Discussion:
There is no valid construction of the real numbers.
(too old to reply)
John Gabriel
2015-09-02 11:06:25 UTC
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If you want to learn from me, then go here:

http://www.spacetimeandtheuniverse.com/math/8073-no-valid-construction-real-number-exists.html#post45690
Dan Christensen
2015-09-02 12:26:20 UTC
Permalink
If you want to...
What you should know about the Psycho Troll John Gabriel, in his own words:

JG's God Complex:

"I am the Creator of this galaxy."
-- March 19, 2015

"I am the last word on everything."
-- May 6, 2015

"Whatever I imagine is real because whatever I imagine is well defined."
-- March 26, 2015

"Unless I think it's logic, it's not... There are no rules in mathematics... As I have repeatedly stated, if there were to be rules, I'd be making the rules."
-- March 17, 2015


JG's Final Solution:

"Hitler was a genius and a very talented artist... As from a moral point of view, again his actions can't be judged, because his morals are different." (Like JG's morals?)
-- March 18, 2015

"I will point out a few facts about Hitler that most of you arrogant idiots didn't know or refused to acknowledge because your Jewish overlords do not allow you...

"Unfortunately, Hitler's henchmen got the wrong Jews...

(Note: When repeatedly asked if they should have gotten Jews like Albert Einstein, JG has refused to comment. You figure it out, folks.)

"It would be a very good idea to round up all the academic idiots, gas them and incinerate the useless lot. Only those that pass John Gabriel's exam should be allowed to live."
-- July 13, 2014

"All those who don't accept New Calculus, you better say goodbye to your kids... Because John Gabriel is coming." (Charming fellow.)
-- July 9, 2014


JG's Just Plain Stupid:

"1/0 is not undefined."
-- May 19, 2015

"1/3 does NOT mean 1 divided by 3 and never has meant that"
-- February 8, 2015

"The square root of 2 and pi are NOT numbers."
-- May 28, 2015

"By definition, a line is the distance between two points."
-- April 13, 2015

"So, 'is a member of' = 'is a subset of.'"
-- May 16, 2015

"There is no such thing as a continuous real number line."
-- March 24, 2015

"Indeed, there is no such thing as an instantaneous speed -- certainly not with respect to the calculus." (Note: Instantaneous speed is indicated by the speedometer in a car. Another Jewish conspiracy, JG?)
-- March 17, 2015

"Proofs had nothing to do with calculus."
-- May 30, 2015


In his wacky system, JG cannot even prove that 2+2=4. It seems unlikely he would have anything worthwhile to say about mathematics. On the contrary, it seems he is deliberately trying to mislead and confuse any newcomers here.

A special word of caution to students: Do not attempt to use JG's "system" in any course work in any high school, college or university on the planet. You will fail miserably. His system is certainly no "shortcut" to success in mathematics. It is truly a dead-end.


Dan

Download my DC Proof 2.0 software at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com
Archimedes Plutonium
2015-09-02 20:00:05 UTC
Permalink
I don't usually engage the trolls directly. I compile lists of their typical rantings and post them as a warning to others who may be taken in, wasting their valuable time or worse. I don't usually post more than one such warning per thread.
#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. What we need to get to, is a place where all those who offer a proof 
of 
Euclid Infinitude of Primes, give both methods, direct and indirect, 
so that 
both the reader and author have a better chance of delivering a valid 
proof and is not mixing them up.

But then Courant & Robbins 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.
A major error by most authors is that they never actually start with 
what must be started, not the hypothetical assumption but rather with 
the definition of prime number is. This is important because once 
Euclid's number is formed, we refer to the definition to tell us it is 
necessarily prime.
As I keep insisting, if Courant and Robbins had been required to 
deliver both proof methods, then there would not be this sloppy mixing 
up 
of methods that ends in invalidity.

AP1990s Survey
Many of AP's postings can be safely ignored as well. But once he starts peddling his mathematical snake oil promising an "easier way" for students to do calculus, for example, I think they really ought to be warned about him.
Yeah, I probably have too much time on my hand and should get out more. Sigh...
Dan
Dan seems to have lost sight that sci.math is about math, not about hatred of people and plastering hate-sheets all over the place, but when a person is insane, insanity is where "no reasoning can enter". One can only "use insane people like Dan", like one makes use of horse-manure as a fertilizer for the lawn and grounds.

AP
Dan Christensen
2015-09-02 20:04:58 UTC
Permalink
On Tuesday...
More "pearls of wisdom" from AP:

"0 is an infinite irrational number."
-- Archimedes Plutonium, June 28, 2015
https://groups.google.com/forum/#!topic/sci.math/V3KCSKuls0Y


"0 appears to be the last and largest finite number"
-- Archimedes Plutonium, sci.math, June 9, 2015

Link: https://groups.google.com/forum/#!topicsearchin/sci.math/$20AP$20axioms$20of$20Numbers$20versus$20Peano-Dedekind/sci.math/SRq9-cHtTY0


"0/0 must be equal to 1."
-- Archimedes Plutonium, sci.math, June 9, 2015

Link: https://groups.google.com/forum/#!searchin/sci.math/%220$2F0$20must$20be$20equal$20to$201%22%7Csort:date/sci.math/U6x4PEojzhs/BzlroMhJnNgJ


"The last and largest finite number is 10^604."
-- Archimedes Plutonium, sci.math, June 3, 2015

Link: https://groups.google.com/forum/#!topicsearchin/sci.math/largest$20AND$20authorname$3A%22Archimedes$20Plutonium%22$20AND$20before$3A2015$2F06$2F07/sci.math/9ZlZKMFEt-Q


AP is perhaps the most famous math crank on the internet. The insanity goes way back. In his heyday some decades ago, he wrote...

"The totality, everything that there is [the universe], is only 1 atom of plutonium. There is nothing outside or beyond this one atom of plutonium."
-- Ludwig (aka Archimedes) Plutonium, sci.math, April 4, 1994

Link: https://groups.google.com/forum/#!topicsearchin/sci.math/faq$20and$20atom$20AND$20universe$20AND$20before$3A1996$2F01$2F01/sci.math/lIIVtZjeGhk


A word of caution to students: Do not attempt to use AP's "system" in any course work in any high school, college or university on the planet. You will fail miserably. His goofy system is certainly no "shortcut" to success in mathematics. On the contrary, it is a dead end and would be a complete waste of your time.


Dan

Download my DC Proof 2.0 software at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com
Archimedes Plutonium
2015-09-02 20:24:21 UTC
Permalink
I don't usually engage the trolls directly. I compile lists of their typical rantings and post them as a warning to others who may be taken in, wasting their valuable time or worse. I don't usually post more than one such warning per thread.
#4#
--- quoting Davidson's attempt at Euclid's IP ---

Iain Davidson wrote:

 Posted:  Aug 25, 2009 8:43 PM
 On 25 Aug, 20:57, Archimedes Plutonium
Here is the Challenge of proving Euclid's Infinitude of Primes. The
challenge is to write both direct and
indirect methods out.
Because of your limited mathematical ability, you forget
to mention that the key theorem for both the "direct method"
and the "indirect method" is
Every integer >1 is divisible by a prime

Direct 
Th. 1 Every integer >1 is divisible by a prime 
If you can find n primes, then you can find n+1 primes. 
Add 1 to the product of the n primes you have found. 
The resulting number (>1) is not divisble by any of the 
primes that have been found, but by Th.1 this number must have 
another prime divisor. 
Therefore there is an n+1th prime and this implies the number 
of primes is infinite as the process could be repeated 
ad infinitum.

Indirect 
Th. 1 Every integer >1 is divisible by a prime 
Assume that there are only a finite number of primes 
Add 1 to the product of all the primes assumed to exist. 
The resulting number (>1) is not divisble by any of the primes 
assumed to exist, but by Th.1 this number must have a prime divisor. 
Contradiction. Therfore, the number of primes is not finite.

--- end quoting Iain Davidson's attempt at Euclid IP, direct and 
indirect ---

Davidson makes the same myth-mistake, by believing 
that the Direct method can be virtually identical to the Indirect, in 
the 
mechanism of the proof. The error of running a prime factor search in 
both, and failing to recognize that Euclid's Number is necessarily 
prime 
in the Indirect.

Another major error by Davidson, is the error of 
never starting the proof by the definition of prime. When you fail to 
start the Euclid IP proof with the definition, then after forming 
"multiply the 
lot and add 1" you can not have any inspection of that newly formed number, since you have no definition of what is a prime. You easily go astray with not knowing what this new 
number 
is, for you have no first step of the proof of -- definition-- to 
measure this 
new number. If Davidson had started his attempts with 
the 
definition of prime, then after he formed Euclid's Number, he may 
have 
realized that Euclid's Number is necessarily a new prime in the 
Indirect.

So Davidson seems to be unaware of two myths that they 
commit. The myth that direct can be identical to indirect, and the 
myth that 
you can start a proof of mathematics without the vital first step of 
the definitions 
of the concepts under review.

AP1990s Survey
Many of AP's postings can be safely ignored as well. But once he starts peddling his mathematical snake oil promising an "easier way" for students to do calculus, for example, I think they really ought to be warned about him.
Yeah, I probably have too much time on my hand and should get out more. Sigh...
Dan
Dan seems to have lost sight that sci.math is about math, not about hatred of people and plastering hate-sheets all over the place, but when a person is insane, insanity is where "no reasoning can enter". One can only "use insane people like Dan", like one makes use of horse-manure as a fertilizer for the lawn and grounds.

AP
a***@gmail.com
2015-09-05 00:33:15 UTC
Permalink
that is quite a trivial "same two prOOfs
Post by Archimedes Plutonium
Dan seems to have lost sight that sci.math is about math, not about hatred of people and plastering hate-sheets all over the place, but when a person is insane, insanity is where "no reasoning can enter". One can only "use insane people like Dan", like one makes use of horse-manure as a fertilizer for the lawn and grounds.
AP
a***@gmail.com
2015-09-05 20:22:52 UTC
Permalink
I mean,
your dystinction between indirect & direct is a)
a***@gmail.com
2015-09-11 03:03:33 UTC
Permalink
notice that both a.p and j.g ever can respond to me; hm

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