God is the greatest mathematician.
V.Gopal
Euclid, Newton, Einstein and for that matter every individual who
contributed to the advancement of human knowledge was a human being just
like any body - you or me. Mathematics has advanced on the basis of logic
of sense of sight - we can find nothing wrong in mathematics as long as
we try to understand it using the logic of sense of sight - judge the
truth and falsity of each mathematical proposition by checking whether
mind and eye reach a total agreement or not. We always find that whatever
we have accepted as true in mathematics, our mind and eyes always reached
total agreement. The act of making our mind and eye reach total agreement
does not always constitute thinking, although in some cases it does.
That part of mathematical logic, which cannot be understood by using the
logic of sense of sight is revealed by geometry. Geometry contains
certain knowledge that is incommunicable. If one tries to expalin it
and in the process if many of our conventional ideas are proved wrong
it is not going to have any effect on progress in technology. This
way nobody brings any disgrace to any individual living or dead. No body
can become the greatest mathematician; only God is the greatest
mathematician and any difference between one man to another man is
negligible, even if you compare Newton and Einstein with Bob or Knox.
Lovecraftesque
> No body can become the greatest mathematician; only God is the
> greatest mathematician
That's fair enough, assuming that God exists - a big,
unprovable if.
Uncle Al
>
> I believe, and everybody with capacity to think must realize that Zeno,
> Euclid, Newton, Einstein and for that matter every individual who
> contributed to the advancement of human knowledge was a human being just
> like any body - you or me.
You are a goddamned spewing imbecile with psychotic delusions of
competence.
http://www.mazepath.com/uncleal/eotvos.htm
Do something naughty to physics.
http://www.mazepath.com/uncleal/eotvos.pdf
The short form.
Get off your lazy leaden ass and provide literature citations to
justify your outragoeus public stupidities.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
"Quis custodiet ipsos custodes?" The Net!
Superluminal
I have never met God or seen any of his work, do you have any
references or examples? What are his academic qualifications? Not a
very imformative post just a bunch of speculation without proof.
Arfur Dogfrey
God the greatest mathematician?? Come on! He had only one publication-
that was 2000 years ago. It wasn't in a peer reviewed journal. It didn't
have any footnotes and the basic mathematical result in it was that pi = 3.
Arf!
Arfur
mathedman
wrote:
>No body
>can become the greatest mathematician; only God is the greatest
>mathematician and any difference between one man to another man is
>negligible, even if you compare Newton and Einstein with Bob or Knox.
Even if there is a god, what evidence do you have that she was a
mathematician??
Gregory L. Hansen
To be fair, that was a compilation of His publications with editorial
selection. 1500 pages for posterity.
>have any footnotes and the basic mathematical result in it was that pi = 3.
If you have a diameter of 10, what should be quoted for the circumference?
C = pi*d = (3.1415926...)*10 = 30.
10 has one sig-fig, so the answer can only have one sig-fig no matter how
many digits you write out for pi.
See http://www.yfiles.com/pi.html for another opinion.
--
"A nice adaptation of conditions will make almost any hypothesis agree
with the phenomena. This will please the imagination but does not advance
our knowledge." -- J. Black, 1803.
diego
A mathematician is a man who makes mathematics
God is not a man so it is not a mathematician.
Tapio Hurme
"diego" <d...@diego.com> wrote in message
news:arearc$3tg$1...@nntp-m01.news.aol.com...
> HI,
> A mathematician is a man who makes mathematics
> God is not a man so it is not a mathematician.
If "not a man" makes mathematics, then who is that?
Tapio
diego
god is it UFO ?
Gregory L. Hansen
What if a cat managed to make some good mathematics, pawing at the
keyboard to type it up in LaTeX?
Tapio Hurme
> i dont know, it is not an mathematical object.
>
> god is it UFO ?
where is the mighty logic?
Tapio
>
diego
Robert Kolker
V.Gopal wrote:
> I believe, and everybody with capacity to think must realize that Zeno,
> can become the greatest mathematician; only God is the greatest
> mathematician
This is complete bullshit based on wishful thinking and not one fact. I
think you are seriously deranged.
Tell me do you talk to God? (and here is the important question). Does
God talk to you? Have you heard Her voice? Does She sound like your mamma?
Bob Kolker
Robert Kolker
Arfur Dogfrey wrote:
>
> God the greatest mathematician?? Come on! He had only one publication-
> that was 2000 years ago. It wasn't in a peer reviewed journal. It didn't
> have any footnotes and the basic mathematical result in it was that pi = 3.
And what about the Trinity. The would imply that 3 = 1 or 2 = 0, so it
can only work in mod 2 arithmetic.
Bob Kolker
Robert Kolker
Then you say Emi Noether and Julia Robinson were not a mathematicians?
Bob Kolker
Robert Kolker
Gregory L. Hansen wrote:
> What if a cat managed to make some good mathematics, pawing at the
> keyboard to type it up in LaTeX?
Unless the cat intended what he wrote, it would not be mathematics. It
would be accidental pawing at a keyboard.
Did you know that if a million monkeys type at a million keyboards for a
million years they could not come up with a good X-File script.
Bob Kolker
>
Bob Pease
"Lovecraftesque" <Lovecra...@yahoo.com> wrote in message
news:pan.2002.11.19.14...@yahoo.com...
To use a legitimate "Ad hominem", look at the other posts by this poster.
Essentially, he has changed the question to the Snerdish tautology.
"Nobody can be the greatest anything, because you can't get to be equal to
God."
Reminds mo of Sister Mary Paphinootia who was teaching the "Honors" kids at
Catholic High school on Denver.
I was teaching geometry, and Sister suggested that I should post the message
"God is the Great Geometer" on the Bulletin board.
I had to bite my lip at suggesting that maybe
"Geometry is the Great God" or "God is the Great Penguin"
Would be appropriate.
The kids would have liked
"Kill Holy Family!!" better, ( as a football cheer only, of course)
RJ Pease
---
Outgoing mail is certified Virus Free.
Checked by AVG anti-virus system (http://www.grisoft.com).
Version: 6.0.419 / Virus Database: 235 - Release Date: 11/13/02
Bob Pease
> HI,
> A mathematician is a man who makes mathematics
> God is not a man so it is not a mathematician.
>
Substitute "Mr. Data" for "God" and watch the argument collapse !!
Bob Pease
> what is the definition of god ?
>
>
ah, but That's the rub!!
Billy S.
Thad Coons
"Arfur Dogfrey" <dogs...@dog.com> wrote in message
news:b8a07d3f.0211...@posting.google.com...
The earlier work, the one you're standing on, has plenty of footnotes, but
the text has been badly corrupted by entropy. I think you're referring to
the dog-eared copy of a a copy of the appendix and commentary written for
and by the kindergarten class.
Thad Coons
Thad Coons
"Superluminal" <wildcat...@yahoo.com> wrote in message
news:8b70419e.02111...@posting.google.com...
The Book of Nature is his only _scientific_ publication. Based on that work
alone, I'd say his qualifications are pretty impressive. Not an easy read,
either.
Thad Coons
Douglas Eagleson
"V.Gopal" wrote:
You need to consider the abstract knowledge and the usage
as a form of intelligence. And comparing the creator to
a knowledge is not allowed.
But, consider the relationship of existing in harmony with the use of
abstraction in the sensory field. And then the concept of the spirit
of your being is distinct from the usage of abstraction.
So, maintian the distinction, because it is only an allusion as
a knowledge, that you wrote.
Douglas Eagleson
Gaithersburg, MD USA
Jon Cohen
> I have never met God or seen any of his work, do you have any
> references or examples? What are his academic qualifications? Not a
> very imformative post just a bunch of speculation without proof.
I grabbed this off the net ages ago, can't remember where:
Top 10 reasons why God has a Ph.D., but did not get tenure:
1) He had only one major publication.
2) It was in Hebrew.
3) It had no references.
4) It wasn't in a referred journal.
5) It may be true that He created the world, but what has He done since?
6) The scientific community has had a hard time replicating His results.
7) He never applied to the ethics board for permission to use human
subjects.
8) He expelled His first two students for learning.
9) His office hours were infrequent and usually held on a mountain top.
10) Although there were only 10 requirements, most students failed his
tests.
Jon
Robert Kolker
Jon Cohen wrote:
> 10) Although there were only 10 requirements, most students failed his
> tests.
>
613.
Bob Kolker
Superluminal
The book of nature was written by something or someone unknown to us.
If you bible huggers will get your wining, superstious, prayer
spouting, collection grabin asses out of the way, we will have the
real answer for you in a few years.
Spaceman
>Unless the cat intended what he wrote, it would not be mathematics. It
>would be accidental pawing at a keyboard.
Horses can count and type.
It's just we have not made big enough key boards for them.
:)
>Did you know that if a million monkeys type at a million keyboards for a
>million years they could not come up with a good X-File script.
>
But according to "evolution theory" and "known facts about x-files scripts"
Some of them (the typing monkies) did make many good scripts.
:)
James M Driscoll Jr
Spaceman
http://www.realspaceman.com
Rain
writes
>what is the definition of god ?
Madness.
diego
you are right, women men, cat and monkey can make mathematics. (and can
write in latex also)
Nikita
> ... No body
> can become the greatest mathematician; only God is the greatest
> mathematician and any difference between one man to another man is
> negligible, even if you compare Newton and Einstein with Bob or Knox..
What precisely do you suggest? We don't want to be unthinking robots
do we?
Part of what makes us human is our great desire and ability to think
and to reason, to ignore this would be to ignore what makes us human.
Nikita
> ...That's fair enough, assuming that God exists - a big,
> unprovable if.
Yes, we cannot prove it, but we can ponder about it. We humans are
gifted(?) with limited intelligence(three digited i.q.). Many facts
that are today widely known and taken for granted were once unknown
and out of reach. For instance, someone generations ago could have
claimed that planets do not exist outside of our solar system,
justifying this by saying (correctly during their time) that such a
statement could not be proven. But we today know that planets do
indeed exist outside of our solar system. Claiming in the past that
they didn't exist, just because the proof was out of our reach, didn't
make the existence of these planets false. Likewise, claiming today
that God does not exist simply because proof of his existence is
beyond us, doesn't actually disprove God. I think that skepticism
about God can be healthy in that it opens the door to our
ethical/spiritual department. If one is totally
uninterested/unrelated God, then one would not even talk/think about
it.
George Dance
(Premise A)
> I believe, and everybody with capacity to think must realize that Zeno,
> Euclid, Newton, Einstein and for that matter every individual who
> contributed to the advancement of human knowledge was a human being just
> like any body - you or me.
snip
> No body
> can become the greatest mathematician; only God is the greatest
> mathematician and any difference between one man to another man is
> negligible, even if you compare Newton and Einstein with Bob or Knox.
Is God the greatest mathematician?
1. By Premise A, every individual who contributed to the advancement
of human knowledge was a human being.
2. God is not a human being.
3. God has not contributed to the advancement of human knowledge. (1,2
MT)
4. The greatest mathematician must necessarily be a great
mathematician.
5. All great mathematicians have contributed to the advancement of
human knowledge.
6. God is not a great mathematician. (3,5 MT)
7. God is not the greatest mathematician.
Tapio Hurme
> Hi,
>
> you are right, women men, cat and monkey can make mathematics. (and can
> write in latex also)
Yeah, not so bad observation!
Even I can do some mathematics with errors, so I don't have doubts about
God's ability.
(I recommend the Czech movie "The 8th day".
Motto: "After creating the Universum God relaxed on the 7th day. He noticed
the result was perfect.... and to emphazise the perfect World without
errors, ...He decided to create something imperfect. So I came into the
World")
Mark Fergerson
>
> I believe
<snip>
Why should anyone, in any of the
groups you posted to, care what you
believe?
Mark L. Fergerson
V.Gopal
> "R. Srinivasan" <srad...@in.ibm.com> wrote in message
> news:f8cdd05c.02111...@posting.google.com...
> > vgop...@rediffmail.com (V.Gopal) wrote in message
> news:<38af3945.02111...@posting.google.com>...
> >
> >
> > > ... God is the greatest mathematician ...
> >
> > What does "God" mean?
> > What does "greatest" mean?
> > What does "mathematician" mean?
> > Indeed, what does "is" mean?
> > I have no problem with "the" in your sentence.
> >
> > Sincerely,
> > R. Srinivasan srad...@in.ibm.com
>
> I have problems with "The" as well
> It implies uniqueness .
> In usual context, the word "God" includes
> having the property of being the greatest in every category.
> This reduces the statement to a moronic tautology.
> > What the guy is REALLY saying is
> > "Look at me..I'm cool because I am pointing out ALLAH U'AKBAR
> again for the edification of you unenlightened folks."
> > RJ Pease
> > Outgoing mail is certified Virus Free.
> Checked by AVG anti-virus system (http://www.grisoft.com).
> Version: 6.0.419 / Virus Database: 235 - Release Date: 11/13/02
I am not getting proper replies to my postings on Numerical logic,
can I expect impersonal replies? I do not believe in any religion,
you can abuse any God, I do not care.
God is One who can create something as big as the universe, out
of nothong that we call as 'space-time singularity'.
The Greatest is One who creates something that no one else can
create out of 'space-time singularity'.
A Mathematician is One who can define the size of 1 (one of many
sizes) without relation to anything external. This compels all
others to use 'standardized unit' or a scale to communicate sizes.
'Is' means that which is permanent and and timeless.
I am very poor in grammer 'the' is unnecessary term in all arguments.
I do not like any praise, I am comfertable with abuses, it has
become a routine. Coolness is good for health.
Steve Leibel
vgop...@rediffmail.com (V.Gopal) wrote:
> I do not like any praise, I am comfertable with abuses, it has
> become a routine.
Have you considered meditation, medication, talk therapy, or alt.abuse?
Bob Pease
"Steve Leibel" <ste...@bluetuna.com> wrote in message
news:stevel-9F1114....@news-central.giganews.com...
Sounds like the opening sentence from "The Troll Manifesto"
RJ Pease
---
G=EMC^2 Glazier
Bert
Herman Jurjus
"Robert Kolker" <bobk...@attbi.com> wrote in message
news:3E0249B2...@attbi.com...
Well, if He created the universe, He must have been quite a mathematician.
Because, as quantum physics shows,
the workings of nature are well beyond the reach of human comprehension.
(And we may safely assume that
they were not the accidental result of biological evolution ;-) .)
Cheers,
Herman Jurjus
PS. Bashing believers is a crime. It is called discrimination.
Herman Jurjus
Hmmm.
4 year old children cannot understand the difference between 'i wash you'
and 'i am washed by you'.
Monkeys cannot play chess. We may safely assume that the (adult) human brain
has some limitations, too.
Don't you think so?
Funny, your example shows just the opposite of what you intend to say.
Because when it comes to trinity, you can't exclude the alternative
possibility, namely that whoever understands trinity,
must have a _greater_ intellectual grasp of some kind, than those who don't.
Besides, common sense reasoning contains many things that look weird and
contradictory at first glance,
but that we can all understand very well.
For example, if you tie your shoelaces today and tomorrow, have you done 2
actions or '1 action twice'?
And what if you say 'i fit into my pyjamas when i have them on, but in those
conditions, they do not fit into my suitcase;
my pyjamas-folded-together fit into my suitcase, but then i do not fit into
them'.
Most of us would still call them 'the same pyjamas'. Although one 'version'
has different properties than the other.
Two equal objects with different properties? Doesn't that violate Leibniz
rule? Not at all, no big deal.
If you think about them, all these formulation sound weird, but by
experience, we all know what is going on, here.
So, the fact that some wording sounds contradictory does not make the facts
expressed therein irrational or delirious.
At least not a priori.
Cheers,
Herman Jurjus
George Dance
(Premise A)
> I believe, and everybody with capacity to think must realize that Zeno,
> Euclid, Newton, Einstein and for that matter every individual who
> contributed to the advancement of human knowledge was a human being just
> like any body - you or me.
snip
> No body
> can become the greatest mathematician; only God is the greatest
> mathematician and any difference between one man to another man is
> negligible, even if you compare Newton and Einstein with Bob or Knox.
Is God the greatest mathematician?
1. By Premise A, every individual who contributed to the advancement
of human knowledge was a human being.
2. God is not a human being.
3. God has not contributed to the advancement of human knowledge. (1,2
MT)
4. The greatest mathematician must necessarily be a great
mathematician.
5. All great mathematicians have contributed to the advancement of
human knowledge.
6. God is not a great mathematician. (3,5 MT)
7. God is not the greatest mathematician. (4,6 MT)
QED
Ms O. Philia
news:6312c50b.02112...@posting.google.com...
Brilliant proof, George. Could you address this one small doubt about
"2. God is not a human being."?
Perhaps rather than the infinite God usually supposed our universe's
creator might be a limited god - more specifically a future mathematician
who travels back in time to initiate the big bang as implied by a small
extension of Clifford Pickover's essay on time travel at
(http://www.pbs.org/wgbh/nova/time/through2.html)
The future of time travel
----------------------------------------------------------------------------
----
Various researchers have proposed ways in which backward and forward time
machines can be built that do not seem to violate any know laws of physics.
Remember that the laws of physics tell us what is possible, not what is
practical for humans at this point in time. The physics of time travel is
still in its infancy. While all physicists today admit that time travel to
the future is possible, many still believe time travel to the past will
never be easily attainable. Don't believe anyone who tells you that humans
will never have efficient technology for backward and forward time travel.
Accurately predicting future technology is nearly impossible, and history is
filled with underestimates of technology:
"Heavier-than-air flying machines are impossible." (Lord Kelvin,
president, Royal Society, 1895)
"I think there is a world market for maybe five computers." (Thomas
Watson, chairman of IBM, 1943)
"There is no reason for any individual to have a computer in their home."
(Ken Olsen, president, chairman and founder of Digital Equipment Corp.,
1977)
"The telephone has too many shortcomings to be seriously considered as a
means of communication. The device is inherently of no value to us."
(Western Union internal memo, 1876)
"Airplanes are interesting toys but of no military value." (Marshal
Ferdinand Foch, French commander of Allied forces during the closing months
of World War I, 1918)
"The wireless music box has no imaginable commercial value. Who would pay
for a message sent to nobody in particular?" (David Sarnoff's associates, in
response to his urgings for investment in radio in the 1920's)
"Professor Goddard does not know the relation between action and reaction
and the need to have something better than a vacuum against which to react.
He seems to lack the basic knowledge ladled out daily in high schools." (New
York Times editorial about Robert Goddard's revolutionary rocket work, 1921)
"Who the hell wants to hear actors talk?" (Harry M. Warner, Warner
Brothers, 1927)
"Everything that can be invented has been invented." (Charles H. Duell,
commissioner, US Office of Patents, 1899)
Wouldn't it be a wild world to live in if time travel devices played
important roles in the development of humanity -- like the computer and the
telephone? Mathematicians dating back to Georg Bernhard Riemann (1826-1866)
have studied the properties of multiple connected spaces in which different
regions of space and time are spliced together. Physicists, who once
considered this an intellectual exercise for armchair speculation, are now
seriously studying advanced branches of mathematics to create practical
models of our universe.
Science-fiction stories about space travel have already inspired humans to
travel to the moon. Similarly, will time-travel stories inspire us to create
real time-travel mechanisms? Will we ever find a way to overcome the
Einstein speed limit and make all of spacetime home?
I wonder what humanity will discover about spacetime in the next century.
Around four billion years ago, living creatures were nothing more than
biochemical machines capable of self-reproduction. In a mere fraction of
this time, humans evolved from creatures like Australopithecus. Today humans
have wandered the moon and have studied ideas ranging from general
relativity to quantum cosmology. Who knows into what beings we will evolve?
Who knows what intelligent machines we will create that will be our ultimate
heirs? These creatures might survive virtually forever, with our ideas,
hopes, and dreams carried with them.
There is a strangeness to the cosmic symphony that may encompass time
travel, higher dimensions, quantum superspace, and parallel universes --
worlds that resemble our own and perhaps even occupy the same space as our
own in some ghostly manner. Stephen Hawking has even proposed using
wormholes to connect our universe with an infinite number of parallel
universes. Edward Witten is working hard on superstring theory, which has
already created a sensation in the world of physics because it can explain
the nature of both matter and spacetime. By realizing that the fundamental
laws of physics appear simpler in higher dimensions, string theory can unite
Einstein's theory of gravity with quantum theory in ten dimensions. Our
heirs, whatever or whoever they may be, will explore space and time to
degrees we cannot currently fathom. They will create new melodies in the
music of time. There are infinite harmonies to be explored.
Spaceman
> The future of time travel
>----------------------------------------------------------------------------
>----
> Various researchers have proposed ways in which backward and forward time
>machines can be built that do not seem to violate any know laws of physics.
<ROFLOL>
actually,
each and every time machine violates Newtons laws of motion.
clocks do not "regulate" time.
time is a ratio of the ticker count vs a "made up" unit called
a second.
There is no "real" time to travel in at all.
Current physics is far from time travel,
once they find the "reaction causes" instead of this silly
time causing crap.
Then maybe,
Time travel will be possible,
but definitely not with current dung about "time dimensions"
but possible with "Planet action reversing"
Big problem still is.
forcing a different human to "move backwards in time"
time travel is "stuck in SciFi"
for a long long long "amount of Earth revs"
:)
God will be found before time travel.
andi babian
step form, but it goes like this:
God is all-powerful.
He or she can be whatever he or she wants.
He or she may want to be human if he or she wants.
Thus, though, translation from hypothetical statements to statements
of fact is not a well studied branch of logic theory, we can
add a concluding step that:
God _can_ be the greatest mathematician if he or she wants.
It really does depend on the logical system you wish to accept,
but it can be shown that the proof is in error.
Bob Pease
"andi babian" <aba...@cruzio.com> wrote in message
news:3DDE499D...@cruzio.com...
> Cool, a doubt I can remedy! I won't put the argument in numbered
> step form, but it goes like this:
>
> God is all-powerful.
> He or she can be whatever he or she wants.
> He or she may want to be human if he or she wants.
> Thus, though, translation from hypothetical statements to statements
> of fact is not a well studied branch of logic theory, we can
> add a concluding step that:
> God _can_ be the greatest mathematician if he or she wants.
>
> It really does depend on the logical system you wish to accept,
> but it can be shown that the proof is in error.
The proof seems to follow nicely
(Once you get up off of the floor from laughing at the premises)
ruri muharto
> "Bob Pease" <bobp...@concentric.net> wrote in message news:<argelb$4...@dispatch.concentric.net>...
> > "R. Srinivasan" <srad...@in.ibm.com> wrote in message
> > news:f8cdd05c.02111...@posting.google.com...
> > > vgop...@rediffmail.com (V.Gopal) wrote in message
> news:<38af3945.02111...@posting.google.com>...
> > >
> > Checked by AVG anti-virus system (http://www.grisoft.com).
> > Version: 6.0.419 / Virus Database: 235 - Release Date: 11/13/02
>
> I am not getting proper replies to my postings on Numerical logic,
> can I expect impersonal replies? I do not believe in any religion,
> you can abuse any God, I do not care.
> God is One who can create something as big as the universe, out
> of nothong that we call as 'space-time singularity'.
> The Greatest is One who creates something that no one else can
> create out of 'space-time singularity'.
> A Mathematician is One who can define the size of 1 (one of many
> sizes) without relation to anything external. This compels all
> others to use 'standardized unit' or a scale to communicate sizes.
> 'Is' means that which is permanent and and timeless.
> I am very poor in grammer 'the' is unnecessary term in all arguments.
> I do not like any praise, I am comfertable with abuses, it has
> become a routine. Coolness is good for health.
As you live in the world, you'd better prepare yourself to have
consensus on god existence, the one who created you, who formed the
universe and everything surrounding you.
Then you try to learn the "everything surrounding you", everything may
be seen and be touched. Common sense tells you that such way you learn
may be simply called as "Science". The faculty of thingking which is
emerged tells you that science does not need any "God". All seems to
move based on its own meachanism.
I believe that capturing and elaborating both of these concepts is the
reason why we are living..
sincerely,
-rurie-
Thomas Klimpel
> travel to the moon. Similarly, will time-travel stories inspire us to create
> real time-travel mechanisms? Will we ever find a way to overcome the
> Einstein speed limit and make all of spacetime home?
Did you ever notice, that trains may be late, but may not be soon.
(Even the words are missing...)
Well actually it's possible, but some people might get upset if they
miss their train, because of the train being soon.
Solutions to overcome this problem might have dramatic influence on
the future of public transport.
just a thought about time...
Thomas
Lovecraftesque
what you mean by "God", the assertion is pretty meaningless.
Barb Knox
<h.ju...@hetnet.nl> wrote:
> "Robert Kolker" <bobk...@attbi.com> wrote in message
> news:3E0249B2...@attbi.com...
> >
> > V.Gopal wrote:
> > > I believe, and everybody with capacity to think must realize that Zeno,
> > > can become the greatest mathematician; only God is the greatest
> > > mathematician
> >
> > This is complete bullshit based on wishful thinking and not one fact. I
> > think you are seriously deranged.
> >
> > Tell me do you talk to God? (and here is the important question). Does
> > God talk to you? Have you heard Her voice? Does She sound like your mamma?
>
> Well, if He created the universe, He must have been quite a mathematician.
Not necessarily. We know of one more-or-less successful universe-creation
event, but we can have no knowledge of the possibly infinite number of
failed attempts. So, rather than having planned the physics of this
universe in detail ahead of time, maybe He/She/It/They just hacked around
until they got something interesting. IOW, being more of an artist or a
computer programmer than a mathematician.
> Because, as quantum physics shows,
> the workings of nature are well beyond the reach of human comprehension.
Ahem. What species was it which did that showing (by developing QM)? It
was humans, right? Certainly some humans understand QM. If all you're
saying is that there is no good mapping of QM to human understandings and
intuitions of the macroscopic world then that certainly seems true, but so
what.
> (And we may safely assume that
> they were not the accidental result of biological evolution ;-) .)
That depends on what you mean by "safely". In ordinary life we may assume
lots of sometimes counterfactual things without any risk to our physical
safety, so long as we get certain things right (e.g., looking both ways
before crossing a street).
But sometimes matters of faith affect one's personal life and even public
policy. When James Watt was the US Secretary of the Environment, as a
fundamentalist Christian he wasn't worried much about pollution or
biodiversity, because he knew the end of the world was coming soon
anyway. Similarly, believing that humans are a special creation apart
from the rest of nature would affect one's views on the care of the earth,
biodiversity, etc.
> Cheers,
> Herman Jurjus
>
> PS. Bashing believers is a crime. It is called discrimination.
"Bashing"? Maybe in a face-to-face conversation calling someone
"seriously deranged" would be seriously offensive, but in Usenet it's just
a moderate rebuke. If you *really* want to offend someone on Usenet you
should call them a Nazi, or a newbie.
And *words* are not actionable as discrimination. In what jurisdiction is
it a crime to think (and say) that religious folks are generally deranged,
as long as one treats such folks fairly according to the local
anti-discrimination laws?
Words can be actionable as defamation (damage to one's good reputation),
but that's a separate issue that does not appear to apply here.
--
---------------------------
| BBB b \ barbara minus knox at iname stop com
| B B aa rrr b |
| BBB a a r bbb |
| B B a a r b b |
| BBB aa a r bbb |
-----------------------------
Bob Pease
> Which God would that be? Until you define precisely
> what you mean by "God", the assertion is pretty meaningless.
Even if "God" is defined in such a way to make it meaningful, it becomes a
case of
"OK..Next..."
RJ Pease
---
V.Gopal
"Accordingly I shall now suppose, NOT that a true God, Who as such
must be supremely good and the fountain of truth, but some
malignant genius exceedingly powerful and cunning, has devoted
all his powers in deceiving me; I shall suppose that the sky,
the earth, colors, shape, sound and all external things are
illusions and imposters of which this evil genius has availed
himself for abuses of my crudility; I shall consider myself as
having no eyes, no flesh, no blood, nor any senses, but as
falsely opining myself to possess all these things,"
If God is a mathematician then he (not HE) cannot ceceive
you, YOU ARE YOURDELF GOD or at least you can be sure that you
possess all you believe you possess.
Barb Knox
> "Bob Pease" <bobp...@concentric.net> wrote in message
news:<armmqs$4...@dispatch.concentric.net>...
> > "Lovecraftesque" <Lovecra...@yahoo.com> wrote in message
> > news:pan.2002.11.22.21...@yahoo.com...
> > > Which God would that be? Until you define precisely
> > > what you mean by "God", the assertion is pretty meaningless.
> >
> > Even if "God" is defined in such a way to make it meaningful, it becomes a
> > case of
> > "OK..Next..."
> >
> > RJ Pease
> >
> >
> > ---
> > Outgoing mail is certified Virus Free.
> > Checked by AVG anti-virus system (http://www.grisoft.com).
> > Version: 6.0.419 / Virus Database: 235 - Release Date: 11/13/02
> Next? Ok. This is what Descarte said:
[snip]
> If God is a mathematician then he (not HE) cannot ceceive
> you, YOU ARE YOURDELF GOD or at least you can be sure that you
> possess all you believe you possess.
Bizarre. There are plenty of people who believe they posess a winning
system for roulette or picking horserace winners, but as a matter of
verifiable fact they do not. There are plenty of people who believe they
possess some sort of eternal life, but they could be wrong. There are
plenty of people who believe they possess useful arguments to post on
Usenet, but they don't. Etc.
Hey, VG, how come you haven't responded to my detailed reply to your "What
is wrong in geometry-part2". And how about giving a specific response to
each of my points, rather than your usual all-run-together-at-the-end
style?
Mike Oliver
> Which God would that be? Until you define precisely
> what you mean by "God", the assertion is pretty meaningless.
Most of the time that people ask other people to "define God"
it's a category error. "God" is a proper name; "define God"
makes no more sense than "define Abraham Lincoln".
That's why the supposed logical proofs that God exists
or does not exist are doomed from the word go. They
all necessarily start with some "definition" of God -- how
else could you expect to prove either proposition from
just logic? But such definitions inevitably change
the question being asked, and in a detrimental way. I'm
not frankly very interested in whether there is "that than
which nothing greater can be imagined"; that could be something
purely abstract. If God is an abstraction, that's not *God*,
not as I think of God anyway.
Lovecraftesque
one though: given the large number of vastly different, antagonistic
deities that have been, and many still are, worshipped by different
societies, I was just wondering which one of them is the greatest
mathematician.
V.Gopal
Dear BK, In "What is wrong in geometry? part2"
Your questions did not pertain to the topic raised by me, they were
personal and had nothing to do with mathematical logic.
I do not want to answer any question that is not concerned with
mathematical logic. Please forgive me.
I am not running away, I am eager to answer any question, provided
the question is impersonal and relevent to the topic raised by me.
George Dance
> > Brilliant proof, George. Could you address this one small doubt about
> > "2. God is not a human being."?
> Cool, a doubt I can remedy! I won't put the argument in numbered
> step form, but it goes like this:
>
> God is all-powerful.
> He or she can be whatever he or she wants.
> He or she may want to be human if he or she wants.
> Thus, though, translation from hypothetical statements to statements
> of fact is not a well studied branch of logic theory, we can
> add a concluding step that:
> God _can_ be the greatest mathematician if he or she wants.
Your counter-argument depends on only one premise (which I will
number, only because I'll refer to it later) that:
i. God is all powerful.
That is a reasonable enough premise, I think, if we interpret it
correctly.
First of all, we shouldn't interpret it as meaning God can do things
that are logically impossible - that eliminates such paradoxes as the
question, "Can God create a rock so big that He or She can't lift it?"
So we have to add a rider that:
ii. Even an all-powerful being cannot do anything logically
impossible.
What we do want to capture is the notion that God can do things that
human beings cannot do. So, I think, we need a further premise that:
iii. Human beings are not all-powerful.
That is sufficient to criticize your conclusion, that:
iv. God can be a human being (and thus the greatest mathematician) if
God wants to.
There is nothing logically impossible about becoming a human being -
indeed, all of us managed it - then God can be a human being. If God
became a human being, then He would not be all-powerful (by iii), and
if he were not all-powerful, then He would not be God (by the converse
of i). In order for Him to be both God and a human being, he would
have to be both all-powerful and not all-powerful; and since this last
is a logical impossibility, then God cannot (by ii) both become a
human being and still be God. For God to become a human being, then
(given the premises) would mean for him to cease to be God - forever,
since, no longer being all-powerful, he would not be able to change
himself back into God at a later time.
So if God became a human being (and thus the greatest mathematician),
he would not be God, and "God is the greatest mathematician" would
still be false.
> It really does depend on the logical system you wish to accept,
> but it can be shown that the proof is in error.
Not by the above line of argument.
V.Gopal
If large number of different deities are worshiped by different
societies
then it is not His mistake. If one day scientists successfully
construct
a predictable system or develop a Theory of Everything then we will
find
that God cannot interfere in the affairs of the world. But Theory of
Everything will prove that there can be only one God and one religion.
If man imagines different deities then the deities names can only
serve
as different names or proper nouns of one and the same God. What I
mean
is man and God are identical in essence, both are mathematicians. The
only difference is man cannot create something out of nothing.
Robert Kolker
V.Gopal wrote:
> If large number of different deities are worshiped by different
> societies
> then it is not His mistake. If one day scientists successfully
> construct
> a predictable system or develop a Theory of Everything then we will
> find
> that God cannot interfere in the affairs of the world. But Theory of
> Everything will prove that there can be only one God and one religion.
You mean -at most- One God.
Bob Kolker
Mike
"V.Gopal" wrote
> If large number of different deities are worshiped by different
> societies
> then it is not His mistake. If one day scientists successfully
> construct
> a predictable system or develop a Theory of Everything then we will
> find
> that God cannot interfere in the affairs of the world. But Theory of
> Everything will prove that there can be only one God and one religion.
> If man imagines different deities then the deities names can only
> serve
> as different names or proper nouns of one and the same God. What I
> mean
> is man and God are identical in essence, both are mathematicians. The
> only difference is man cannot create something out of nothing.
A TOE can only be a matter of faith. Even if we discover a Theory of
Everything through the requirement of logical consistency, it would still be
a matter of faith that everything in the universe complies with that theory.
For we cannot measure all things and observe all events to confirm that this
theory holds everywhere. But if we do find a theory that does seem to
explain everything in terms we can understand, then that would only show
that things are as we believe they are and according to our faith will it be
done - faith being defined as something we understand.
Moufang Loop
>
> I believe, and everybody with capacity to think must realize that Zeno,
> contributed to the advancement of human knowledge was a human being just
> like any body - you or me.
That's a nice thought! Thank you.
> Mathematics has advanced on the basis of logic
> of sense of sight - we can find nothing wrong in mathematics as long as
> we try to understand it using the logic of sense of sight - judge the
> truth and falsity of each mathematical proposition by checking whether
> mind and eye reach a total agreement or not. We always find that whatever
> we have accepted as true in mathematics, our mind and eyes always reached
> total agreement. The act of making our mind and eye reach total agreement
> does not always constitute thinking, although in some cases it does.
> That part of mathematical logic, which cannot be understood by using the
> logic of sense of sight is revealed by geometry. Geometry contains
> certain knowledge that is incommunicable. If one tries to expalin it
> and in the process if many of our conventional ideas are proved wrong
> it is not going to have any effect on progress in technology. This
> way nobody brings any disgrace to any individual living or dead. No body
> can become the greatest mathematician; only God is the greatest
> mathematician
If one believes in God and if one believes that he created the universe,
_and_ if one sees the universe as having a mathematical "pattern". Then
that might tempt one to the view that God is a mathematician. But,
might it not be the case that we see the universe as having a
mathematical pattern because we are trying to make sense of something
(so far) inexplicable by imposing our order on it; and our order is a
man-made mathematical order? That is possible even if there is a God,
though I don't believe in Him myself.
ML
Moufang Loop
>
> vgop...@rediffmail.com (V.Gopal) wrote in message news:<38af3945.02111...@posting.google.com>...
>
> > I believe, and everybody with capacity to think must realize that Zeno,
> > Euclid, Newton, Einstein and for that matter every individual who
> > contributed to the advancement of human knowledge was a human being just
> > like any body - you or me.
>
>
> > No body
> > can become the greatest mathematician; only God is the greatest
> > negligible, even if you compare Newton and Einstein with Bob or Knox.
>
>
> of human knowledge was a human being.
>
> 2. God is not a human being.
>
> MT)
This only follows if God is an indivdual. I know too little about
theology to know whether God is considered an individual or not.
>
> 4. The greatest mathematician must necessarily be a great
> mathematician.
>
> 5. All great mathematicians have contributed to the advancement of
> human knowledge.
Perhaps not. Perhaps God is the One Exception?
>
> 6. God is not a great mathematician. (3,5 MT)
>
> 7. God is not the greatest mathematician.
Going a bit further, and assuming that your argument _is_ valid: the
op's Subject and your 7 lead by reductio to the conclusion that at least
one premise is false. Perhaps the Trinity requires the denial of your
2?
ML
Andy Landen
the universe, perhaps because it is not operate by any set of universal
laws, then we will soon find that our observations disagree with the
predicted model. Our observations include more than just sight, but every
recording of every type of instrument devise from sound to heat to IR and
EUV, etc. In attempting to reconcile our mathematical models with our
observations of our universe (telescopes can see very far out there), we
will find that any universe that refuses to follow any sort of order will
introduce inconsistencies into our mathematical models. Mathematics allows
for no inconsistencies and requires perfect order/universal laws.
If there is no order in the universe, then we MUST ask, "What directs
the affairs of the universe?" Something MUST dictate the interactions that
we observe. If it is a supreme being, then how does that being come to
decide what happens. If every interaction is determined by the decisions of
the smallest particles, then how do they decide and how is it that we can
observe any consistencies in this world and predict anything? While we find
it difficult to predict many things perfectly, we can predict most things
with remarkable accuracy. Therefore our observable universe follows laws
that are very close to our mathematical models. Note: That we refrain from
imposing any specific mathematical model, but instead we allow the universe
to describe the model that it follows.
Before we ask how that model was chosen (a question reserved for God),
we must first know the laws perfectly. God may act in a world of laws just
as we also may act. Should we compare His power to act versus ours, an easy
analog could be seen with our own power to act versus the cavemen of ancient
times. The laws have never changed by our learning them, but our power to
act has increased with our understanding of them. So also with God, a being
who has such great mastery of the knowledge of the laws (which He Himself ma
y have created), that comprehension of His power would require a complete
knowledge of His understanding and skills.
"Moufang Loop" <Moufan...@btinternet.com> wrote in message
news:3DE11218...@btinternet.com...
Andy Landen
All great mathematicians, of which we have record (or know), have
contributed to human knowledge.
Neither 6 nor 7 must follow from this revised premise. We do not have
record or know of God. Furthermore, "Greatness" does not require the
individual(s) to share that greatness. Finally, we cannot prove that he has
not shared some of his knowledge with at least many of the great
mathematicians or scientists or philosophers by the revelation of ideas into
their minds. Interesting that few men give God any credit, but that those
who do are often the ones who contribute the most to human knowledge.
"Moufang Loop" <Moufan...@btinternet.com> wrote in message
news:3DE11C8B...@btinternet.com...
Ronald Stepp
news:qV9E9.20958$hi6....@nwrddc02.gnilink.net...
> If there is no order in the universe, then we MUST ask, "What directs
> the affairs of the universe?" Something MUST dictate the interactions
that
There is order in the universe. You're just to ignorant to recognize it
since you have a pet theory which biases you ahead of time.
Barb Knox
> s...@sig.below (Barb Knox) wrote in message
news:<see-241102...@192.168.1.2>...
[snip]
> > Hey, VG, how come you haven't responded to my detailed reply to your "What
> > is wrong in geometry-part2". And how about giving a specific response to
> > each of my points, rather than your usual all-run-together-at-the-end
> > style?
>
> Dear BK, In "What is wrong in geometry? part2"
> Your questions did not pertain to the topic raised by me, they were
> personal and had nothing to do with mathematical logic.
A couple of my questions were personal, so if that's what puts you off
I've edited them to eliminate the personal questions. So, VG, please now
provide some answers to the several non-personal questions, below.
> I do not want to answer any question that is not concerned with
> mathematical logic. Please forgive me.
You will be forgiven if you answer the non-personal questions below.
> I am not running away, I am eager to answer any question, provided
> the question is impersonal and relevent to the topic raised by me.
OK, here's your chance to not run away...
In article <38af3945.02110...@posting.google.com>,
vgop...@rediffmail.com (V.Gopal) wrote:
> It seems that the cunning policy: "It is better to be vague and partly
> correct than to be precise and completely wrong" is applied
> particularly to coordinate geometry form the very beginning.
[personal question snipped]
> It seems
> that even among mathematicians there is a difference of opinion on the
> following fundamental issues:
Seems to whom? Please cite a *single* bona-fide mathematician (not some
Usenet crank) who has the slightest problem with the foundations of
co-ordinate geometry.
> (1) Whether a point occupoies space or does not occupy space.
This actually can be a meaningful question in point-set topology. As
applied to Euclidean space, a point does NOT occupy space. Do you have a
cite of some mathematician who claims that it does?!?
> (2) Does a point specify only 'location' and not a number?
Huh? In co-ordinate geometry, a location IS a tuple of numbers. Do you
have an example of the distinction between the two that you are trying to
get at?
> (3) Whether each point has to represent the same number
> OR a point can represent any number from 0 to infinity,
Since each point IS a tuple of numbers, why ask whether it can be several
different tuples? Clearly it can not.
> e.g. any value of TanA.
[personal question snipped]
> (4) Whether a line becomes contiguous/continuous if we
> ADD points to a line one AFTER another (assign value of X, then
> calculate the value of Y and finally place the point on its
> appropriate position) or it requires a different condition.
There is no disagreement among mathematicians about this; it does require
"a different condition" in the general case. Clearly, a line with a
countable number of point holes in it can be filled in by the procedure
you describe. But, as Cantor showed, the number of points in a line
segment (such as a gap in your discontinuous line) is vastly greater than
the number that can be filled in one-at-a-time.
HTH, really.
andi babian
You're just making me laugh harder.
And yes, Uncle Al and I are in the same High IQ society:
http://www.hbci.com/~ispe/pageindex.html
I got his address from their roster. I could be wrong about it,
though. Just a bit of friendly rivalry ;)
agb
Lovecraftesque
> If large number of different deities are worshiped by different
> societies
> then it is not His mistake.
So, you answer would be - what? Which of those
deities, if any, are talking about?
V.Gopal
to you or any person; it is a general remark and may not be applicable
to you.
Any concept that does not occupy even a 'point' cannot indicate location.
If a point does not occupy space then location will be forgotten as soon
as our attention shifts to the next location. A countable singularity
must occupy at least a point. The gentleman who postes the 2nd answer
in the thread does accept that a point occupies point and you differ!
In geometry a point or a location cannot represent more than one
number. Here the number itself is a countable singularity! I do not
know the meaning of "tuple of numbers". In any case you cannot
associate one point with "tuple of numbers" or any plurality.
All the 'points holes' on a line, however small the line may be, can
not be filled, for however long you may try (1mm*N/N=1mm here
N can be infinite.)In all my postings I found disagreements
between mathematicians.
Barb Knox
Thank you for finally replying to the substance of my comments, sort of.
It really would help if you interspersed your replies in-line after each
comment you're replying to, like most posters manage to do. It would then
be clearer when you were actually addressing the issues, and when you
weren't. For the sake of clarity, I've moved each of your replies to
after the comment being replied to.
> s...@sig.below (Barb Knox) wrote in message
news:<see-251102...@192.168.1.2>...
> > In article <38af3945.02112...@posting.google.com>,
> > vgop...@rediffmail.com (V.Gopal) wrote:
> >
> > > s...@sig.below (Barb Knox) wrote in message
> > news:<see-241102...@192.168.1.2>...
> > [snip]
> >
> > > > Hey, VG, how come you haven't responded to my detailed reply to your
> > > > "Whatis wrong in geometry-part2". And how about giving a specific
> > > > response to each of my points, rather than your usual
> > > > all-run-together-at-the-end style?
> > >
> > > Dear BK, In "What is wrong in geometry? part2"
> > > Your questions did not pertain to the topic raised by me, they were
> > > personal and had nothing to do with mathematical logic.
> >
> > A couple of my questions were personal, so if that's what puts you off
> > I've edited them to eliminate the personal questions. So, VG, please now
> > provide some answers to the several non-personal questions, below.
> >
> > > I do not want to answer any question that is not concerned with
> > > mathematical logic. Please forgive me.
> >
> > You will be forgiven if you answer the non-personal questions below.
> >
> > > I am not running away, I am eager to answer any question, provided
> > > the question is impersonal and relevent to the topic raised by me.
> >
> > OK, here's your chance to not run away...
> >
> >
> > In article <38af3945.02110...@posting.google.com>,
> > vgop...@rediffmail.com (V.Gopal) wrote:
> >
> > > It seems that the cunning policy: "It is better to be vague and partly
> > > correct than to be precise and completely wrong" is applied
> > > particularly to coordinate geometry form the very beginning.
>
> My observation, "It seems that the cunning policy ....." is not directed
> to you or any person; it is a general remark and may not be applicable
> to you.
I didn't take it personally. And even if I had done so I would just have
ignored it. It usually doesn't pay to be personally touchy on Usenet.
> > [personal question snipped]
> >
> > > It seems
> > > that even among mathematicians there is a difference of opinion on the
> > > following fundamental issues:
> >
> > Seems to whom? Please cite a *single* bona-fide mathematician (not some
> > Usenet crank) who has the slightest problem with the foundations of
> > co-ordinate geometry.
> >
> > > (1) Whether a point occupoies space or does not occupy space.
> >
> > This actually can be a meaningful question in point-set topology. As
> > applied to Euclidean space, a point does NOT occupy space. Do you have a
> > cite of some mathematician who claims that it does?!?
>
> Any concept that does not occupy even a 'point' cannot indicate location.
We agree that in Euclidean co-ordinate geometry a point is defined by its
location (the X and Y co-ordinates for 2D). Therefore a point does
"occupy" a location in one sense. But it isn't any sort of "exclusive
occupancy". That is, a point does not "take up" any space; other points
can be arbitrarily close to it.
> If a point does not occupy space then location will be forgotten as soon
> as our attention shifts to the next location.
Huh? A co-ordinate pair doesn't change behind my back when I'm not
looking at it. And an isolated geometric point would be invisible in any
case, since it has zero area (and therefore would have a zero
cross-section for reflecting photons). Human perceptual intuitions can be
VERY MISLEADING when considering things other than our usual macroscopic
physical reality. In particular, visual intuitions can lead one astray
when dealing with geometric abstractions that do not exist in the
macroscopic world (such as points and lines).
> A countable singularity must occupy at least a point.
Huh? What's a "countable singularity"? What sense of "occupy" are you using?
> The gentleman who postes the 2nd answer
> in the thread does accept that a point occupies point and you differ!
Not my problem. Just please answer my objections; if you have replies for
other posters then deal with them directly.
> > > (2) Does a point specify only 'location' and not a number?
> >
> > Huh? In co-ordinate geometry, a location IS a tuple of numbers. Do you
> > have an example of the distinction between the two that you are trying to
> > get at?
> In geometry a point or a location cannot represent more than one
> number.
Huh? In 2D co-ordinate geometry each distinct point corresponds to a
distinct pair of real numbers. So each point represents 2 numbers. In
higher dimensions each point represents more than 2 numbers.
> Here the number itself is a countable singularity!
This reads as gibberish. It would help if you tell us what you mean by
"countable singularity".
> I do not know the meaning of "tuple of numbers".
Then that would appear to disqualify you from any serious discussion of
co-ordinate geometry. Your highly idiosyncratic terminology also
indicatea that you haven't really studied the subject. At the risk of
asking a personal question, is that indeed the case?
> In any case you cannot
> associate one point with "tuple of numbers" or any plurality.
Since you just said you don't know what a "tuple of numbers" is, how can
you claim with any certainty that a point cannot be "associated" with one?
Your use of "plurality" at the end seems to imply that you view a point as
a "singularity" (which it is in one sense) but a pair of numbers as a
"plurality". Well, the fact is that in co-ordinate geometry each 2D point
IS DEFINED TO BE a pair (2-tuple) of numbers. If your metaphysics chokes
on that elementary fact then a serious re-think on your part seems called
for.
> > > (3) Whether each point has to represent the same number
> > > OR a point can represent any number from 0 to infinity,
> >
> > Since each point IS a tuple of numbers, why ask whether it can be several
> > different tuples? Clearly it can not.
> >
> > > e.g. any value of TanA.
> >
> > [personal question snipped]
> >
> > > (4) Whether a line becomes contiguous/continuous if we
> > > ADD points to a line one AFTER another (assign value of X, then
> > > calculate the value of Y and finally place the point on its
> > > appropriate position) or it requires a different condition.
> >
> > There is no disagreement among mathematicians about this; it does require
> > "a different condition" in the general case. Clearly, a line with a
> > countable number of point holes in it can be filled in by the procedure
> > you describe. But, as Cantor showed, the number of points in a line
> > segment (such as a gap in your discontinuous line) is vastly greater than
> > the number that can be filled in one-at-a-time.
>
> All the 'points holes' on a line, however small the line may be, can
> not be filled, for however long you may try (1mm*N/N=1mm here
> N can be infinite.)
> >
> > HTH, really.
> In all my postings I found disagreements between mathematicians.
As requested earlier, please provide A SINGLE CITE from a bona-fide
mathematician supporting your views. I specifically asked for cites for
your points (1) and (4), and so far you haven't provided any. (I would be
very surprised if you had any to provide.)
V.Gopal
If you talk of 'distinct pair of real number numbers' then each real
number is a set and each set (real number) is a countable singularity.
Please try to understand, IF YOU CAN, that if one (single) point in
Euclidean space is a 'tuple of numbers' then you cannot talk of
'relation' between those two numbers, which obviously means that
YOU CANNOT TALK OF ANY "RELATION" BETWEN X AND Y, THEY BECOME
INDEPENDENT VARIABLES SIMPLY BECAUSE THEY ARE "TUPLE OF NUMBERS"
AT ONE POINT. If geometry is not a subject of relation between X
and Y then it the whole of geometry is useless. I think I have to
explain it to many of those like you whose mind works like digital
and not like the human brain.