Re: Provably unprovable eliminates incompleteness (cardinality is incorrect)

82 views
Skip to first unread message

peteolcott

unread,
Sep 11, 2019, 1:05:56 PM9/11/19
to
On 9/11/2019 2:31 AM, Reinhardt Behm wrote:
> On 9/10/19 11:38 PM, peteolcott wrote:
>> The next real number after 3.0 is the geometric point on the number
>> line that is immediately adjacent to 3.0 on its right side. This geometric
>> point is an infinitesimally larger than 3.0: encoded as the first point in
>> the interval: (3,4]
>
> And between 3.0 and your "next" number (xnext) to the right is another real number: (3.0+xnext) / 2.
>

I specified a whole Infinitesimal number system:
Real_Part[Infinitesimal_Part] where the Infinitesimal_Part is the number
of geometric points offset from the real part.

0.0[1,∞] specifies the entire set of geometric points with a value
greater than zero on the number line which self-evidently corresponds
to the entire set of positive reals.

Notice that this entire set is countable using the set of positive integers.

Copyright 2019 Pete Olcott

--
Copyright 2019 Pete Olcott All rights reserved

"Great spirits have always encountered violent
opposition from mediocre minds." Albert Einstein

Arnaud Fournet

unread,
Sep 11, 2019, 8:25:44 PM9/11/19
to
Can you, please, address the issue of metaphor proving all your castles of pseudo-theoretical garbage wrong?

peteolcott

unread,
Sep 13, 2019, 2:03:08 PM9/13/19
to
On 9/13/2019 12:14 PM, André G. Isaak wrote:
> On 2019-09-13 10:36 a.m., peteolcott wrote:
>> On 9/13/2019 10:41 AM, André G. Isaak wrote:
>>> On 2019-09-13 9:09 a.m., peteolcott wrote:
>>>> On 9/13/2019 12:16 AM, André G. Isaak wrote:
>>>>> On 2019-09-12 11:10 p.m., peteolcott wrote:
>>>>>> On 9/12/2019 11:04 AM, Fred wrote:
>>>>>>> On 12/09/2019 16:49, peteolcott wrote:
>>>>>>>> On 9/12/2019 10:05 AM, André G. Isaak wrote:
>>>>>>>
>>>>>>>
>>>>>>>>> Assuming that X is the length of [3.0, 4.0) and y is the length of (3.0. 4.0), then what is
>>>>>>>> (x-y)/2? // singe geometric points are indivisible.
>>>>>>>>
>>>>>>>> What is 1/(x-y)?  // I am not sure. I would have to think about it.
>>>>>>>>
>>>>>>>> This is basically 1.0 divided by infinitesimal. This may be disallowed too
>>>>>>>> because it seems analogous to dividing by zero.
>>>>>>>
>>>>>>> Oh dear.  Your first post to sci.logic in this thread began "I specified a whole Infinitesimal number system:"  But you didn't "specify" to such a degree that you can give an account of division?
>>>>>>>
>>>>>>
>>>>>> Account for this division:  x = 1.0 / 0.0
>>>>>> The same thing goes for dividing a single indivisible point.
>>>>>
>>>>> So are you claiming that this indivisible point is equal to zero?
>>>>
>>>> NOT AT ALL. Where the Hell did you get the idea that infinitesimal = 0.0 ?
>>>
>>> Because you claimed that dividing by an infinitesimal would be analogous to dividing by zero. If your infinitesimal isn't equal to zero, then why would dividing by it be analogous to dividing by zero?
>>>
>>
>> If you identify an single geometric point on a number line you
>> already know that it is indivisible.
>
> I have no idea what that is supposed to mean. 4.0 would be a single geometric point on a number line and it is divisible. 10.0 would be a different single point on a number line and it is divisible.
>
>>>
>>>>> If so, then [3.0, 4.0) and (3.0. 4.0) will have the *exact* same length. If your indivisible point is not equal to zero, then you should be able to tell us exactly how many of these indivisible points are present in each of the above intervals.
>>>
>>> So if you're going to ignore the above, let's try asking it in a different way. You claim numbers have a 'real' part and an 'infinitesimal part' where you express the infinitesimal part in brackets. So 1.0[1] is just slightly larger than 1.0. So
>>> consider the equation
>>>
>>> 1.0[x] = 2.0[0]
>>>
>>> Solve for x.
>>>
>>> André
>>>
>>>
>>
>> There is a bijection between all of the geometric points on a number line and all of the numbers on a numbers line.
>
> What is the bijection?
>
> If you can actually express a bijection between your infinitesimals and the numbers on the number line you should be able to eliminate the real part from your theory altogether and just talk about the infinitesimal portion.
>
> So how does that work?
>
> André
>

Because infinity is a process rather than a number it does not work that way.

It is obvious that all of the points on a number line correspond to all of the numbers
and that all of the numbers correspond to all of the points, in this sense there is a
bijection between numbers and points exists.

Since infinitesimal numbers can be proven to exist on the basis of the
difference in length of these two intervals: (0.0, 1.0] - (0.0. 1.0)
creating a notational convention to uniquely identify infinitesimal
numbers is logically justified.

(0.0, ∞] specifies all of the points corresponding to all of the positive numbers.

>> There is no bijection between all of the numbers on a number line and the real numbers on a number line.
>> Your RHS is a real and the LHS is an infinitesimal there is no bijection for this.

peteolcott

unread,
Sep 14, 2019, 1:55:24 AM9/14/19
to
On 9/14/2019 12:53 AM, peteolcott wrote:
> On 9/13/2019 8:30 PM, Ben Bacarisse wrote:
>> peteolcott <Here@Home> writes:
>>
>>> On 9/11/2019 7:42 PM, Ben Bacarisse wrote:
>>>> peteolcott <Here@Home> writes:
>>>> <cut>
>>>>>>> On 9/11/2019 2:31 AM, Reinhardt Behm wrote:
>>>>>>>> On 9/10/19 11:38 PM, peteolcott wrote:
>>>>>>>>> The next real number after 3.0 is the geometric point on the number
>>>>>>>>> line that is immediately adjacent to 3.0 on its right side. This geometric
>>>>>>>>> point is an infinitesimally larger than 3.0: encoded as the first point in
>>>>>>>>> the interval: (3,4]
>>>>
>>>> There is no next real number after 3.0.  There is not even a next rational
>>>> number after 3.0, and the rationals /are/ countable!  I.e. you don't
>>>> need there to be a successor function on points that respects the
>>>> usual ordering of points to get a countable set between 3 and 4.  As it
>>>> is, you open yourself up to the obvious problem:
>>>
>>> The line segment [3.0, 4.0) is exactly one geometric point longer than
>>> (3.0. 4.0).
>>
>> The line segment [3, 4) contains exactly one point more than the segment
>> (3, 4).  It is not "longer".  Do you know any measure theory?
>>
>> It may be PO-longer but (a) will you be able to say what PO-longer
>> really is (without waffling), and (b) will anyone care?
>>
>>> There is a geometric point immediately adjacent to 3.0 on the number
>>> line.
>>
>> Translation: there is PO-geometric PO-point immediately PO-adjacent to 3.0
>> on the PO-number line.  I am sure there is.  Does anyone care?
>>
>>> This geometric point does correspond to a number because it is on the number line.
>>>
>>> Now I have to correct my prior reasoning. All of the geometric points on
>>> the number line correspond to all of the numbers that exist. Some of these
>>> are not real numbers.
>>>
>>> Since we can count all of these numbers with integers using the infinitesimal
>>> number system we have proven that the set of real numbers is not larger
>>> than the set of integers.
>>>
>>> Real_Part[Infinitesimal_Offset]
>>>
>>> 0.0[1 to ∞] forms a bijection between the positive integers and all of
>>> the positive numbers through all of the positive points on the number line.
>>
>> After initially appearing to want to answer questions about these
>> PO-infinitesimals, you seem to have given up.  I spent some time on a
>> reply to your first round of answers, but you seem to a abandoned that
>> sub-thread.  I won't make the mistake of spending time on a reply in
>> future!
>>
>
> YOU LIED !!!
> YOU LIED !!!
> YOU LIED !!!
> YOU LIED !!!
> YOU LIED !!!
> YOU LIED !!!
> YOU LIED !!!
> YOU LIED !!!
> YOU LIED !!!
> YOU LIED !!!
> YOU LIED !!!
> YOU LIED !!!
> YOU LIED !!!
>
> On 9/14/2019 12:51 AM, peteolcott wrote:> On 9/12/2019 8:00 PM, Ben Bacarisse wrote:
> >> No.  The common notational convention used for intervals shows that
> >> adjacent points do not exist.  While [0, 1] has a least member, (0, 1]
> >> does not.  You can remove the first number in [0, 1] to get (0, 1] but
> >> you can't remove the first and second.
> >>
> >
> >
> > https://en.wikipedia.org/wiki/Straw_man
> > Intentional deceptive straw_man WHY LIE?  Does lying give you kicks?
> >
> > IT IS CLEAR THAT I HAVE BEEN ALWAYS USING REAL ENDPOINTS.
> >
> > YOUR SWITCH TO INTEGERS IS PRETTY DAMN STUPID.
> > DID YOU THINK YOU WOULD GET AWAY WITH THAT?
> >
> > The first point in this interval: (0.0, 1.0] very obviously
> > comes immediately after the first point in this interval: [0.0, 1.0].

Arnaud Fournet

unread,
Sep 14, 2019, 2:15:24 AM9/14/19
to
This post of yours contains nothing new, psycho-shitter.

Franz Gnaedinger

unread,
Sep 14, 2019, 3:09:24 AM9/14/19
to
On Wednesday, September 11, 2019 at 7:05:56 PM UTC+2, peteolcott wrote:
>
> Copyright 2019 Pete Olcott
> Copyright 2019 Pete Olcott All rights reserved
>
> "Great spirits have always encountered violent
> opposition from mediocre minds." Albert Einstein


Hyperkooks take over, dominate and finally ruin a forum by
starting up to five threads a day (sci.logic, sci.math, humanities.
lit.authors.shakespeare and others). I develop a counter-strategy
against their HIV strategem. A member of sci.logic accused PO
of having ruined several fora "singlehandedly."

(Allgod)

Meanwhile Peter Olcott officially announced that he is God, repeatedly
and in all earnest. Being God, and the only one, he can discard proven
proven theorems of mathematical logic (Goedel, Turing ) and suffocate
sci.logic and sci.lang and other fora by starting ever more parallel threads.

(lesson on logic, fatal deficit of academe)

I see the main problem in academe that has no clear idea of logic, or rather
a one-sided one, regarding mathematical logic as logic per se. Mathematical
logic is the logic of building and maintaining based on the formula a = a
while there is a wider logic formulated by Goethe: All is equal, all unequal ...,
known to artists of all times.

Goedel is very hard to understand for laymen when you consider mathematical
logic the only real logic, but most easy when you have a look at both sides.
Goedel proved that mathematics can't really and completely be separated from
general logic and the principle of equal unequal, it can only be secured
from case to case, for example divisions by zero are forbidden. Why? these
divisions yield infinite, which is equal unequal in itself. If you restrict logic
to mathematical logic you encounter paradoxa, which are quite natural
in the real world.

The problem is academe. Universities are not really universal. Allgod tries
to solve the problem by cramming the realm of wider logic (that includes
for example language) into mathematical logic, hoping he will thus regain
totality and completeness - absolute and complete and total being his
mantra words - and does it for the price of his career and sanity.

The logic of equal unequal blossoms in language. Allgod can't have that,
He tries to force language into the logic of a = a with his "mathematics
of the meaning of words" that led him nowhere. He castrates language
in the name of mathematical logic, and mathematical logic by dismissing
proven theorems.

(on the liar paradox)

A Cretan says all Cretans are liars. He is right. Psychologists found that
we are lying many times a day, and in different ways. We humans are liars,
Cretans are humans, ergo they are liars. QED. The famous liar paradox arises
when the natural logic of equal unequal is reduced to the mathematical logic
of a = a. A liar is a liar, alaways lying, only ever lying. But such a person
does not exist in the real world, on the contrary, a professional liar cares
to tell the truth as often as ever possible in order to gain the confidence
of a potential victim.

(rigor vs rigid denial)

Allgod tries to reduce natural logic to mathematical logic, however,
he can't escape the equal unequal, it haunts him in the form of
proven = proven = not proven. He replaces Goedel's rigor with
his naive but rigid denial. Every advice to come down from his trip
and write a modest but useful program that may then be extended
was in vain. He is a satellite that flies too low, destined to burn out
in the atmosphere. All warning failed.

(can sunshine be sweet and chubby?

Yes, if a mother calls her toddler 'my sunshine, my sweet little chubby
sunshine'. Language is flexible, the meaning of words can't be reduced
to 'semantic atoms', and, what Pater Rupert Ruhstaller OSB told me
in a private lesson: speakers find a way around any rule.

Ambiguity or better flexibility is the genius of natural language
that escapes from the cage of any formal system.

(Einstein and Goedel)

Einstein and Goedel were good friends who held each other's work
in high esteem. What would Einstein say about a naive Goedel denier?

(by the way)

I defend sci.lang also against those who can only argue on meta-levels
and drop verdicts from above instead of leading a topic discussion.
Kooks are also found on the academic side of the fence. ACB suggested
that proven theorems of mathematics can be discarded (referring to
Andrew Wiles without knowing the story en détail). Allgod thanked him
for confirming the Truth. Blasphemy (the claim of being God) and
pseudo-logic are correlated. Neither one took back his claim or
suggestion.

(triangle of language, briefest summary of half a century of research)

Word language can be seen as a triangle whose corners are life with
needs and wishes / mathematics as logic of building and maintaining
based on a = a / and art as human measure in a technical world,
based on Goethe's world formula and ever turning key 'All is equal,
all unequal ...', a formula known to artists of all times.

(book of nature, divine library)

Famous dictum by Galileo Galilei: The book of nature is written
in the language of mathematics ... Well, God may understand all
of nature in mathematical terms, while we humans deciphered only
the first lines on the first page in the first volume on the first shelf
in the first hall of the divine library.

Mścisław Wojna-Bojewski

unread,
Sep 14, 2019, 4:16:36 AM9/14/19
to
- Cave art gives us no clue to how the people of Lascaux or Altamira
spoke.

- The pictographic symbols in Göbekli Tepe give us no clue to how the
people of Göbekli Tepe spoke.

- Anyone stating the opposite must make available some evidence that
can be scrutinized by other scholars, and the clues this person claims
to have found, must be observable and recognizable by other people.

- Moreover, the discoverer must be able to explain, in commonsense
logical terms, how he or she has arrived at his results. His chain of
conclusions must be "nachvollzogen" by other scholars.

- You have not been able to present us with either evidence or
conclusions. Instead, you have repeatedly attacked and poured scorn
over people who have demanded such things.

- On the other hand, PIE is based on solid evidence and its proponents
have left us clear instructions, evidence, and reasonings to be
"nachvollzogen".

- Their conclusions are based on a comprehensive understanding and
comparison of the languages involved.

- On the other hand, you are demonstrably ignorant of several branches
of Indo-European. You have admitted that you know not a single Slavic
language.You actually pour scorn and disdain over people who have
learnt languages unknown to you.



peteolcott

unread,
Sep 14, 2019, 12:36:29 PM9/14/19
to
Don't you get sick of the smell of your big farts?

Arnaud Fournet

unread,
Sep 14, 2019, 6:46:21 PM9/14/19
to
Once again talking about yourself, psycho-shitter.

peteolcott

unread,
Sep 14, 2019, 10:38:16 PM9/14/19
to
On 9/14/2019 8:54 PM, Ben Bacarisse wrote:
> peteolcott <Here@Home> writes:
>
>> On 9/14/2019 7:32 PM, peteolcott wrote:
>>> On 9/14/2019 7:26 PM, Ben Bacarisse wrote:
>>>> peteolcott <Here@Home> writes:
>>>> <cut>
>>>>> My ONLY point is that Cantor was wrong and all infinities are exactly the
>>>>> same "size" in that infinity doesn't actually have a size because it is
>>>>> not a number it is the process of {more}:
>>>>
>>>> Which only makes you wrong.  Specifically about what you thought Cantor
>>>> was saying.
>>>>
>>>> Cantor's theorem states that, for every set S
>>>>
>>>>    |S| < |P(S)|
>>>>
>>>> where P(S) denotes the power set of S and
>>>>
>>>>    |X| < |Y|
>>>>
>>>> means that there is no surjective function from X to Y.
>>>>
>>>> In order to leverage people's intuition, it makes sense to describe |X|
>>>> as the size of X, but it's the existence of functions between sets that
>>>> actually matters.
>>>>
>>>> There is a bijection between R and P(N) so |R| = |P(N)| and hence |N| < |R|.
>>>>
>>>
>>> It does not matter what he said as long as the set of all numbers is countable
>>> with integers then the whole concept of
>>
>> infinite sets with differing cardinality
>>
>>> is refuted.
>
> Provided "the set of all numbers" includes R as a subset, then what
> Cantor said does matter, because he proved that your "as long as..." is
> a counter factual.
>

If the set of ALL numbers can be counted using integers then
there is no such thing as infinities with differing cardinality
and whatever anyone ever said to the contrary is fully refuted
because a bijection between integers and numbers has been shown.

peteolcott

unread,
Sep 14, 2019, 10:44:49 PM9/14/19
to
As it turns out I am (no matter how crazy it sounds) I am the
judge of all. I may make Christ's words perfectly literal
thus you will be judged by your own words, big farty party.

Peter T. Daniels

unread,
Sep 15, 2019, 9:05:56 AM9/15/19
to
On Saturday, September 14, 2019 at 10:38:16 PM UTC-4, peteolcott wrote:

> If the set of ALL numbers can be counted using integers then

But they can't, because some of those numbers are irrational, cannot be
fully specified, so can't be counted.

Now do you see why you don't belong in sci.lang?

peteolcott

unread,
Sep 15, 2019, 11:48:57 AM9/15/19
to
The set of real numbers is represented on the number line as geometric
points and the set of adjacent geometric points can be counted using
the infinitesimal number system.

Arnaud Fournet

unread,
Sep 15, 2019, 1:33:01 PM9/15/19
to
you're a total shithead.
Who's gonna take you in earnest, psycho-shitter?

peteolcott

unread,
Sep 16, 2019, 10:31:26 AM9/16/19
to
When you meet me at the gates of the Kingdom of Heaven and you
find that I am the gatekeeper things might get much more real.
I could forgive your blasphemy and say welcome in, or I could say
depart from me you evil doer.

One thing that woefully fallible humans can't seem to get past
is that totally unbelievable does not actually ever equate to false.
The key thing the prevents the correct analysis of this is human pride.

Arnaud Fournet

unread,
Sep 16, 2019, 1:57:38 PM9/16/19
to
Anyway, you're not Heaven's gatekeeper, psycho-shitter. No doubt.

peteolcott

unread,
Sep 16, 2019, 3:57:49 PM9/16/19
to
That woefully fallible humans have no doubt is not at all the same thing
as logically justified complete certainty. The most horrendous human
error (with the worst detrimental consequences) is that humans have no doubt
and are none-the-less incorrect.

People asserting they belong to a certain religious group kill many innocent
civilians having no doubt that this is the will of God.

Arnaud Fournet

unread,
Sep 17, 2019, 2:47:10 AM9/17/19
to
Anyway, your sin is that you believe you can reconfigure humanity into 0/1 bits that function logically. Does not make any sense.

>
> People asserting they belong to a certain religious group kill many innocent
> civilians having no doubt that this is the will of God.

I hope that the crimes of Islamists do not prove you are God (or Allah)...
easy, dude, easy...

peteolcott

unread,
Sep 17, 2019, 12:33:30 PM9/17/19
to
I am not saying this. My [ What's in it for me ] adaptation of Christ's Gospel
will cause humanity to become benevolent because they will finally understand
that selflessness maximizes their own peace and joy. If everyone in the world
is looking out for your own best self-interests, then you don't have to.

>>
>> People asserting they belong to a certain religious group kill many innocent
>> civilians having no doubt that this is the will of God.
>
> I hope that the crimes of Islamists do not prove you are God (or Allah)...
> easy, dude, easy...
>

They are Satanists:
https://en.wikipedia.org/wiki/Shaitan
https://en.wikipedia.org/wiki/Iblis

They claim that they are Islamists yet are unaware that they lie even
to themselves. I made the laws of God much simpler making it much more
difficult for people to be lead astray:

Love one another with as much empathy as possible.

This single law will be applied to everyone equally:

Matthew 7:16 (KJV)
16 Ye shall know them by their fruits.
20 Wherefore by their fruits ye shall know them.

Benevolence versus Malevolence, beneficial versus harmful.

Arnaud Fournet

unread,
Sep 17, 2019, 4:31:37 PM9/17/19
to
Looking at your posts does not bode anything good, psycho-shitter...

peteolcott

unread,
Sep 17, 2019, 5:48:55 PM9/17/19
to
To the tune of When Irish Eyes Are Smiling... (Written by Chauncey Olcott)
When Biased Minds are Lying...

Encouraging humanity focus on benevolence IS BY DEFINITION A GOOD THING.
That you say it is not is an indication of dishonesty.
Reply all
Reply to author
Forward
0 new messages