answer either true or false to the above questions. It would help
> if you could do so concisely, e.g. something like:
>
> 1) is ____
>
> 2) is ____
>
> --Bill Dubuque

No, I gave you answers

Euclidean geometry is composed of Elliptic geom unioned with
Hyperbolic geom

Euclidean geometry are All Possible Digit Arrangements of infinite
rightward strings
containing both negative and positive signed numbers

Elliptic geom is All Possible Digit Arrangements of Positive Signed
infinite leftward strings
with the tacking on of two imaginary numbers for the North and South
Pole

Hyperbolic geom is All Possible Digit Arrangements of Negative Signed
infinite leftward
strings with one imaginary number for the zero point

Geometry is above Algebra of its Group and Ring and Field theory.

In fact, Field theory requires us to have the Reals in order to invent
Field theory with its
continuity postulate --- between any two Reals is a new Real or
derived in the Archimedean Postulate
n*e > M combined with Euclidean Completeness Postulate-- every
positive number has a positive
square root.

So Field Algebra was invented after we had Euclidean Geometry and
invented by trying to distill the
features of Euclidean Geometry. So Field Algebra is a attempt at
capturing the essence of Euclidean
geometry.

But Algebra misses the essence of Euclidean Geometry for it is merely
the All Possible Digit Arrangements.

So Bill, what is the Real Number between

0.0000....000000 and 0.0000.....000001

or, what is the Real Number between

0.00000.....0000005 and 0.00000.....0000006

In the old math where Bill comes from, they never had FrontView and
they never realized the importance
of "All Possible Digit Arrangements". Absent of FrontView and All
Possible Digit Arrangements, they
went on to build these phony house of cards that comes tumbling down.

Euclidean Geometry is All Possible Digit Arrangements of both negative
and positive signed numbers
of infinite rightward strings.

There is no continuity in Euclidean Geometry for there are holes
between every numbers, just as there
are big holes between the Counting Numbers going from 1 to 2 or 2 to
3.

What makes Euclidean geometry flat is that the strings are infinite
rightwards and contain both positive
and negative numbers.

If we separate out all the positive Reals and flip them around so the
string is infinite leftwards, what we
have done is created Elliptic geometry and with the negative Reals if
we flip them around as infinite
leftwards we have created Hyperbolic geometry. So that Elliptic and
Hyperbolic were nested inside
of Euclidean geometry.

So it is pointless of me in answering Bill's question which is
dinosaurish math that was dead in the last
century. Pointless to ask me what AP-adics are in the fake Algebras of
the last century. Bill just may
as well ask me whether a fire breathing dragon has red eyes or green
eyes or uses butane or propane,
which is all pointless since no fire breathing dragon exists.

But this is typical of a mathematician of the last century whose mind
is submerged in falsehoods. Can
anyone show Bill that Algebras are phony baloney beyond what Galois
used them for in the quintic.
When you stretch something beyond its use, such as Galois theory or
mortgage lending or dot.com
finances, when you stretch something beyond their use, you run into
fakery and phonyness.

I built AP-adics from geometry, something true and everlasting, not
the overstretched Galois theory built
only to address the quintic problem of centuries past.

It is easy for the modern day mathematician to get sucked into
phonyness of the Reals having a Cantor
infinity or having "absolute continuity". Easily sucked in because no-
one really asked
"Well, aren't the Reals just the same as All Possible Digit
Arrangements?"

I mean, what an utterly simple question and which virtually every
practicing mathematician used
during their lifetime of study and teaching math. I know I used that
expression "all possible digit
arrangements" thousands of times when doing mathematics.

So why did not any mathematician in the 20th century ever say "the
Reals are nothing more than
All Possible Digit Arrangements"

Now if you couple "All Possible Digit Arrangements" with FrontView,
well you really revolutionize
the subject of Mathematics.

So Bill Dubuque who loves playing games of algebra. What Real Number
is between these two
Reals:

0.00000.......00008 and 0.00000.....00009 for there is none. There is
a hole between those two
Real Numbers just as there is a hole between the largest Real in the
interval 0 to 1 as
0.99999.....99999 which is 0.0000....00001 away from 1 itself.

So how can you expect me to answer you algebra question when your
algebra is nothing but
phony fakery. You tossed away the true theory of Geometry and you
spent your life in a quagmire
of fakery of Galois theory.

[lwa...@lausd.net]

On Jul 14, 8:02 am, Bill Dubuque <w...@nestle.csail.mit.edu> wrote:

Archimedes Plutonium gives a partial answer to this
question in another thread, post #581:

>> The way I have set up the AP-adics is that they form the intrinsic
>> numbers that lie one the surface of
>> a ellipsoid (set of all positive AP-adics) and lie on the surface of
>> a pseudosphere (set of all negative
>> AP-adics).

So there definitely exist positive and negative AP-adics.

[plutonium....@gmail.com]

Euclidean Geometry can be thought of as a box with the zero point in
the middle
and the Cartesian coordinate system radiating outwards from the zero
point.

Every point in this Euclidean Space covered by a number which is an
All Possible
Digit Arrangement of infinite rightward string, both positive and
negative signed.
So Euclidean Space is a network where the points are numbers but where
there
are always holes between numbers

Here is all possible digit arrangements of two digits to the two place
value:
00 01

10 11

So there are 4 numbers in that category and no more (no more to
concoct a phony
Cantor diagonal). Notice also that in that category you cannot have
"absolute continuity"
for there is a hole between 00 and 01 or between 00 and 10.

Likewise do the same for All the Reals which would be a matrix that
would be infinite cardinality
and not just a 4 cardinality. And these Reals would be all possible
digit arrangements and would
have a hole between any two Reals. Cantor diagonal does not work here
either.

Now, if we pluck out of the All Reals those that are negative signed
such as (-) 0.3333....3333
and flipped them around we have (-) 3333.....33333 which is a negative
AP-adic.

The collection of all the negative signed Reals when flipped around
form the negative AP-adics
and form a Hyperbolic geometry that is the pseudosphere.

Now if we take all the positive Reals such as for example
0.6666....6666 and flip them around
would be 6666....66666 a positive AP-adics and would form Elliptic
geometry with the tacking on
of two imaginary numbers for the North and South Pole.

So the Reals are All Possible Digit Arrangements of infinite rightward
strings, both positive and negative
signed. They form Euclidean geometry

We can pluck out all the positive Reals, flip them over to make
infinite leftward strings and they form
Elliptic geometry

We can pluck out all the negative Reals, flip them over and they form
Hyperbolic geometry.

So algebra never enters the picture in this program. This program is
all about Geometry and what numbers
are intrinsic to geometry.

After we have all the numbers and geometry settled, can we go back and
then reflect on what Algebra
exists for the AP-adics and what exists for the Reals, since both of
them started from
All Possible Digit Arrangements. That means most of the Algebra of the
past century is flawed and phony.

[lwa...@lausd.net]

On Jul 8, 11:01 am, plutonium.archime...@gmail.com wrote:
> The string 9999.....999999 is clearly composite because 9 divides it.
> However, the string 9999....99997 is it composite or prime because of
> 7? Does it depend on the length of nines digits as what I responded to
> that argument in 2007.

Is 9999....99997 prime? Here's my take on this issue:

> --- quoting a 2007 post ---

> Dik T. Winter wrote:
> >  > .....999997
> > Is divisible by 7.  Using your method:
> >    7 into 9 is 1 with 2 remaining
> >    7 into 29 is 4 with 1 remaining
> >    7 into 19 is 2 with 5 remaining
> >    7 into 59 is 8 with 3 remaining
> >    7 into 39 is 5 with 4 remaining
> >    7 into 49 is 7 with nothing remaining.
> > We repeat the block of 142857 where we have 142857142857 and 7 dies
> > divide 7 evenly, so the entire number is divisible by 7.  Note that
> > using this method the number is also divisible by 97, 997, 9997, etc.
> Good try but not true.

> 7 into 97 is 13.8
> 7 into 997 is 142.4
> 7 into 9997 is 1428.1
> 7 into 99997 is 14285.2
> 7 into 999997 is 142856.7
> 7 into 9999997 is 1428571
> 7 into 99999997 is 14285713.9
> and the fractional radix repeats in a block
> So the Cauchy sequence of the above never eliminates the radix, does
> it, so it is Prime not composite.

Actually, I disagree with both AP and Winter here.

> Just because you can find one smooth even division every periodically
> in the sequence does not make it overall Composite.

But just because you can find one division that's
_not_ even doesn't make it prime either!

I believe that it does depend on the length of
the block of nines. Of course, AP usually tells
us that there are 9999....99999 nines before the
seven in 9999....99997.

Notice that the block of remainders repeats every
six nines. This follows from Fermat's Little
(_not_ Last!) Theorem. Therefore, if we reduce the
number of nines (which is 9999....99999) mod 6,
then this will tell us how to reduce 9999....99997
mod 7, which is the original problem.

Now 9999....99999 is easy to reduce mod 6, since
it's clearly odd and divisible by three. Thus:

9999....99999 == 3 (mod 6)

and therefore we can reduce 9999....99999 to a
number with only three nines:

9999....99997 == 9997 (mod 7)
== 1 (mod 7)

So 9999....99997 is not divisible by seven, so
Dik Winter is wrong here.

But AP is also wrong to say that 9999....99997
is prime. Suppose we were to divide it by the
prime 13 instead of seven. By Fermat's Little
Theorem the remainders should repeat every
twelve nines. Thus we must reduce the number
of nines, 9999....99999 mod 12. Once again
it's divisible by three, and since the last
two digits are 99 it's equivalent to 3 mod 4,
so we conclude:

9999....99999 == 3 (mod 12)

so that:

9999....99997 == 9997 (mod 13)

And 9997 divided by 13 is exactly 769. Thus:

9999....99997 == 0 (mod 13).

Therefore 9999....99997 is divisible by 13,
hence 9999....99997 is not prime.

Notice that in principle, it should be
possible to divide _any_ infinite AP-adic
by _any_ finite number in this manner.

BTW, I believe that infinite prime AP-adics
exist, but that one can't construct them. It
would be just like trying to construct a
well-ordering of the reals, or a nonprincipal
ultrafilter on N. Although AC implies that
these must _exist_, they can't be _constructed_,
and the same is true for an infinite AP-adic
that's also prime.

[plutonium....@gmail.com]

My understanding of AP-adics changes as I learn more about them. I am
of the
opinion that only the Reals and Negative AP-adics go to infinity and
so there
are 9999....999998 nines in 99999....999997 for the Real
1.9999....9999 and
for the negative-AP-adic (-)9999....99997

I get the feeling that in positive AP-adics that the South Pole as
imaginary number (pi)
limits the number of nines in 9999....99999 so that it may be limited
by the finite number
of 10^40 as the point in which pi as we know it stops having digits in
its number. So if that is
the case, then it depends on how many finite nines are in
9999....999997 which has
39 nines in its string of digits. So with 39 nines the number is not
divisible evenly by either
7 or by 13 which lwal computes below.

So by reasoning that the South Pole of positive AP-adics is pi and
since pi ceases to become
a number at some place-value such as 10^40 or maybe 10^60, where it no
longer has a digit
for further place values, (this being the ultimate meaning of a
transcendental number --ceases
to have digits), means that the predecessor of pi as the South Pole
has to be cut short of its
nines so as to be the predecessor. So that the number 9999....99997 is
a finite number having
39 nines. Now is that prime to both 7 and 13? If not, well, pi as
10^41 or pi as 10^43 and so forth
will eventually deliver a number that is finite looking like this
9999...99997 which is prime.

Thanks for discussing this in depth. But I think that your program
does not work on this
infinite integer AP-adic ......151413121110987654321

Now look at this sequence:
321 is it prime
4321 is it prime
54321 is it prime
654321 is it prime
and on and on up the ladder chain

In this ladder chain you reach the first prime then going further you
reach a second prime.

And we could have done it with 9999...999997
97 is it prime
997 is it prime
9997 is it prime
99997 is it prime

So to say that the infinite integer AP-adic of 9999...99997 is not
prime is like saying that "form"
of nines with a lone 7 is a finite form. I find that hard to accept.

We could do it with primes of form 10000....00001
101 is it prime
1001 is it prime
10001 is it prime
ad infinitum

So if that is not prime then primes of that form are finite. And again
I find that hard to accept.

So confronted with this data, I am increasingly thinking that the
definition of prime is a anthropomorphism
and not something of importance or characteristic of mathematics. Much
like a face in a rock cliff may
look like a face but is only rocks.

If we examine Elliptic geometry and points on an ellipse surface and
assign them numbers then the only
special numbers would be the poles and perhaps the unit number 1. All
the other numbers have no outstanding
characteristic. So a "primeness" concept is only subjective and
manmade and nothing fundamental about
the numbers that make up a ellipse.

The number .....151413121110987654321 is indeterminant as to whether
its infinite string is prime or
composite. It is not the only indeterminate number as per primeness.
Since it is indeterminate, means
for me anyway, that the concept of prime for the Natural Numbers is an
illusion just as a rock cliff is an
illusionary face.

The concept of rational versus irrational also breaks down in Reals
where this Real is neither
rational nor irrational 1.000000.....0000010 where the "1" digit in
the far right is the 999...99998th
place value. As Reals are all possible digit arrangements that is one
digit arrangement wherein
it is neither Rational nor Irrational as a Real.

So here we have a concept on Reals which like primeness on Natural
Numbers dissolves and vanishes
away.

That does not leave many things which are fundamental to numbers,
except for even and odd, for being
unit or not-unit. One characteristic that is true is whether
transcendental or algebraic, but here we have
in All Possible Digit Arrangements no infinite set of Transcendentals
and we have only two numbers
that are transcendental pi and e.

So we end up with a dearth of features of numbers and a lack of
characteristics that are fundamental
to numbers. But is this probably what is expected, because in physics,
when you come to think of it,
a fundamental particle such as a electron or proton or muon etc etc.
Well, they have really only a few
characteristics such as mass, charge. So why would mathematics of its
numbers have these long list
of characteristics when physics has so few for what makes up the
Cosmos.

[Bill Dubuque]

plutonium....@gmail.com wrote:
>Bill Dubuque <w...@nestle.csail.mit.edu> wrote:
>>plutonium....@gmail.com wrote:
>>>Bill Dubuque <w...@nestle.csail.mit.edu> wrote:
>>>>plutonium....@gmail.com wrote:
>>>>>
>>>>> Where Natural Numbers = AP-adics ..
>>>>

>>>> Archie, before I can comment you need to answer the following
>>>> questions about your ring of AP-adics, henceforth called AP.
>>>>
>>>> 1) Is the hypothesized ring AP a (totally) ordered ring, i.e.
>>>> does AP have a subset P of "positives", closed under + and *,
>>>> with every elt either positive (in P), negative (in -P) or 0 ?
>>>>
>>>> 2) Are the positive elements P well-ordered, i.e. does every
>>>> nonempty subset of P have a least element?
>>>>

>>>> Lurkers please refrain from commenting until AP responds.
>>>
>>> Well, Bill, the reason I wanted you to give a Euclid Infinitude
>>> of Primes proof, both Integers, which is an ill-defined set [...]
>>

>> I didn't see an answer to my questions. Could you please plainly
>> answer either true or false to the above questions. It would help
>> if you could do so concisely, e.g. something like:
>>
>> 1) is ____
>>
>> 2) is ____
>

> No, I gave you answers. Euclidean geometry is composed of Elliptic geom
> unioned with Hyperbolic geom [...]

Archie, I can only help you if you answer my questions concisely
by filling in the blanks above with either "true" or "false".

--Bill Dubuque

[plutonium....@gmail.com]

Bill Dubuque wrote:
(snipped)

> >> 1) is ____
> >>
> >> 2) is ____
> >
> > No, I gave you answers. Euclidean geometry is composed of Elliptic geom
> > unioned with Hyperbolic geom [...]
>
> Archie, I can only help you if you answer my questions concisely
> by filling in the blanks above with either "true" or "false".
>
> --Bill Dubuque

Well then I guess it is sorry to the both of us. I never set up the AP-
adics with Group theory
motivation. And the AP-adics changes Group theory as presently
practiced. Maybe LWAL
can fill in your blanks.

I am guided by geometry, not algebra. All the positive AP-adics lie on
the surface of a sphere.
All the negative AP-adics lie on the surface of a pseudosphere. The
two can be joined together
to form 3D Euclidean geometry. What need is there for algebra?

I can say one thing about the setting up of AP-adics, is that I simply
used the same definitions
for the operators as what the Reals have as operators, with one slight
adjustment. I use a Cauchy
Convergence Sequence as a final answer. The Hensel p-adics were all
base dependent on a prime.
By a Cauchy Convergence, I get rid of base dependency.

So that multiplication on Reals say of 0.666.... x 0.3333... is
straightforward but the multiplication
on the AP-adics of 6666....6666 x 3333....3333 is the very same thing
as on Reals, with a Cauchy
Convergence at the end.

So I do not see where any algebra is going to do any difference at
this stage of development.

66 x 33 = 2178
666x 333 = 221778
6666x 3333= 22217778

So the final answer in the AP-adics multiplication is 22222....77778

So the major help of Group theory is to have the definitions of
operations well defined. And certainly
I would have that well defined because all I do is borrow the same
definition from Reals with an added
twist-- take a Cauchy Convergence Sequence as the final answer. So
that insures the AP-adics algebra
is identical to the Reals algebra, after tacking on some imaginary
numbers.

So noone can criticize my definitions of operations for AP-adics,
because, every definition is
borrowed from the Reals. And we all know Reals operations are well
defined.

So, if the Reals as all possible digit arrangements is a Well Ordered
Field, then AP-adics is a
Well Ordered Field.

I need a geometer more than a algebraist, to see how a sphere and
pseudosphere form a Euclidean box.
I also need a geometer to see how to deconstruct the lines of latitude
of a sphere and then place them
together to form a pseudosphere. When we have hoola-hoops we can
construct a hemisphere by resting
successively smaller rings on top of one another. But how do we
construct a pseudosphere with successive
hoola-hoops? Do successive ones become smaller and sort of wedged
inside the previous hoop?
Seems odd to me that wedging inside previous hoops delivers negative
curvature.

So geometry help is what I need most of all.

There are algebra problems to be sure. How do I define multiplication
on Negative P-adics when every
multiply answer has to be a negative signed answer so when I have -2 x
-3 the answer has to be -6.
So that in Negative AP-adics, the answer is always another negative
sign. Just as the curvature is
always negative.

Most of the answers will come from geometry.

[plutonium....@gmail.com]

Well I never discussed this apparent conflict or seeming-
contradiction. I speak of the fact that
Reals are infinite strings rightward yet they form straight lines in
Euclidean Geometry.

And the AP-adics are the inverse in that they are infinite strings
leftward.

So here is the seeming contradiction. How is it that infinite
rightwards yields straightlines while
infinite leftwards yields curved lines of Elliptic and Hyperbolic.

I believe I have the answer. But it will make a slight change to the
Cartesian Coordinate System.

Remember I said that between any two Reals is a hole or gap and that
the Reals is not a continuous
plane in 2D but rather like a goretex cloth in 2D that if you get
small enough to where you see one Real
next to another Real, you will see a hole or gap between them.

Well, in AP-adics, the positive AP-adics forms positive curvature of a
sphere and the negative AP-adics
forms negative curvature of a pseudosphere.

Now Reals have both postives and negatives also.

So the change in the Cartesian Coordinate System for the Reals, is not
that we have the negatives to
one side of the zero point and the positives on the other side, but
that the Negative Reals rest in the hole
alongside the positive Real and where the negative Real cancels out
the curvature of the positive Real
and thus the lines in Euclidean geometry formed by the set of all
Reals are straightlines.

In the AP-adics, the positive AP-adics are separated away from the
negative AP-adics and thus their
respective curvatures are formed.

So when we draw a Cartesian Coordinate System, we should really just
use three rays emanating
from a zero point and where the negative reals rest alongside the
positive Real in the lines and rays.
So that a line in Euclidean Geometry is really that of -1 next to +1
and where -1.5 is next to 1.5 etc
etc.

[plutonium....@gmail.com]

Now that idea above better conforms to physics idea of Space where any
portion of space
has what is known as the Dirac Ocean of Positrons. So that if I apply
energy to any piece of
Space, I can extract positrons. Positrons are the negative particle of
a electron. So that we
can envision space as a checkerboard pattern of matter alongside
antimatter, and likewise
a positive Real sits next to a negative Real.

And, by the way, the above positrons is what produces the force we
commonly know of as
gravity.

So, here, I am doing pure math, and in so doing have found a
prediction of physics, that
every matter seen in the universe has the same amount of antimatter
resting alongside it.

[plutonium....@gmail.com]

lwal...@lausd.net wrote:
(snipped)

>
> 9999....99999 == 3 (mod 12)
>
> so that:
>
> 9999....99997 == 9997 (mod 13)
>
> And 9997 divided by 13 is exactly 769. Thus:
>
> 9999....99997 == 0 (mod 13).
>
> Therefore 9999....99997 is divisible by 13,
> hence 9999....99997 is not prime.
>
> Notice that in principle, it should be
> possible to divide _any_ infinite AP-adic
> by _any_ finite number in this manner.
>
> BTW, I believe that infinite prime AP-adics
> exist, but that one can't construct them. It
> would be just like trying to construct a
> well-ordering of the reals, or a nonprincipal
> ultrafilter on N. Although AC implies that
> these must _exist_, they can't be _constructed_,
> and the same is true for an infinite AP-adic
> that's also prime.

We sort of get a hint of "primeness" eroding away into nonsense with
the Hensel p-adics
in that the p-adics become like the Reals where everything is
divisible and hence no
concept of primeness.

But I like to ask LWAL a few questions about the above.

Can we not say that this sequence is a "form of prime" just as we said
2k-1 is a form of
primeness?

So that this sequence:
97
997
9997
99997
999997
.
.
.
is a particular "form of primeness"

Now the first few primes in the sequence are 97 and then 997. I have
not been able to locate the
next two primes in that sequence.

Now a question LWAL, if we consider 9999....999997 as composite, then
do we not say that
in effect that the sequence of primes of that form is a finite set?

So that if 9999...99997 the infinite integer is not prime, well, LWAL,
are we not saying that
primes of this form are finite?

Seems reasonable to me.

And it seems reasonable to me, that the way to get out of this impasse
is that the concept of
primeness is so muddy and dirty that it ceases to exist as a valid
concept over all the Natural-Numbers.
That the number 9999.....9997 is indeterminate as to whether it is
prime or composite. If it is composite
means primes of this form are finite, which defies commonsense.

So what has to give is the concept of primeness. That it was alright
for Natural-Numbers with alot of
zeroes to the left such as 00000....00000015 where the zeroes could
mask the muddy and ill-formed
concept of primeness. Where the zeroes served as a magnificent carpet
to sweep all questions about
the legitimacy of the primeness definition.

But once you start wondering if 22222.....2222227 is prime, well, you
do not have that great carpet of
zeroes to sweep annoying questions away. When every question of
primeness dealt with numbers
having 00000 strings to the left, well, noone could imagine how dirty
and blemished was the definition
of primeness.

So I think the solution, LWAL, is that 9999....99997 is neither prime
nor composite. That mathematics
finds it impossible to make a definition of prime to handle all AP-
adics. And since it is impossible to
clarify if 9999...999997 is prime or not prime, means the thing that
has to be ejected overboard is not
the number 9999....9997 or the AP-adics, but the concept and
definition of prime.

To me, the definition of prime was a parochial definition that worked
okay when your universe of Natural
Numbers were all preceded leftwards by 0000zeroes. So mathematicians
had a case of a short sighted
view of Natural Numbers where primeness definition could hold up.

Another question would also be helpful. How much of a workhorse is the
definition of prime? That is,
how much of mathematics is dependent on primeness. And as far as I can
tell, if we chuck out
primeness tomorrow, barely a ripple runs through the house of
mathematics, and about the only major
casualty is my rival of p-adics. The way I see it, is that primeness
in mathematics is like a teenager
in his youth who reads comic books. Now that may be a worthwhile time
spent in reading comic books
but certainly not essential for a human life, and likewise, primeness
in mathematics was a corner in which
we build a fictional concept and amused ourselves to a very large
extent. Primeness and the fascination
of "where is the next prime number" is akin to a group of teenagers
wasting or spending their time in
a comic book bazaar, when they could have spent that time over in the
science section reading some
science.

[plutonium....@gmail.com]

Bill Dubuque wrote:

>> Archie, before I can comment you need to answer the following
>> questions about your ring of AP-adics, henceforth called AP.
>>
>> 1) Is the hypothesized ring AP a (totally) ordered ring, i.e.
>> does AP have a subset P of "positives", closed under + and *,
>> with every elt either positive (in P), negative (in -P) or 0 ?
>>
>> 2) Are the positive elements P well-ordered, i.e. does every
>> nonempty subset of P have a least element?

>>

>> I didn't see an answer to my questions. Could you please plainly
>> answer either true or false to the above questions. It would help
>> if you could do so concisely, e.g. something like:
>>
>> 1) is ____
>>
>> 2) is ____
>

> --Bill Dubuque

My program involves numbers and geometry where the geometry determines
how the numbers
fit.

However, I seem to get assailed by the math community from the window
of algebra. As if noone
there in mathematics, understands geometry.

I keep telling Bill Dubuque that my program is superior with its
geometry as the leader of discovery
and where the endresult of geometry is going to alter algebra. So my
thesis is that geometry is
far superior to any algebra program on AP-adics.

So I cannot agree with much of what Bill questions above since my
program alters his algebra.

So let me ask Bill two questions for he is under the premiss that the
Reals are not "All Possible Digit
Arrangements" of rightward infinite strings with a finite leftward
portion.

Question #1 ______ Do you agree, Bill, that if Reals were thus defined
as All Possible Digit Arrangements
that the algebra on Reals is no longer the algebra taught in Colleges?
Simple yes or no will do, or
better yet an elaboration will do better.

Question#2 ______ Do you agree that if Reals are taken as All Possible
Digit Arrangements, that the
betweeness postulate or theorem no longer holds and that there is a
hole between every two Reals?

I cannot answer your questions Bill, because the AP-adics with
geometry is larger than your algebras
and changes your knowledge of algebras.

[lwa...@lausd.net]

On Jul 15, 11:44 am, plutonium.archime...@gmail.com wrote:
> But I like to ask LWAL a few questions about the above.
> Can we not say that this sequence is a "form of prime" just as we said
> 2k-1 is a form of primeness?
> So that this sequence:
> 97
> 997
> 9997
> 99997
> 999997
> .
> .
> .
> is a particular "form of primeness"
> Now the first few primes in the sequence are 97 and then 997. I have
> not been able to locate the next two primes in that sequence.
> Now a question LWAL, if we consider 9999....999997 as composite, then
> do we not say that
> in effect that the sequence of primes of that form is a finite set?
> So that if 9999...99997 the infinite integer is not prime, well, LWAL,
> are we not saying that primes of this form are finite?

Here's what I believe:

-- If the sequence 97, 997, 9997, 99997, 999997, ... has
only finitely many primes, then 9999....99997 must
necessarily be composite.

-- If the sequence 97, 997, 9997, 99997, 999997, ... has
only finitely many composites, then 9999....99997 must
necessarily be prime.

But we know that 97, 997, 9997, 99997, 999997, ... has
infinitely many composites. Indeed, I proved in my
previous post that every twelfth member of this
sequence beginning with 9997 is divisible by 13 and
hence composite.

I don't know for sure, but I suspect that the
sequence has both infinitely many primes and infinitely
many composites. Then the primality may be determined
by how many nines are in the expression.

I assume that 9999....99997 has 9999....99999 nines
followed by a 7.

[plutonium....@gmail.com]

Another question. Could it be that the concept of primeness is just
incompatible with infinite sets. If we take any set of finite Reals we
can
define primeness because some divisors are absent and thus some
members would be prime. Now if we use only a partial set of Natural
Numbers, here again
because some of the members are missing leaves some members as prime,
only because other members are missing.

For example, let us say that a set of Natural Numbers where "2" is not
a member,
then we could have an infinite set of even primes.

So I am wondering if the definition of primeness is only compatible
for finite sets, and the
instant you have a infinite set, it is likely to make the primeness
definition untenable.

Are the concepts of infinity contradictory with primeness? That the
Euclid proof of infinitude
of primes is hollow since primeness was not a valid definition. I keep
looking at the Reals,
where there is no primeness, so why should there be primeness on AP-
adics.

Question: is there some other property or characteristic of numbers
that can have a well-defined
concept for finite sets, but once the set is infinite, that concept is
untenable?

At the moment I can only think of "primeness", but maybe in the
history of math or physics there
were other concepts that look reasonable for both finite and infinite
sets, but were in fact only
tenable for finite sets.

Lwal, can you think of any other definition that has validity if the
set is finite but dissolves with an
infinite set?

I can think of two examples that are reverse, where they make sense in
infinite sets and untenable
in finite sets-- the calculus of integration, differentiation and
convergence of sequences.

Maybe primeness is the first and only example of where a definition
makes sense for finite sets but
is nonsense with infinite sets. I wish I could think of another
definition that breaks apart with infinite
sets.

Searching for more examples.

[David R Tribble]

lwal...@lausd.net wrote:
> Therefore 9999....99997 is divisible by 13,
> hence 9999....99997 is not prime.
>
> Notice that in principle, it should be
> possible to divide _any_ infinite AP-adic
> by _any_ finite number in this manner.

Which stands to reason. As I've asked AP before (and of course
received no reply), does it not make sense that any given
infinite integer is the product of an infinite number of primes
(and if not, why not)?

> BTW, I believe that infinite prime AP-adics
> exist, but that one can't construct them. It
> would be just like trying to construct a
> well-ordering of the reals, or a nonprincipal
> ultrafilter on N. Although AC implies that
> these must _exist_, they can't be _constructed_,
> and the same is true for an infinite AP-adic
> that's also prime.

Likewise, the AP-adics cannot be simply mapped to the reals,
since they possess an ordering.

[David R Tribble]

Archimedes Plutonium wrote:
> So confronted with this data, I am increasingly thinking that the
> definition of prime is a anthropomorphism
> and not something of importance or characteristic of mathematics.

It's also an incredibly simple definition from basic integer
arithmetic:
A number is either divisible by at least one other number, or it's
not.

If primeness is anthropomorphic, in what way are people prime
or composite?

[David R Tribble]

lwal...@lausd.net wrote:
> I assume that 9999....99997 has 9999....99999 nines followed by a 7.

How?

Does that mean that 999...999 has 999...999 nines followed
by another nine?

Is so, is the left number 1/10 the value of the right number?
If not, are the two numbers equal?

[plutonium....@gmail.com]

David R Tribble wrote:
> lwal...@lausd.net wrote:
> > I assume that 9999....99997 has 9999....99999 nines followed by a 7.
>
> How?
>

The reasoning here is that the quantity of the largest number would
also
correlate with the existence of that many place-values.

So if the number 12 exists then a 12 place-value should exist. If a
infinite number exists
then an infinite-place-value exists.

So if a number exists, it represents a quantity, and that quantity can
form that many place-values.

[plutonium....@gmail.com]

The meaning I was implying there was that mathematics of infinite sets
did not have primeness as intrinsic and that we are foisting a feature
onto
numbers which the numbers do not have. So that is a form of
anthropomorphism,
just like saying rocks in a cliff form a human face.

But your argument melts away and my argument melts away all in the
stroke of
merely producing a counterexample. A number that is neither prime nor
composite.

Here are three such numbers:

9999....999997

9999....999991

9999.....999989

Each of those numbers are sometimes prime, sometimes composite. There
is no definition
of prime that satisfies every AP-adic and leaves deterministic final
answer as to whether they
are prime or composite. I call them indeterminate as to whether prime
or composite.

So if there exists no definition of prime that we can say definitively
that number is prime or that
number is composite.

Then the definition of prime was never really a feature of
mathematics.

Now it maybe the case that prime as a definition can only exist in
finite sets. So if you have a finite
set, then some members may be divisible only by 1 and itself. So that
if you have an infinite set, then
the definition of prime is likely to be contradictory to infinity.
Somehow primeness and infinity are
incompatible.

So a counterexample is all that is needed to squelch the debate.

Noone can deliver a definition of prime that settles the question of
whether any given AP-adic is
prime or composite.

[lwa...@lausd.net]

On Jul 15, 8:07 pm, David R Tribble <da...@tribble.com> wrote:
> lwal...@lausd.net wrote:
> > I assume that 9999....99997 has 9999....99999 nines followed by a 7.
> How?
> Does that mean that 999...999 has 999...999 nines followed
> by another nine?

Actually, at one point AP stated that
numbers such as 999...997 have only
999...998 nines followed by a seven,
so that 999...999 has 999...999 nines,
thus avoiding this problem.

I have worked out the mod values for
999...999 nines with a seven, but I
could have done it just as well for
999...998 nines with a seven.

> Is so, is the left number 1/10 the value of the right number?
> If not, are the two numbers equal?

It appear that in AP-adics, the
number of nines in 999...999 is meant
to be (close to) itself. This doesn't
happen with large finite numbers,
where the number of digits in n is
approximately log_10(n), which is
much, much smaller than n. (And
therefore AP-adics are not standard
finite numbers.) I believe that there
may actually be a way to make this all
more rigorous.

[plutonium....@gmail.com]

lwal...@lausd.net wrote:
> On Jul 15, 8:07�pm, David R Tribble <da...@tribble.com> wrote:
> > lwal...@lausd.net wrote:
> > > I assume that 9999....99997 has 9999....99999 nines followed by a 7.
> > How?
> > Does that mean that 999...999 has 999...999 nines followed
> > by another nine?
>
> Actually, at one point AP stated that
> numbers such as 999...997 have only
> 999...998 nines followed by a seven,
> so that 999...999 has 999...999 nines,
> thus avoiding this problem.
>

It seems reasonable to me, that since these are infinite numbers that
we
can have a number 9999....99999 as the largest integer just one metric
unit
away from the South Pole and also have 9999....99999 place-value. In
infinity
a line segment can have a 1-1 correspondence with a larger line
segment,
since both are infinity.

But I think the best persuasion is the geometrical development of AP-
adics.
We have no problem with picturing the Real Number 1.99999.....999 as
it
is very close to 2.000....0000. So that 1.9999...9999 has a place-
value for
its rightmost 9 of the FrontView. And we can speak of the Real Number
1.9999....999990 or the Real Number 1.99999....999995 and talk about
the rightmost digit place-value of the "0" or the "5" respectively.

So if anyone is unclear about AP-adics, unclear about place-value, I
would
just simply start talking about the clarity or unclarity of the
counterpart of
Reals.

Why should numbers that are integers at infinity bother someone, yet
numbers that are "infinite smallwise" such as the approach to 2.000...
by 1.999...9999 not bother them.

> I have worked out the mod values for
> 999...999 nines with a seven, but I
> could have done it just as well for
> 999...998 nines with a seven.
>
> > Is so, is the left number 1/10 the value of the right number?
> > If not, are the two numbers equal?
>
> It appear that in AP-adics, the
> number of nines in 999...999 is meant
> to be (close to) itself. This doesn't
> happen with large finite numbers,
> where the number of digits in n is
> approximately log_10(n), which is
> much, much smaller than n. (And
> therefore AP-adics are not standard
> finite numbers.) I believe that there
> may actually be a way to make this all
> more rigorous.

The development of AP-adics was the development of the numbers that
form NonEuclidean Geometry.
To find the numbers that actually are native and intrinsic to
NonEuclidean Geometry. And
where this relationship holds up:

Euclidean geometry = the union of Elliptic plus Hyperbolic geometry.

Now that may have a factor of some inverse factor since
1.9999....99999 is not equal to 9999...99999r1 so I may need to
include some factor
in the equation to so to speak flip over a Real to make an AP-adic or
flip over an AP-adic
to make the counterpart Real.

So we have no problems in Reals when we picture the Reals between 1
and 2 such as
1.9999....99998 then 1.9999....99999 and finally the next point in
Reals of 2.0000...0000
so we have no problems of place-value in Reals in this approach to 2

Likewise we should not have problems of place-value of 9999....999997
then
the next AP-adic of 9999...99998 and then the next AP-adic of
9999...99999
and finally the next AP-adic of the South Pole which I think is the
number pi.

Since we never have problems of place value in Euclidean geometry as
we get close
to 2 in Reals, we should not have problems of place-value in
NonEuclidean geometry
of AP-adics as we approach the South Pole.

I am grateful that Lwal has interest in this mathematics and has
worked on making it more
clear, but the clarity, I feel has to be the geometry, and not any
algebra clarity. It is all
geometry motivated and the algebra can come near the end.

[plutonium....@gmail.com]

Archimedes Plutonium wrote:
>
> I can think of two examples that are reverse, where they make sense in
> infinite sets and untenable
> in finite sets-- the calculus of integration, differentiation and
> convergence of sequences.
>
> Maybe primeness is the first and only example of where a definition
> makes sense for finite sets but
> is nonsense with infinite sets. I wish I could think of another
> definition that breaks apart with infinite
> sets.
>
> Searching for more examples.
>

I know what has to be done now. I am not going to throw away
"primeness", but
instead, deliver it to its proper home.

What if we had a world of science where they taught that Homo sapiens
was a species
that belonged in the elm family of trees Ulmus instead of Homo. So
that in school we
are taught that our species is Ulmus sapiens. And that no longer did
we teach we are
an animal but that we are part of the plant kingdom. Pretty
ridiculous, you would say.

Well that has been the situation for the definition and concept of
prime and of factorial
for the past centuries and milleniums. Their rightful home was not the
Counting Numbers
but that "finite portion" on the Reals. Reals are infinite strings
rightward with a finite portion
leftwards so that the Real Number 10.3333..... or 11.595959.... has a
finite porion of 10
and 11 respectively and where the 10 is composite and the 11 is prime
relative to all other
finite portions of Reals.

The definition and concept of prime makes sense only a that portion of
the Reals.

Here is another analogy or example but rather a poor one. There are
laws prohibiting smoking
in many parts of Europe and USA where you cannot smoke in a public
place and you cannot smoke
in a restaurant, except if the restaurant has an outdoor patio where
you can smoke in the patio.

Well likewise for the concept of Primeness and Factorial, it never
existed legitimately in the Natural
Numbers, but existed only in the finite portion of Reals. Just as it
is wrong and silly to put Homo
sapiens in the family of evolution of the Elms in botany.

Now here is an example of a huge mistake in mathematics of this false
home. The Equation
e^(i)(pi) = -1 or sometimes written e^(i)(2pi) = 1.

So if we study biology and went to study the evolution of our species
and was escorted to a botany
class where they had put our species as in the family of Ulmus sapiens
well we should rightfully
rebel and protest and say, "you guys are not doing a good job of
biology, where you have the ridiculous
mixup of putting our species in the wrong kingdom"

In mathematics, all numbers fit into either these two categories

category 1 : Reals of finite portion leftwards, infinite string
rightwards of a decimal point

category 2 : AP-adics of finite portion rightwards, infinite string
leftwards of a radix point

So where does the concept of Primeness and Factorial exist? It exists
only with that finite
portion on Reals.

Now why does factorial belong with finite portion on Reals? Because
when you multiply in AP-adics
of say 3 x 999....99999 you get as an answer a number smaller than
9999...99999 as that of
2999....999997. So the concept of factorial breaks down in Natural-
Numbers (as AP-adics) and the
concept only makes its original intent-sense in that finite portion on
Reals.

Now let me get back to that Equation that has bothered and mystified a
large portion of those who
encountered it. The equation e^(i)(2pi) = 1 is nothing more than that
2pi is 0 and thus 0 exponent
makes it equal to 1. So you have e^0 = 1. Where is the mystery? Where
is the great new knowledge?
There is none in the equation, except for where is the "home" of that
equation.

The home of that equation is not the Reals. If you think the e and pi
and i are in the Reals for that
equation then you are mystified. But if you realize that the e and pi
are imaginaries in AP-adics whose
value is 0 so you have 0^0 = 1. Well, you really do not have much math
of shocking mystery. The e
and pi serve as imaginary numbers in AP-adics as the origin point or
as the North and South Pole
points.

So much of mathematics has definitions and concepts and which were
created and discovered when
mathematics has only one Number System where Natural Numbers were made
as an axiom set which
grew into the Reals.

But what I discovered is that Mathematics has two Number Systems that
are independent of one
another but are mirror images and complimentary to one another. Where
one number system the Reals
are the points of Euclidean geometry and the other number system are
the points of NonEuclidean
geometry.

So the concept and definitions of Primeness and Factorial, although
discovered and thought to be at
home in Natural Numbers were wrong and mistaken. They are at home only
in that "finite portion"
on Reals.

We have a right to bulk and protest if biology classifies our species
in the plant kingdom. Likewise
we should protest when a math class teaches primeness in Number theory
when the concept belongs
over in a class on Reals.

The entire subject of mathematics needs to have a house-cleaning,
where we clean house and say where
concepts and definitions rightfully belong, whether with Reals or with
AP-adics.

Now maybe one solution is this idea that Counting Numbers are not
Natural-Numbers but rather that
finite-portion on Reals. And a very good start is to chuck-out, or
throw-out or trashcan the Peano Axiom
system for it is the cause of so much wrongness in mathematics. The
Peano Axiom system in math
is akin to having modern biology have Lamarkian theory as the
centerpiece of biology. And the second
piece of mathematics that causes so much wrongness is the Dedekind
development of Reals. The developement
of Reals and AP-adics should be from "All Possible Digit Arrangements"
coupled with this geometry
axiom-- Eucl geom = Elliptic geom unioned with Hyperbolic geom

Physics had a housecleaning in the early part of the 20th century by
quantum mechanics. Mathematics
never had a housecleaning for which it so sorely needs. Mathematics is
chuck full of nonsense and
error.

[plutonium....@gmail.com]

Archimedes Plutonium wrote yesterday:

>
> In mathematics, all numbers fit into either these two categories
>
> category 1 : Reals of finite portion leftwards, infinite string
> rightwards of a decimal point
>
> category 2 : AP-adics of finite portion rightwards, infinite string
> leftwards of a radix point
>

So this is a great outlet. That we find primeness and factorial as not
fundamental concepts,
but we do not toss them out. What we do is realize they are secondary
issues of the finite
portion on Reals. So that is a relief, that we do not toss them out.
Of course we lose somethings.
We lose Euclid's proof that primes are infinite. They no longer are
infinite since they exist
only on a finite set-- the finite portion on Reals.

So here I spent 15 years correcting people of their faulty proof of
Euclid's Infinitude of Primes
and come to find out that primes cannot be an infinite set.

But I wonder about something more important. In the above two
categories, there are two
different infinities. One infinity on the Reals is a microscopic
infinity whereas the infinity on
AP-adics is a large scale infinity of telescopic range. Both
infinities are containing holes between
their numbers.

So I wonder about calculus of its integration and differentiation. I
never studied calculus in depth, but
know there are a plethora of calculus of patchwork to patch some
problem.

So I wonder, if some of those problems of Calculus exist because the
old-timers had only the Infinity
of Reals to work with and who did not realize the Reals have holes
between numbers and did not
realize there was a separate and different infinity of numbers of the
AP-adics.

So I wonder if the problems of old in Calculus, whether many of them
can be made to vanish, upon the
realization that the Reals have holes in them, and that the AP-adics
have the infinity of Elliptic and
Hyperbolic geometry?

I also wonder about this idea. As to whether we can make the Reals be
continuous if we fill the holes
with the negative Reals.

One hole example is the two Reals of 1.9999...99997 and
1.9999....99998 So there is no Real between
those two Reals. But now, we fill that hole with the negative Real
-1.9999....99997. By doing so,
I wonder if that gives us a form of continuity?

Now we all know the history of mathematics when they discovered
negative numbers and then when
Descartes set up his famous Cartesian coordinate system which has come
down to us this day as
essentially unchanged. But what I am proposing is that why throw all
the negative Reals to the opposite
side of the positive Reals separated by zero? Why do that? Was it
because, noone had any reason
not to do that? Was it because, well, where else do the negative Reals
belong?

The reason I want to fill each hole between positive Reals with a
negative Real is that it straightens out
the line and makes it a Euclidean straight line. The positive AP-adics
also have holes between two numbers
and they bend back around to form a circle or ellipse. So if I put the
negative AP-adics in between each
hole, then again I straighten out the Elliptic geometry and form
Euclidean.

So I wonder, by filling the holes with negative numbers, does that
give me some Continuity and rid me
of a goretex like surface of holes between every two Reals?

And, because there are two number systems--Reals and AP-adics, does it
then allow us to redefine
the Calculus of integration and differentiation to the point where we
clean up the house of Calculus of
its myriad forms of definitions that run rampant? I wish I had an in
depth knowledge of the huge number
of integrals and derivatives-- three of which I remember as the
Lebesgue, the Riemann, and the Borel
but there are many more plugs and fixes.

So what does the reality that there are two number systems for which
the Calculus must be applied
and not just the one old one of Reals?

[plutonium....@gmail.com]

Now in my last post of #598 I voiced a wish, a wish that I was very
familar to the problems of Calculus
and why the history of Calculus has a plethora of patchwork to mend
flaws in definitions. A plethora of
integration and differentiation. Where a student who wants to become
an expert in Calculus, can spend an
entire lifetime just in study of the thousands of patches to mend the
Calculus.

But I enter the fray with several new concepts that may just clear up
the entire body of knowledge of the
Calculus. I enter with these new concepts:
(1) Reals form Euclidean Geometry and the Reals have holes between any
two Reals
(2) FrontView gives us a snapshot picture of the smallest neighborhood
of any two Reals
(3) How negative Reals should fit with positive Reals

So those three new concepts and others may just provide me with the
ability to overhaul and revise
modern day Calculus and give the concept of Limit and Continuous
Function new life.

One of the troubles of the old Calculus is the definition of Limit
with its "delta-epsilon" The idea here is
that as you arbitrarily make one interval smaller, you can make the
other interval smaller still, and thus
producing a Limit. Is there anything wrong with this old definition of
Limit?

Well yes, because it assumes continuity.

The old definition never had a snapshot of a tiny neighborhood of
Reals. But with the concept of FrontView
we can now have a snapshot picture of a tiny neighborhood of Reals and
what we see is that any two
Reals are never contiguous but have tiny holes between them.

In the old days of mathematics we believed that between any two Reals
existed an infinity of more
Reals. With FrontView we learn differently. That there exists the Real
1.5555....55555
and adjacent to that Real exists these two Reals 1.5555....55554 and
1.5555...555556

So there are no Reals between 1.5555....55554 and 1.5555....5555
Instead there is a hole or gap
between those two Reals. Granted, between the two Reals
1.4444....44444 and 1.5555....55555 there
does exist an infinity of other Reals. But the statment, between any
two Reals is another Real no longer
is true.

Now there are problems also in the old math as to the concept of
"Continuous Function"

Let me quote a passage from "Calculus, by Gilbert Strang, 1991, page
87
--- quoting from CALCULUS, Strang ---
It is amazing but true that the definition of "continuous function" is
still debated (Mathematics
Teacher, May 1989). You see the reason-- we speak about a
discontinuity of 1/x, and at the same
time call it a continuous function.
The definition misses the difference between 1/x and (sin x)/x The
function f(x) = (sin x)/x can be
made continuous at all x. Just set
f(0) = 1.
--- end quoting Strang ---

Now I quoted that passage for the reason, also, of trying to
illustrate how muddy is all of Calculus
and why there is a plethora of integrals and derivatives.

And I think I can change all of that muddiness and put the Calculus on
a much sounder foundation
with its Limit and its Continuity.

What I propose is that the Euclidean Geometry is straightline geometry
because of the arrangement
of its points. That its positive Reals has this hole and gap between
any two Reals, but, if we insert
into that hole a negative Real. That such an insertion straightens out
the line to be a straightline. If we
had only positive Reals, they would form a curved and bent line such
as the positive AP-adics and form
an ellipse. But because of an insertion of a negative Real, in between
two positive Reals of their smallest
size interval, that we have Euclidean geometry of straightlines and we
have Continuity and we have
a better idea of Limit.

So as the example of 1.5555...55554, 1.5555....55555, 1.55555....55556
that those adjacent Reals have those gaps and holes by a metric of
0.0000.....000001

So here we have to consider that this metric spoils the old definition
of Limit of its epsilon and delta.

But, now, the solution.

We fill those two holes with negative Reals:

1.5555...55554,(-)1.5555...5555, 1.5555....55555, (-)1.55555....5555
1.5555....55556

And we thus define Continuity on the Reals and Continuity on Functions
by the sandwiching in between
any two positive Reals with their negative Real counterparts.

We picture this sandwiching as a straightening out of a curved line if
the positive Reals were left alone
with their holes. But because there are negative Reals sandwiched in
between the lines are straightened
out. And the negative Reals form a bridge between the two positive
Reals, and that bridge thus creates
Continuity.

We transfer this negative Real sandwiching over to the Functions.

You see the problem with the old math of their Limit and Continuous
Function is that they assumed the
Reals were continuous, but that is not true.

And then when you get to functions that are continuous everywhere yet
differentiable nowhere do we really
see how the above revision can give us a clear picture of what is
going on.

Now I wish I was familar with the plethora of Calculus integrals and
derivatives and the source of problem
for which they caused a large number of mathematicians to create
patches for these problems. Because
I have the suspicion that if they knew of FrontView and how Reals are
setup and how AP-adics
are setup, that all of those problems of the past would simply melt
away as no-problem.

[plutonium....@gmail.com]

In Calculus there are two forms of Continuity, and I should make
effort to
keep them separate and clear. There is the Continuity assumed in the
Coordinate System and that usually means the Cartesian Coordinate
System. Strang starts off his book with Velocity and Distance. That is
an
amiable starting point for those looking at the Calculus for the first
time.

However, in the future, the starting point of Calculus should be the
Reals
as All Possible Digit Arrangements as a vast grid of points with tiny
holes
between them.

Now how to fill the holes so that the Coordinate System is Continuous?

And the second Continuity is whether a function can be Continuous?

Does my slipping of a negative Real, sandwiched between the closest
two positive Reals, does that provide Continuity?

Maybe I made a mistake there where it should be
1.5555...55554,(-)1.5555...5555, 1.5555....55555, (-)1.55555....5556
1.5555....55556

I do not know as yet whether a negative number sandwiched between
every positive
Real is going to provide Continuity of the Coordinate System.

I would hope it does so for that would be the easiest way of setting
up a coordinate system
that is continuous on the Reals, where given any Real number, except
0, has a negative Real
attached below itself and is the same except for a negative sign.

So give me say 7.3 then below it is (-)7.3.

Now can we have the Cartesian Coordinate System with its four
quadrants? I see why not? With
the proviso that the negative Reals have a positive Real attached
below.

What I do not know is whether this pointwise attachment is sufficient
for continuity or whether an
interval needs to fill the hole.

If an interval needs to fill the hole, then what I would propose is
that the interval

1.5555...55554, 1.5555....55555, 1.5555....55556

be filled with AP-adics like this

1.5555...55554, 45555...5555r1 through to 5555...555r1,
1.5555....55555

So that if a pointwise inclusion of a negative Real between two
positive Reals is insufficient for
continuity, then insert an interval between the hole between two
Reals. And the easiest interval
I can think of is the AP-adic interval.

Now all of this work is going to be for nothing if it does not predict
anything new
and true. All of this work is for nothing even if it clears up and
throws out the window
all the dirty and messy definitions and various forms of integration
and differentiation.

So even if the above clears up and clears out the Calculus, it is
still unworthy unless
it predicts something new and true to mathematics.

[plutonium....@gmail.com]

Just minutes ago I wrote:

>
> Now all of this work is going to be for nothing if it does not predict
> anything new
> and true. All of this work is for nothing even if it clears up and
> throws out the window
> all the dirty and messy definitions and various forms of integration
> and differentiation.
>
> So even if the above clears up and clears out the Calculus, it is
> still unworthy unless
> it predicts something new and true to mathematics.
>

I believe it makes a pretty and new prediction in mathematics. That in
the end there are
three possible Coordinate Systems, one in Euclidean one on the surface
of a sphere
and one on the surface of a pseudosphere and where the function can be
transferred
over to any one of these three and apply with different answers.

So if I set it up just right, then a trig function would have
pertinent answer in Euclidean
geometry, and then transferred to the surface of the sphere and have a
different pertinent
answer and then be transferred to a pseudosphere and have yet again a
different pertinent
answer.

I remember someone saying that the lines of longitude in Riemann
geometry become straight
lines under a transformation. Well that is the sort of thing the above
is expecting.

The old math had only one coordinate system for all functions. Where
we prepped every function
into a Cartesian function. Where we never had a "function of
Riemannian geometry" or a function
in "Lobachevskian geometry" but everything was wrestled to the ground
and bent into some shape
to be inputted into Euclidean geometry of Cartesian coordinate system.

So what is a trig function on the surface of a sphere with its
intrinsic points of AP-adics? Would
lines of latitude by a trig function in Riemannian geometry?

The new math would have 3 independent coordinate systems that deliver
3 different answers to
a given function.

[plutonium....@gmail.com]

What is the best example of continuity in physics? Well to be honest,
that is what Quantum Mechanics
speaks to, in the fact that there is no such thing as "absolute
continuity" where there are always holes
and gaps. Where Planck's constant is the gap and hole.

So if the Reals have holes in them such as 1.5555....55555 and
1.5555....55556 has a hole
of 0.0000....000001 between them. Why should math, a subset of physics
have "absolute continuity"?

There are bigger holes in the AP-adics where 0000...00001 has a
integer hole between 0000...00002
We can sort of fill in the hole with the radix but the AP-adics holes
are larger than the tiny hole
in Reals.

But what I am complaining about, is that physics has no absolute-
continuity and so why should
math even strive for such a thing? It should not.

And the Calculus with its Limit works perfectly well with a Space
riddled with tiny holes in the Reals.

So maybe I ought to drop the conversation of continuity as the pursuit
of fantasy.

However, the idea of sticking a negative Real in between every
positive Real is still a very good
idea. I see nothing in the mathematics literature that warrants
placing all the Negative Reals
opposite the Positive Reals separated by zero. So why not stick them
between every positive
Real?

[plutonium....@gmail.com]

I have been playing around with this idea of where the Negative Reals
should really go in a Coordinate
System. Been toying with the possibility of having only Positive Real
axis (call them rays) and
eliminate the negative-axis. Where the negative-Reals are all
sandwiched in between positive Reals
and only positive Reals as ray-axes. Been toying around with it, and
if I can get the periodic functions
like the trig functions with positive-axes where the negative-Reals
all sandwiched in between positive-Reals.

For example, these Positive Reals:

0.3333....3333333, 0.3333....333334, 0.3333...333335,
0.33333.....333336

would look like this

0.3333....3333333, (-)0.3333....333334, 0.3333...333334,
(-)0.33333.....333335,
0.3333....3333335

So whereever there are Two Reals there are negative-Reals sandwiched
between them
in order to fill up the hole-metric that exists in Reals of at least a
separation metric
of 0.0000....000001 distance of a hole.

I was thinking I could get rid of the entire negative Real axes.

Now why would I insist on doing this? For two reason, none of which
are continuity.

(1) It makes the space flat Euclidean for the positive adjacent to a
negative unbends the space
into being flat plane. Keep in mind that the positive AP-adics forms
Elliptic space and
the negative AP-adics forms Hyperbolic space, so in the old Cartesian
picture, the positive
Reals should be a circular shape and the negative separated out from
the positive would be
hyperbolic shaped. So by sandwiching them between one another we have
flat plane Euclidean
(2) because physics has this feature of space wherein there is matter
there exists adjacent
antimatter

I thought I was doing it especially for continuity sake, but since
physics has no continuity but has
tiny holes everywhere, then math cannot have continuity.

Physics describes the discontinuity as Planck Length 10^-35 meters
divided into 10^35 meters (Length of Cosmos)
So we have 10^70.

So mathematics makes sense with Reals that have 70 place-values and
cease to make sense beyond
that. In a sense, the Planck metric of Mathematics is 0.0000....00001
and that metric is sharpened even
further as 10^-70.

So, can we fit the periodic functions such as trigonometric functions
easily into this new Coordinate
System where the positive and negative Reals alternate on a line?

So is there any immediate benefit?

[plutonium....@gmail.com]

I wrote earlier today:

>
> For example, these Positive Reals:
>
> 0.3333....3333333, 0.3333....333334, 0.3333...333335,
> 0.33333.....333336
>
> would look like this
>
>
> 0.3333....3333333, (-)0.3333....333334, 0.3333...333334,
> (-)0.33333.....333335,
> 0.3333....3333335
>
> So whereever there are Two Reals there are negative-Reals sandwiched
> between them
> in order to fill up the hole-metric that exists in Reals of at least a
> separation metric
> of 0.0000....000001 distance of a hole.

Now in the old math, we had a central concept of Limit for the
Calculus. It is going
to have to be changed and modified for it really does not exist in
true mathematics,
because it does not and cannot exist in physics. Physics is all about
Quantum Mechanics
and to mean "quantum" means there is no absolute continuity, or any
lesser form of
continuity. If the world had continuity-- no holes in lines of space--
then there would not
be Quantum Mechanics.

Let us briefly review what the Limit concept is in math. It basically
is the equivalent statement
that between any two Reals is a new third Real. This is often given as
a axiom or postulate of
math. And when we alter that axiom so as to include concepts of
neighborhood and epsilon
delta, what we are merely doing is stating that between any two Reals
is a new third Real.
So the epsilon delta of Limit is another way of saying between any two
Reals is another Real.

What the AP-adics program does is point out that numbers are geometry
and geometry are
numbers and that it is impossible to create a system of numbers where
you have "absolute
continuity"

In the old math, they could never recognize this because they lacked
the FrontView of a number,
so they were blind.

Once you have FrontView, absolute continuity melts away as a
falsehood, just as absolute-space
and absolute-time melted away as falsehoods once Quantum Mechanics
took over.

So there must be a change in the concept of Limit to accomodate that
smallest metric of a hole
in the Reals. That metric is 0.0000....00001. It is why the number
0.9999....99999 is not equal to
1 but is 0.0000....000001 shy of 1. Those old alleged proofs of .
999.... = 1 contained flaws of reason.

FrontView is a important and critical turning point in mathematics for
it is a new tool that lets us
see infinite numbers in the full scope. Like only seeing the one side
of the Moon or one side of a
star and not able to see the full star even though the full star is
there. Just because a number is
infinite does not mean we can only see one end of it.

So the old concept of Limit of the old math needs a revision because
between any two Given Reals
does not necessarily provide a new third Real.

If we use the program above of where between any two positive Reals is
a negative Real such as this:

0.3333....3333333
(-)0.3333....333334
0.3333...333334
(-)0.33333.....333335
0.3333....3333335

Still, there is no new third Real between (-)0.3333....333334 and
0.3333...333334

Now some may want to patch each hole with a interval that is infinite
and that would solve
the problem, but a new problem would arise in that you would then no
longer have flat Euclidean
Space as a interval that is infinite positive or negative is a bent
space. What makes Euclidean
flat space where given two parallel lines and a point not on those
lines has one and only one
line parallel to the given two, is the idea or fact that each positive
Real has an adjacent negative
Real so as to unbend the tendency of positives to bend elliptically
and negatives to bend hyperbolically.
(I may just have been the first person to use the terms elliptically
and hyperbolically).

So the betweenness axiom is no longer true, and probably contradictory
to other parts of mathematics.

So what changes need to be made to the Limit concept? Well, we need to
include this metric hole
of 0.0000....00001 that exists between any two positive Reals. It is a
very tiny hole and according to
physics is of the caliber of 10^-70.

So everything in math which includes both geometry and algebra, have
holes between points in geometry
and have holes between numbers in algebra.

Continuity, whether absolute continuity or weak form of continuity
(sandwiching negative Reals between
positive Reals) was a chimera of the past. Physics does not have
continuity, means math has
no continuity. Continuity was like our old false perceptions of time,
of thinking time is something absolute.

Now what this revision of the Limit does for the Calculus and its
horde of forms of integration
and differentiation is something I am awfully curious to find out.
Does it clean up that messy house?

[plutonium....@gmail.com]

Let me get into the heart of some of this. Where I throw out the
Descartes Cartesian Coordinate System.
I throw it out because in Euclidean Geometry, the way you get
straightlines and you get flat plane geometry
is by sandwiching the Negative-Reals in between the Positive Reals.
And now there is no more need
of 4 quadrants where the negatives are separate from the positives. In
AP-Coordinate System the
Reals form a checkerboard of points. Why put them alongside one
another? Because all positives
forms a bent curved space and all negative do the same thing. To have
a flat Euclidean space
you have to put the negatives sandwiched between the positives where
one flattens out the other.

Now the graph of the function y = x^2 is a parabola in Cartesian
coordinates. But what is this
same function graphed in AP-Coordinate System? Well, I need only one
quadrant.

When x is 1 then y is 1 and when x is -1 then y is 1. When x is 2 then
y is 4 and when x is
-2 then y is 4.

So the -1 is the point just before +1 and the point -2 is the point
just before +2, like this schemata:

-1.00000....0000
+1.00000.....00000
-1.00000.....00001
+1.00000.....000001
-1.0000....0000002
+1.0000....000002
etc etc

So in the AP-Coordinate System we have what I would call one-half of a
parabola, however, it
appears as though it has tiny sharp risers as you have (-1,1) before
you have (1,1)

Now let me see what this new AP-Coordinate System does for the
trigonometric functions. I suspect
it turns them into a series of mountain peaks instead of the peaks and
troughs of water waves.

Anyway, it is nice to see that this new Coordinate system can
accommodate most every function
that the Cartesian Coordinate System handled. Perhaps mine can do even
more. Perhaps the
equation of a circle can now be a function in AP-Coordinate System??

[plutonium....@gmail.com]

This is the part of the Internet where it is not easy to show or
explain things because of the
inability to draw pictures.

We all have seen what the sine function and cosine function look like
in Cartesian Coordinate
System where sine and cosine bounce up and down between 1 and -1. and
we can describe
this as peaks and troughs on the x-axis. So the sine and cosine
fluctuate back and forth
rising to 1 then going to 0 and submerging below 0 to go to -1,
periodically.

Now graphing sine and cosine in AP-Coordinate System where the Reals
have only one
quadrant and the negative-Reals are checkerboarded between the
positive-Reals. Why in the
world (you would ask) have a coordinate system like this? The answer
is that Euclidean Geometry
demands it to be like this. That the Descartes Cartesian Coordinate
system was a fake system
all along. In order to have flat plane Euclidean geometry, a negative
Real has to sit next to a positive
Real so that the opposite signs unbend or uncurve one another. In
Descartes system having all the
positive-Reals on one side forms a highly curved space of Riemannian
geometry whilst the negative-Reals
on the opposite side of zero forms a hyperbolic space, although no-one
in math ever realized it. They
thought that you could have plane geometry and just simply fill them
with any kind of numbers you pleased.

This is why I keep telling algebraists in mathematics, that it is more
important that you properly connect
numbers to geometry before you fiddle around with the algebra on
numbers.

Now to graph sine and cosine in the AP-Coordinate System of Euclidean
Geometry, (for there is also
a AP-Coordinate for Elliptic and for Hyperbolic geometry) we need only
one quadrant and the sine
function and cosine function no longer fall below the x axis. And the
sine and cosine no longer undulate
like a water wave with peaks and troughs. They now look more like a
mountain range, like a series of
peaks.

Now the immediate question is which of these two Coordinate Systems
better describes Physics?
And the answer is the AP-coordinate system for if you look at the
Single Slit Experiment or Double
Slit Experiment in the old Cartesian Coordinate system the diffraction
pattern is described as

d sin (theta) = n (lambda)

But in the new AP-Coordinate System that equation is streamlined since
the sine function is already
a diffraction pattern itself.

Now where in physics does it matter the most whether we use Cartesian
or AP Coordinate system?
I think the light wave is where it matters the most and the light wave
is a transverse wave that never
dips below zero. So the lightwave is a AP-Coordinate System wave.

So apparently physics is written in AP-Coordinate System, not the
Cartesian Coordinate System

[plutonium....@gmail.com]

I knew better than to call it "risers" for it is a tiny step and
reminds me of the step-function.
Only the step function most people are aware of are step intervals.
Here we have a step
function on points.

[David R Tribble]

lwal...@lausd.net wrote:
>> I assume that 9999....99997 has 9999....99999 nines followed by a 7.
>

David R Tribble wrote:
>> How?
>

Archimedes Plutonium wrote:
> The reasoning here is that the quantity of the largest number would
> also correlate with the existence of that many place-values.

Then you have a contradiction, because "the largest number"
cannot then be the largest number, because there exists an
even larger number with that many place-values. And likewise
an even larger number exists with that even larger number of
place-values, and so on. None of these numbers can be the
"largest" number, because you can always construct an even
larger number from each one, without end.

> So if the number 12 exists then a 12 place-value should exist.

Exactly, so then a 10^12-digit value should exist, and so then
a 10^10^12-digit value should exist, and so on, none of which
can ever be the "largest" value.

> If a infinite number exists ...

But you've never explained how you go from counting finite
numbers having finite numbers of digits to counting infinite
values having infinite numbers of digits.

[David R Tribble]

Archimedes Plutonium wrote:
> But your argument melts away and my argument melts away all in the
> stroke of
> merely producing a counterexample. A number that is neither prime nor
> composite.
>
> Here are three such numbers:
> 9999....999997
> 9999....999991
> 9999.....999989
>
> Each of those numbers are sometimes prime, sometimes composite.
> There is no definition of prime that satisfies every AP-adic and leaves
> deterministic final answer as to whether they
> are prime or composite. I call them indeterminate as to whether prime
> or composite.

Or a third possibility: perhaps they are not numbers at all.

> So if there exists no definition of prime that we can say definitively
> that number is prime or that number is composite.

True, as long as you ignore the obvious:
a number is either divisible by another number, or it's not.

> Noone can deliver a definition of prime that settles the question of
> whether any given AP-adic is prime or composite.

Or even if it's actually a number.

[plutonium....@gmail.com]

Let me describe how to set up the AP-Coordinate System in 2D
Euclidean, 2D Elliptic and 2D Hyperbolic
All three of these are Digital Coordinate Systems whereas the old
Cartesian is an Analog system.

2D Euclidean

.
.
.
.
+0.000....00002
-0.0000...00002
+0.0000...00001,
-0.0000....000001 , +0.0000....000001, -0.0000...00002,
+0.000....000002, ......
0

The 0 sort of sticks out like a sore thumb but all the rest of the
Reals, both positive
and negative form a huge matrix.

Now a graph of a function in 2D Euclidean Geometry would be that
matrix above

2D Elliptic without the radix

pi
9999...99999
.
.
.
000....00003
0000...00002
0000...00001,
0000....000001 , 0000....000002, 0000...00003, 000....00004, ......
9999....99999, pi
2pi

2D Elliptic with the radix

pi
9999...99999r
.
.
.
000....00003r
0000...00002r
0000...00001r,
r, 0000....000001r , 0000....000002r, 0000...00003r,
000....00004r, ...... 9999....99999r, pi
2pi

2D Hyperbolic without the radix

pi or e as imaginary
-9999...99999
.
.
.
-000....00003
-0000...00002
-0000...00001,
-0000....000001 , -0000....000002, -0000...00003,
-000....00004, ...... -9999....99999, pi
2pi and or e as imaginary points

Major difference between Elliptic and Hyperbolic is that Elliptic is
all positive numbers
and forms the numbers on a sphere surface whereas the Hyperbolic are
all negative
numbers on a pseudosphere surface.

All of these three geometries are Digital since there is no continuity
in any one of them.

What makes Elliptic and Hyperbolic so bent and curved in space is the
fact they do not
have a negative sandwiched in between every positive as the Reals do
and thus straighten
out or flatten out the geometry.

So to graph a function in any one of the three geometries of 2D, we
simply plot the points
in the matrix

[Archimedes Plutonium]

Let me try the previous post again to get the typing format
to fit all the matrix points on the same line. They form a
square Matrix, but the carriage format would confuse.

Let me describe how to set up the AP-Coordinate System in 2D
Euclidean, 2D Elliptic and 2D Hyperbolic
All three of these are Digital Coordinate Systems whereas the old
Cartesian is an Analog system.

2D Euclidean

.
.
.
.
+0.000....00002
-0.0000...00002
+0.0000...00001,

-0.0...001,+0.0...001,-0.0...002,+0.0...002,..
0

The 0 sort of sticks out like a sore thumb but all the rest of the
Reals, both positive
and negative form a huge matrix.

Now a graph of a function in 2D Euclidean Geometry would be that
matrix above

2D Elliptic without the radix

pi
9999...99999
.
.
.
000....00003
0000...00002
0000...00001,

000...0001 ,000...0002,000...0003, ......,999...999, pi
2pi

2D Elliptic with the radix

pi
9999...99999r
.
.
.
000....00003r
0000...00002r
0000...00001r,

r, 00...001r,00...002r,00...003r,...., 999...999r, pi
2pi

2D Hyperbolic without the radix

pi or e as imaginary
-9999...99999
.
.
.
-000....00003
-0000...00002
-0000...00001,

-00...001 , -00...002, -00...003,..... ,-999...999, pi

[plutonium....@gmail.com]

Archimedes Plutonium wrote:

Let me correct some mistakes first:

>
> Let me describe how to set up the AP-Coordinate System in 2D
> Euclidean, 2D Elliptic and 2D Hyperbolic
> All three of these are Digital Coordinate Systems whereas the old
> Cartesian is an Analog system.
>

By analog, I mean they thought they had absolute-continuity between
points. A digital
coordinate system has a matrix of points and a graph of a function
ignores the holes
and gaps between points.

> 2D Euclidean
>
> .
> .
> .
> .
> +0.000....00002
> -0.0000...00002
> +0.0000...00001,
> -0.0...001,+0.0...001,-0.0...002,+0.0...002,..
> 0
>

.
.
.
.
+0.000....00002
-0.0000...00002
+0.0000...00001

-0.000...00001
0, -0.0...001,+0.0...001,-0.0...002,+0.0...002,..

I should have included 0 in the x-ray and the y-ray instead of leaving
it out of both rays.

For 3D Euclidean involves 3 rays.

Euclidean geometry no longer needs a negative numbers by themselves
occupying the
opposite half of a line axis.

To plot points and a graph, we simply plot them in the matrix of
points.

> The 0 sort of sticks out like a sore thumb but all the rest of the
> Reals, both positive
> and negative form a huge matrix.
>
> Now a graph of a function in 2D Euclidean Geometry would be that
> matrix above
>
> 2D Elliptic without the radix
>
> pi
> 9999...99999
> .
> .
> .
> 000....00003
> 0000...00002
> 0000...00001,
> 000...0001 ,000...0002,000...0003, ......,999...999, pi
> 2pi
>

Here again I should have moved 2pi upwards to be included in the x-ray
and the y-ray

Such as this:

pi
9999...99999
.
.
.
000....00003
0000...00002
0000...00001,

2pi, 000...0001 ,000...0002,000...0003, ......,999...999, pi

> 2D Elliptic with the radix
>
> pi
> 9999...99999r
> .
> .
> .
> 000....00003r
> 0000...00002r
> 0000...00001r,
> r, 00...001r,00...002r,00...003r,...., 999...999r, pi
> 2pi
>

Here again I should have moved the 2pi upwards to be included in the
coordinate rays.

> 2D Hyperbolic without the radix
>
> pi or e as imaginary
> -9999...99999
> .
> .
> .
> -000....00003
> -0000...00002
> -0000...00001,
> -00...001 , -00...002, -00...003,..... ,-999...999, pi
> 2pi and or e as imaginary points
>

Here again, I should have moved the 2pi upwards.

> Major difference between Elliptic and Hyperbolic is that Elliptic is
> all positive numbers
> and forms the numbers on a sphere surface whereas the Hyperbolic are
> all negative
> numbers on a pseudosphere surface.
>
> All of these three geometries are Digital since there is no continuity
> in any one of them.
>
> What makes Elliptic and Hyperbolic so bent and curved in space is the
> fact they do not
> have a negative sandwiched in between every positive as the Reals do
> and thus straighten
> out or flatten out the geometry.
>
> So to graph a function in any one of the three geometries of 2D, we
> simply plot the points
> in the matrix

I wonder why the Descartes coordinate system ever became named
Cartesian. A dictionary
says Cartesius is a Latin form of Descartes. Maybe in past times,
places and names had
Latin versions.

Now my changes of the coordinate system was brought about not due to
continuity, but
keeping in mind that continuity brought me to this sandwiching of
negatives inbetween positives.
But what has kept me with the idea that the Reals must have a
negatives sandwiched inbetween
positives is that this must be so in order to have lines straight and
not curved. That the sandwiching
of negatives in between positives is what straightens out and flattens
out the geometry, where
the negative sign counterbalances the positive sign.

Now that idea was not new to me prior to the past week for many times
I mentioned in my posts
that the reason the Reals are Euclidean geometry is that the negatives
and positve Reals are
together. But only this past week did I realize how close together I
had to put them, in order to
have straight-lines and flat plane geometry. They had to be
checkerboarded close together so that
as you move from a positive Real you land on a negative Real and vice
versa.

In the history of science, trouble is that often we do not have an
accurate accounting of the process
of discovery. In my case of the discovery of AP-coordinate system,
there were signs that I knew
of negative Reals with positive Reals is what makes Euclidean geometry
flat and straight-lined, but
I never knew until last week of how close together the negative Reals
had to be positioned with the
Positive Reals. And what drove that home was my foray adventure into
the holes created in Reals by
the FrontView and my attempt to plug those holes with Negative Reals.

So the chain of discovery of AP-coordinates was like this:
(1) perhaps about 10 years ago some of my posts showed signs of me
saying-- Reals make
Euclidean geometry because the negative Reals cancel the positive
Reals leaving flat and straightlined
geometry
(2) FrontView discovery circa 2007 leads me to see that Reals have a
hole of at least the metric
0.0000....00001 between any two Reals
(3) In July 2008 my desire to plug those 0.000...00001 to regain
continuity in Reals and plug each
of those holes with a negative-Real
(4) I abandon continuity, since physics has no continuity it is
preposterous for math.
(5) That still leaves me with a negative Real sandwiched inbetween 2
positive Reals, and now
I do not want to abandon that because it is the full-picture of what I
wanted 10 years ago.

Us, scientists have a tendency of not being fully accurate or honest
about our discoveries. With the
Internet as a archive of my posts, it is going to be evident that the
above is the chain of events that
lead me to this AP-Coordinate System discovery. Most of us like to
think that our rational and logical
minds is a working straight arrow shot to a conclusion, but as the
true story above shows, a major discovery is often a
round about drive.

Now let me spend a few moments talking about why negative Reals
sandwiched inbetween positive Reals
is a better coordinate system for the common average person who knows
little about math or science
and why this system is better than the old Cartesian system.

Many of us see graphs, especially in finance and business and
stockmarket and we know that the graph
is usually in the positive quadrant where one of the axis is the price
and the other is the time axis
and we see a nice rise in the price over time. Or the graph could be
life in general where we see progress
made over the days and weeks and years to certain goals. Now the
negative numbers in Cartesian would
be there but far away. And negative numbers seem to be rare as far as
the price of a stock or the progress
in our every day lives. But are negative numbers really rare? And
should a graph that contains alot of
positive numbers but all of a sudden shifted into a different quadrant
because of a negative number?

Recently in the past decade many companies have become bankrupt, where
their worth is a negative
number. Just in the past week a bank in California when bankrupt,
Indybank? (name?) and there was
rumors that FannieMae and FreddieMac were in some troubles. And in our
own personal lives, do we
not have days in which it seems we have negative progress, such as all
those flood victims in Iowa
this last Spring or those fire victims in California recently.

So what I am saying is that negative numbers are not far away from
positive numbers as the Cartesian
Coordinate system displays. But that a graph of alot of positive
numbers such as in the AP-coordinate
system, well, the negative numbers are right there by you all the way.
And that the normal plot
of most graphs is that of negative numbers along with positive
numbers.

I am simply pointing out, that it makes more sense that a graph of a
function has a checkerboard of
negatives with positives than the old Cartesian coordinate system
where the positives are all together,
totally separate from negatives.

Also, we should consider the history of a Coordinate System. That it
is natural for Descartes to discover
a system that can graph functions and where he would say, well, let us
have four quadrants for plane
geometry and let us put all the positives separated from negatives. It
would have been totally weird
or irrational for Descartes to have said, well, let us checkerboard
the coordinate system. There is nothing
in science that would have supported a checkerboard coordinate system
until after Dirac found that
Space is filled with positrons-- Antimatter exists everywhere there is
Matter. Once physics
found that fact, could a checkerboard coordinate system be plausible
for mathematics.

But now, what I am driving home is that numbers form geometry and
geometry has intrinsic numbers,
and for there to be a flat plane straightlined geometry, the negatives
have to be checkerboarded sandwiched
inbetween positive.

I may even have to revise our idea of "function" by the time this is
settled. What I mean by that, is if
you look at the sine and cosine function, it is begot from the unit
circle. The unit circle is already a
"poisoned well of water". So the graphing of the sine and cosine into
the AP-Coordinate System,
which I previously said was a mountain range or it was the shape of a
saw blade with its tips rounded.
That may even have to be revised.

I knew I would be changing alot of math as early as the 1990s, but I
never in my wildest dreams
ever think that I would be changing "all of mathematics". By tossing
out the Cartesian Coordinate
System and replacing it with the AP-Coordinate System changes all of
mathematics.

[ju...@diegidio.name]

On 22 Jul, 07:25, plutonium.archime...@gmail.com wrote:
> Archimedes Plutonium wrote:

> I wonder why the Descartes coordinate system ever became named
> Cartesian. A dictionary
> says Cartesius is a Latin form of Descartes. Maybe in past times,
> places and names had
> Latin versions.

Renatus Cartesius is the latinized name, he was French. It was very
common to have such latinized names because, since at least the middle
ages, all that was doctus or otherwise sacred was writen and spoken in
Latin.

> Now my changes of the coordinate system was brought about not due to
> continuity, but
> keeping in mind that continuity brought me to this sandwiching of
> negatives inbetween positives.

I find your system very interesting. I hope I'll understand it
someday!

-LV

[plutonium....@gmail.com]

ju...@diegidio.name wrote:
> On 22 Jul, 07:25, plutonium.archime...@gmail.com wrote:
> > Archimedes Plutonium wrote:
>
> > I wonder why the Descartes coordinate system ever became named
> > Cartesian. A dictionary
> > says Cartesius is a Latin form of Descartes. Maybe in past times,
> > places and names had
> > Latin versions.
>
>
> Renatus Cartesius is the latinized name, he was French. It was very
> common to have such latinized names because, since at least the middle
> ages, all that was doctus or otherwise sacred was writen and spoken in
> Latin.
>

Okay, thanks, I can see the rationale behind a Latinized name. Maybe
in the
futue we will have a repeat of this sort of practice of naming, where
a scientist
has a atomized name. And perhaps it has already started with
Archimedes Plutonium.

>
> > Now my changes of the coordinate system was brought about not due to
> > continuity, but
> > keeping in mind that continuity brought me to this sandwiching of
> > negatives inbetween positives.
>
>
> I find your system very interesting. I hope I'll understand it
> someday!
>
> -LV

Most people already understand it, only they do not use it.

Let us take the most simple function of y = x which is a diagonal line
splitting the first
and third quadrants, where the 1st is all positive and the 3rd is all
negative
in Cartesian Coordinate System:

|
|
| /
| /
|/---------------->

Now in AP-Coordinate System-Euclidean it is the same as that above
graph only the
diagonal resides in only one quadrant since the negatives are
checkerboarded between
positives.

Now a graph in AP-Coordinates looks the same as Cartesian until you
get to very small
distances where you have tiny holes. In Cartesian there was assumed
"absolute continuity".

The graph of y = x in AP-Coordinates for Elliptic Geometry is
intriguing. Here the Cartesian
system never works for it can not apply itself. In the old math, we
did everything in Cartesian and
transfered that to a sphere surface. We never used a "intrinsic
coordinate system for Elliptic or
Hyperbolic"

Picture a globe of its lines of longitude and slice the globe in half
making a hemisphere, and
slice it along the Greenwich Meridian so that we retain the North and
South Poles. Now the x-axis
is the Greenwich longitude from the North Pole to the South Pole and
the y-axis is the Artic Semicircle.
So the plotting of y= x in Elliptic Geometry ends up being the 90
degree West longitude line.

Now I have not yet figured out the x-axis and y-axis on a pseudosphere
to do that y= x
in Hyperbolic geometry, but it should be easy.

What is important is that a function of y = x in Euclidean geometry
may be very much different from
y= x in Elliptic and Hyperbolic geometry.

A photograph picture from a digital camera is a modern day example of
Euclidean Geometry. It does not
have continuity, but rather the points are so small that we visualize
continuity. And, the negative Reals
are alongside the positive Reals in a photograph.

[plutonium....@gmail.com]

Just minutes ago I made this mistake:

>
> The graph of y = x in AP-Coordinates for Elliptic Geometry is
> intriguing. Here the Cartesian
> system never works for it can not apply itself. In the old math, we
> did everything in Cartesian and
> transfered that to a sphere surface. We never used a "intrinsic
> coordinate system for Elliptic or
> Hyperbolic"
>
> Picture a globe of its lines of longitude and slice the globe in half
> making a hemisphere, and
> slice it along the Greenwich Meridian so that we retain the North and
> South Poles. Now the x-axis
> is the Greenwich longitude from the North Pole to the South Pole and
> the y-axis is the Artic Semicircle.
> So the plotting of y= x in Elliptic Geometry ends up being the 90
> degree West longitude line.
>

No it does not. It is not the 90 degree West Longitude. It appears to
be a sinusoidal
curve for it does intersect at
90 degree, 90 degree.

I point I was trying to make is that a function varies in different
geometries.

[plutonium....@gmail.com]

plutonium.archime...@gmail.com wrote:
> Just minutes ago I made this mistake:
> >
> > The graph of y = x in AP-Coordinates for Elliptic Geometry is
> > intriguing. Here the Cartesian
> > system never works for it can not apply itself. In the old math, we
> > did everything in Cartesian and
> > transfered that to a sphere surface. We never used a "intrinsic
> > coordinate system for Elliptic or
> > Hyperbolic"
> >
> > Picture a globe of its lines of longitude and slice the globe in half
> > making a hemisphere, and
> > slice it along the Greenwich Meridian so that we retain the North and
> > South Poles. Now the x-axis
> > is the Greenwich longitude from the North Pole to the South Pole and
> > the y-axis is the Artic Semicircle.
> > So the plotting of y= x in Elliptic Geometry ends up being the 90
> > degree West longitude line.
> >
>
> No it does not. It is not the 90 degree West Longitude. It appears to
> be a sinusoidal
> curve for it does intersect at
> 90 degree, 90 degree.
>
> I point I was trying to make is that a function varies in different
> geometries.
>

I went outside to do some lawnmowing and in the middle of that
realized that the best y-axis
is not a Arctic Circle near the pole, as what we would imagine having
been weened all our lives
on a Cartesian x and y axis. Instead, imagine the whole entire
Greenwich longitude that goes
360 around Earth. Now take the 180 as the x-axis and the remaining 180
as the y-axis. Sort of
like the x and y axis as a large circle. And now all the points on
Elliptic Geometry within that
hemisphere.

And so a function of y = x would be the 90 degree West longitude line.

The reason I tried sticking the y-axis as a tiny Arctic Circle
latitude was because working on this
in late 2007 I wanted multiplication on AP-adics to be the area of a
triangle on a sphere surface.
Hard to picture that what seems to be 2 lines on a sphere can form a
triangle, but apparently that
is true. I had always thought that it requires three line segments to
form a triangle whether in Euclidean
or in Riemannian geometry, but maybe I was mistaken.

So to multiply say 999...9999 x 9999...9999 in Riemannian geometry
would be the area of the
hemisphere minus the polar minuscule leftout. And then in AP-adics
this multiplication

of 50000.....00000 x 9999....999999 would be the area of the northern
hemisphere bounded by the
equator and the Greenwich longitude and whose final answer is
49999....999995 or 1/2 of a hemisphere.

So it seems to all work out with having the Greenwich longitude be the
x and the y axis.

P.S. Now I do not ever remember in my studies of Elliptic (Riemannian
geometry) that says that
triangles can be of two or three line segments. I think the term used
in Riemannian geometry is
that of "lune"

P.P.S. Now as for Hyperbolic geometry of a pseudosphere surface, can
we also have a Greenwich type
longitude? I think it is do-able. Where we have a trumpet shape and we
cut it into half and call it a
hemitrumpet. And the y = x function would be a hyperbola down the
middle. But in multiplication
such as -5000...0000 x -999....99999 I cannot see how that is going to
be 1/2 the area of a hemitrumpet?
Hyperbolic geometry is not symmetrical as Elliptic. So alot more work
has to be done with them.

[David R Tribble]

ju...@diegidio.name wrote:
>> I find your system very interesting. I hope I'll understand it
>> someday!
>

Archimedes Plutonium wrote:
> Most people already understand it, only they do not use it.

It would help a great deal if you could explain your AP-adic
numbers can be used to solve some simple existing problems,
perhaps in a more direct or efficient manner than using normal
arithmetic.

(1) For instance, suppose you have a square with sides of
length L = 100...000. What is the area of the square?

Using standard geometry, we would expect the area to
be A = L * L, which is 100...000 * 100...000, which is what?
Is A = 100...000, and if so, is this the same as L?
Or is A some other value?

(2) The second question is what is the length of the diagonal
D of the square?

Standard geometry gives us D^2 = L^2 + L^2, or
D = sqrt(L^2 + L^2), which is sqrt(100...000^2 + 100...000^2).
How do we calculate D?

[plutonium....@gmail.com]

David R Tribble wrote:
> ju...@diegidio.name wrote:
> >> I find your system very interesting. I hope I'll understand it
> >> someday!
> >
>
> Archimedes Plutonium wrote:
> > Most people already understand it, only they do not use it.
>
> It would help a great deal if you could explain your AP-adic
> numbers can be used to solve some simple existing problems,
> perhaps in a more direct or efficient manner than using normal
> arithmetic.
>
> (1) For instance, suppose you have a square with sides of
> length L = 100...000. What is the area of the square?
>

Last time I looked, it was impossible to have a square in Elliptic
geometry

But we can have area of Lune or Digon.

Area of Digon 9999....999999 x 9999....99999 is almost the entire
hemisphere lacking the
one metric away from North and South Poles

99 x 99 =
999 x 999 =
9999 x9999 =
99999 x 99999 =

I suspect this Cauchy Convergence is 99999.....0001

In AP-adics Elliptic the multiplication often turns out a smaller
number

1000....00000 is 10% of 180 degrees is 18 degrees. and 1000....0000 x
1000...0000 =
1000....0000 the same number.

Do we not have repeat numbers when we multiply say 2pi by 4 which
again is the
same as 2pi in spherical geometry.

Novices will think that 1000...00000 is one unit larger than
9999...9999 but 9999....9999
is the largest integer in AP-adics and the successor of 9999...9999 is
the imaginary number
pi as the South Pole. The number 10000....00000 is 10 percent of the
way to the number
9999....99999

> Using standard geometry, we would expect the area to
> be A = L * L, which is 100...000 * 100...000, which is what?
> Is A = 100...000, and if so, is this the same as L?
> Or is A some other value?
>

If my memory holds up, you can have parallelograms and rectangles in
Elliptic geometry but no squares.

[plutonium....@gmail.com]

Strange how the AP-adics were started to be invented in the early
1990s and a feature of them would
be to revamp the Reals as Euclidean geometry. Strange that a digital
camera encapsulates the main
features of what Reals possess as the intrinsic numbers forming
Euclidean Plane Geometry and what
the Coordinate System on Reals should be.

Unlike the Cartesian Coordinate System for the Reals where the
negative numbers are segregated
away from positives. In AP-Coordinate system the negative Reals are
sandwiched inbetween
the positives in a checkerboard pattern. Now is that the same as a
negative in photography
versus the positive in photography? Is that the same setup in
photography where the negative
is inbetween positive?

And the feature of digital cameras of course had to wait until recent
times but was it true for all
cameras that they were in fact digital when we go down to the
chemistry involved of silver atoms
forming the image. Likewise, for the Reals, that you eventually have
tiny holes and that it is impossible
to have infinitely-small-continuity.

So in our modern day lives, a digital camera is a living experiment of
a piece of scientific equipment
that delivers us the Coordinate System on Reals.

You know how we do a physics experiment to do the Double Slit or the
Coulomb force or the Faraday
electric motor. Well, everytime someone takes a digital camera and
makes a photograph is doing a
mathematics experiment and mapping a function in Euclidean plane
geometry where the coordinate
system is far from anything that Descartes imagined.

Everytime a person does a digital photograph is doing a mathematics
plotting of Reals in Euclidean
plane geometry. Where the negative Reals are checkerboarded between
positive Reals
and where there is no "absolute continuity" but rather tiny gaps. Gaps
so small, that we perceive
continuity.

So that continuity, throughout the history of mathematics was a
pursuit of a illusion or a imagination
gone berserk. Continuity does not exist in physics, and never existed
in physics, yet many rumdummies
in mathematics will spend their entire career in math dreaming about
continuity.

Funny, how a piece of equipment in 2008, the digital camera, knows
more and has more
experience with the Reals and Euclidean plane geometry, than does
every college professor of
mathematics knows about the Reals. Just as every Double Slit Apparatus
knew more about
Quantum Mechanics than the physicists when the Double Slit was
invented.

[plutonium....@gmail.com]

The AP-adic 1000....00000 was brought up in a question and as far as I
know

1000....00000 x 10000....00000 = 1000....00000

So does AP-adics Elliptic have two multiplicative identities of
10000....0000 and the old familar
0000....000001 ?

But it does not stop there, for what about the Reals? Of course we
have the old familar 1.00...0000
but we also have the smallest nonzero Real as a multiplicative
identity of 0.000...00001

Been a very long time since I did Galois algebra, but somewhere in the
hierarchy is a
unique multiplicative identity.

Obviously that is now under doubt and question.