Discussion:
The problem with trying to define rational numbers using set theory.
(too old to reply)
John Gabriel
2016-08-21 20:54:18 UTC
Permalink
The first major stumbling block is that in order to define rational numbers using set theory, we already need to know how to "count". Did you get that?

That's right, you need to be able to compute the cardinality of a given set. Unless you are one of Cantor's delusional followers, cardinal value means NUMBER, not bijective cardinality myths involving sets whose members are not distinct, that is, the illusion of infinitely many points. Wake up you fucking morons!

Now, do you have any clue what effort went into deriving the machinery of counting numbers which came long after ratios of MAGNITUDES ???

Of course you don't. Chances are good you're a retard who has been brainwashed to believe in the bullshit that you do.

Unless you have my read my article, you don't have a clue what it means to be a "number":

https://www.linkedin.com/pulse/how-we-got-numbers-john-gabriel?trk=seokp_posts_primary_cluster_res_photo

After reading that article, ask yourself O moron, does set theory require the natural numbers to be in place? Hint: YES

Does the von Neumann ordinal approach make any sense at all? Hint: NO



Is there any valid construction of irrational number? Hint: NO

https://drive.google.com/open?id=0B-mOEooW03iLSTROakNyVXlQUEU

Since there is no valid construction of irrational number, can there be any valid mathematical concept for real number? Hint: NO
John Gabriel
2016-08-21 21:06:50 UTC
Permalink
Post by John Gabriel
The first major stumbling block is that in order to define rational numbers using set theory, we already need to know how to "count". Did you get that?
That's right, you need to be able to compute the cardinality of a given set. Unless you are one of Cantor's delusional followers, cardinal value means NUMBER, not bijective cardinality myths involving sets whose members are not distinct, that is, the illusion of infinitely many points. Wake up you fucking morons!
Now, do you have any clue what effort went into deriving the machinery of counting numbers which came long after ratios of MAGNITUDES ???
Of course you don't. Chances are good you're a retard who has been brainwashed to believe in the bullshit that you do.
https://www.linkedin.com/pulse/how-we-got-numbers-john-gabriel?trk=seokp_posts_primary_cluster_res_photo
After reading that article, ask yourself O moron, does set theory require the natural numbers to be in place? Hint: YES
Does the von Neumann ordinal approach make any sense at all? Hint: NO
http://youtu.be/qkSE6NoOptQ
Is there any valid construction of irrational number? Hint: NO
https://drive.google.com/open?id=0B-mOEooW03iLSTROakNyVXlQUEU
Since there is no valid construction of irrational number, can there be any valid mathematical concept for real number? Hint: NO
Unless you know how many elements are in a set, it is entirely f..g useless.

The sets {Idiot, retard, imbecile} and {Virgil, dan christensen, freda parkins} are EXACTLY equal. But what does that tell you about the measure of a number you fucking morons? Hint: Nothing.

All it tells you is that there are 6 permutations between the two sets:

Virgil - DC - Parkins
- Parkins - DC

DC - Virgil - Parkins
- Parkins - Virgil

Parkins - DC - Virgil
- Virgil - DC

So, now that your teacher has patted you on the back and called you clever because of your combinatorial skills (*), do you see that it's not possible to define numbers using set theory?

The bumbling moron Robin Chapman may have some tricks up his sleeve wrt combinatorics, but the fucking idiot has no clue what it means to be a number.

(*) I can't tell you how many papers I've read on combinatorics that are not even interesting, never mind useful. The majority are plagiarism of previous works with an added new pattern observed by the monkey compiling a new dissertation. Did I mention that monkeys are able to recognise patterns almost as good as humans? Chuckle. Recognising patterns is not a sure sign of intelligence.
John Gabriel
2016-08-21 21:08:03 UTC
Permalink
Post by John Gabriel
Post by John Gabriel
The first major stumbling block is that in order to define rational numbers using set theory, we already need to know how to "count". Did you get that?
That's right, you need to be able to compute the cardinality of a given set. Unless you are one of Cantor's delusional followers, cardinal value means NUMBER, not bijective cardinality myths involving sets whose members are not distinct, that is, the illusion of infinitely many points. Wake up you fucking morons!
Now, do you have any clue what effort went into deriving the machinery of counting numbers which came long after ratios of MAGNITUDES ???
Of course you don't. Chances are good you're a retard who has been brainwashed to believe in the bullshit that you do.
https://www.linkedin.com/pulse/how-we-got-numbers-john-gabriel?trk=seokp_posts_primary_cluster_res_photo
After reading that article, ask yourself O moron, does set theory require the natural numbers to be in place? Hint: YES
Does the von Neumann ordinal approach make any sense at all? Hint: NO
http://youtu.be/qkSE6NoOptQ
Is there any valid construction of irrational number? Hint: NO
https://drive.google.com/open?id=0B-mOEooW03iLSTROakNyVXlQUEU
Since there is no valid construction of irrational number, can there be any valid mathematical concept for real number? Hint: NO
Unless you know how many elements are in a set, it is entirely f..g useless.
The sets {Idiot, retard, imbecile} and {Virgil, dan christensen, freda parkins} are EXACTLY equal. But what does that tell you about the measure of a number you fucking morons? Hint: Nothing.
Virgil - DC - Parkins
- Parkins - DC
DC - Virgil - Parkins
- Parkins - Virgil
Parkins - DC - Virgil
- Virgil - DC
So, now that your teacher has patted you on the back and called you clever because of your combinatorial skills (*), do you see that it's not possible to define numbers using set theory?
The bumbling moron Robin Chapman may have some tricks up his sleeve wrt combinatorics, but the fucking idiot has no clue what it means to be a number.
(*) I can't tell you how many papers I've read on combinatorics that are not even interesting, never mind useful. The majority are plagiarism of previous works with an added new pattern observed by the monkey compiling a new dissertation. Did I mention that monkeys are able to recognise patterns almost as good as humans? Chuckle. Recognising patterns is not a sure sign of intelligence.
Sorry, there are 9 permutations. It doesn't change my message. It's getting late here. I think I need to rest. Chuckle.
Sergio
2016-08-22 00:17:38 UTC
Permalink
Shut up, asswipe.
John Gabriel
2016-08-22 01:55:48 UTC
Permalink
Post by Sergio
Shut up, asswipe.
I fuck you up so bad if you could get away from your keyboard.

You have a big mouth posting as an anonymous cunt but I would close it for good.

Tell me where we can meet?
Dan Christensen
2016-08-22 03:09:59 UTC
Permalink
The first major stumbling block...
No stumbling block, Troll Boy. Using set theory, you construct integers as ordered pairs natural numbers, then construct rational numbers as ordered pairs of integers. Of course, you also need to construct addition and multiplication functions on each of these sets. Way beyond your abilities, I'm sure. You are still stuck on 2+2=4. You STILL haven't been able to derive this and other elementary results in your goofy system.

Dan
Peter Percival
2016-08-22 11:19:53 UTC
Permalink
Post by Dan Christensen
The first major stumbling block...
No stumbling block, Troll Boy. Using set theory, you construct
integers as ordered pairs natural numbers, then construct rational
numbers as ordered pairs of integers.
Realy? Who does that, apart from you?
--
I have had a tremor of bliss, a wink of heaven, a whisper,
And I would no longer be denied; all things
Proceed to a joyful consummation.
Becket through the pen of Eliot, /Murder in the Cathedral/
John Gabriel
2016-08-22 12:01:07 UTC
Permalink
Post by Peter Percival
Post by Dan Christensen
The first major stumbling block...
No stumbling block, Troll Boy. Using set theory, you construct
integers as ordered pairs natural numbers, then construct rational
numbers as ordered pairs of integers.
Realy? Who does that, apart from you?
You'll notice that the moron DC just ignored the fact that my OP stated clearly that one needs to know how to count, in other words, the natural numbers must already be in place.

One can't argue with an irrational mind such as DC. He's not a troll for nothing.
Post by Peter Percival
--
I have had a tremor of bliss, a wink of heaven, a whisper,
And I would no longer be denied; all things
Proceed to a joyful consummation.
Becket through the pen of Eliot, /Murder in the Cathedral/
Dan Christensen
2016-08-22 13:11:37 UTC
Permalink
Post by Peter Percival
Post by Dan Christensen
The first major stumbling block...
No stumbling block, Troll Boy. Using set theory, you construct
integers as ordered pairs natural numbers, then construct rational
numbers as ordered pairs of integers.
Realy? Who does that, apart from you?
You'll notice...
John Gabriel is a buffoon. He knows NOTHING about mathematics, but seems to delight in confusing and misleading students here, "messing with their minds" as he probably thinks of it. What readers should know about 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 greatest mathematician ever.”
-- June 21, 2016

“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

"There are no axioms required when concepts are well defined. My mathematics is well defined."
--June 21, 2016


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

“All those who don't accept New Calculus, you better say goodbye to your kids. Because John Gabriel is coming.”
-- July 9, 2014

Some months later, JG claimed this posting of July 9, was the work of an impostor. Do we believe him? I'm not inclined to since only four days later, on July 13, he also posted and subsequently confirmed:

"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...

“In the early 20th century, there was a eugenics program in the United States. Too bad it was halted... 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

(Links to an archive of original postings available on request. Serious enquiries only.)


JG's Just Plain Stupid:

“100 years have shown that nothing Einstein predicted is correct.” (“Jewish” science, right, JG?)
-- March 23, 2016

“To claim that all the natural numbers are in the set N, one must be able to list them all from beginning to the end.”
-- December 2, 2015

“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

“A set by definition, cannot be empty.” *** NEW ***
-- July 27, 2016

“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 international Jewish conspiracy, JG?)
-- March 17, 2015

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

"You don't need associativity or commutativity or any other crap."
--June 21, 2016

“Axioms not required in mathematics.”
-- July 4, 2016

JG doesn't like proofs. In his wacky system, he cannot even prove that 2+2=4. It seems unlikely to me that he would have anything worthwhile to say about mathematics. On the contrary, it seems he is deliberately trying to mislead and confuse students 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
Dan Christensen
2016-08-22 13:10:01 UTC
Permalink
Post by Peter Percival
Post by Dan Christensen
The first major stumbling block...
No stumbling block, Troll Boy. Using set theory, you construct
integers as ordered pairs natural numbers, then construct rational
numbers as ordered pairs of integers.
Realy? Who does that, apart from you?
Not you obviously, but anyone who wants to formally develop mathematics from first principles with maximum rigour and zero hand-waving.


Dan

Download my DC Proof 2.0 software at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com
Peter Percival
2016-08-22 13:35:02 UTC
Permalink
Post by Dan Christensen
Post by Peter Percival
Post by Dan Christensen
The first major stumbling block...
No stumbling block, Troll Boy. Using set theory, you construct
integers as ordered pairs natural numbers, then construct rational
numbers as ordered pairs of integers.
Realy? Who does that, apart from you?
Not you obviously, but anyone who wants to formally develop mathematics from first principles with maximum rigour and zero hand-waving.
So give some references.
--
I have had a tremor of bliss, a wink of heaven, a whisper,
And I would no longer be denied; all things
Proceed to a joyful consummation.
Becket through the pen of Eliot, /Murder in the Cathedral/
WM
2016-08-22 15:18:40 UTC
Permalink
Post by Dan Christensen
Post by Peter Percival
Realy? Who does that, apart from you?
Not you obviously, but anyone who wants to formally develop mathematics from first principles
Who would need that? It has been done several times already.
Post by Dan Christensen
with maximum rigour and zero hand-waving.
Not for zero, but for 1, 2, 3, 4, ... handwaving is required because other handwaving would yield 2, 3, 5, 7, ... and handwaving different from that results in 2, 4, 8, 16, ...

Regards, WM
Dan Christensen
2016-08-22 15:34:24 UTC
Permalink
Post by WM
Post by Dan Christensen
Post by Peter Percival
Realy? Who does that, apart from you?
Not you obviously, but anyone who wants to formally develop mathematics from first principles
Who would need that? It has been done several times already.
Is that why you yourself presented your own goofy axioms for the set of natural numbers, Mucke? You couldn't even prove that 1=/=2.
Post by WM
Post by Dan Christensen
with maximum rigour and zero hand-waving.
Not for zero, but for 1, 2, 3, 4, ... handwaving is required because other handwaving would yield 2, 3, 5, 7, ... and handwaving different from that results in 2, 4, 8, 16, ...
More absurd quotes from Wolfgang Muckenheim (WM):

“In my system, two different numbers can have the same value.”
-- sci.math, 2014/10/16

“1+2 and 2+1 are different numbers.”
-- sci.math, 2014/10/20

“1/9 has no decimal representation.”
-- sci.math, 2015/09/22

"0.999... is not 1."
-- sci.logic 2015/11/25

“Axioms are rubbish!”
-- sci.math, 2014/11/19

“No set is countable, not even |N.”
-- sci.logic, 2015/08/05

“Countable is an inconsistent notion.”
-- sci.math, 2015/12/05

“A [natural] number with aleph_0 digits is not less than aleph_0.”
-- sci.math, 2015/08/12

“The notion of aleph_0 is not meaningful.”
-- sci.math, 2015/08/28


Slipping ever more deeply into madness...

“There is no actually infinite set |N.”
-- sci.math, 2015/10/26

“|N is not covered by the set of natural numbers.”
-- sci.math, 2015/10/26

“The set of all rationals can be shown not to exist.”
--sci.math, 2015/11/28

“Everything is in the list of everything and therefore everything belongs to a not uncountable set.”
-- sci.math, 2015/11/30

"'Not equal' and 'equal can mean the same.”
-- sci.math, 2016/06/09



A special word of caution to students: Do not attempt to use WM's “system” (MuckeMath) in any course work in any high school, college or university on the planet. You will fail miserably. MuckeMath is certainly no shortcut to success in mathematics.

Using WM's “axioms” for the natural numbers, he cannot prove that 1=/=2 or the existence of even a single number. 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
Virgil
2016-08-22 18:50:39 UTC
Permalink
Post by WM
Post by Dan Christensen
Post by Peter Percival
Realy? Who does that, apart from you?
Not you obviously, but anyone who wants to formally develop mathematics
from first principles
Who would need that? It has been done several times already.
Post by Dan Christensen
with maximum rigour and zero hand-waving.
Not for zero, but for 1, 2, 3, 4, ... handwaving is required because other
handwaving would yield 2, 3, 5, 7, ... and handwaving different from that
results in 2, 4, 8, 16, ...
Absence of handwaving, at least outside of WM's witless worthless wacky
world of WMytheology, has produced the naturals, but admittedly WM's
handwaving does not!
--
Virgil
"Mit der Dummheit kampfen Gotter selbst vergebens." (Schiller)
Python
2016-08-22 13:22:35 UTC
Permalink
Post by Peter Percival
Post by Dan Christensen
The first major stumbling block...
No stumbling block, Troll Boy. Using set theory, you construct
integers as ordered pairs natural numbers, then construct rational
numbers as ordered pairs of integers.
Realy? Who does that, apart from you?
People using the COQ proving system does that:

https://coq.inria.fr/library/Coq.QArith.QArith_base.html

same in Isabelle/HOL system (read the source!)

afaik, almost EVERY theorem prover in the world defines constructively
rationals that way.

You don't know much about how real software formal provers works,
do you Peter?
Peter Percival
2016-08-22 13:43:59 UTC
Permalink
Post by Python
Post by Peter Percival
Post by Dan Christensen
The first major stumbling block...
No stumbling block, Troll Boy. Using set theory, you construct
integers as ordered pairs natural numbers, then construct rational
numbers as ordered pairs of integers.
Realy? Who does that, apart from you?
https://coq.inria.fr/library/Coq.QArith.QArith_base.html
same in Isabelle/HOL system (read the source!)
afaik, almost EVERY theorem prover in the world defines constructively
rationals that way.
You don't know much about how real software formal provers works,
do you Peter?
I know nothing about how such things work. I was asking Dan to cite
some people who construct integers as ordered pairs natural numbers, and
then construct rational numbers as ordered pairs of integers. The
reason I was asking is that I am familiar (well, you know, more or less)
with the definition of integer as being an equivalence class of pairs of
natural numbers, and the definition of rational number as being an
equivalence class of pairs of integers. Such is the extent of my
ignorance that I do not even know if Dan's "construct" means "define".
--
I have had a tremor of bliss, a wink of heaven, a whisper,
And I would no longer be denied; all things
Proceed to a joyful consummation.
Becket through the pen of Eliot, /Murder in the Cathedral/
Python
2016-08-22 13:46:18 UTC
Permalink
Post by Peter Percival
Post by Python
Post by Peter Percival
Post by Dan Christensen
The first major stumbling block...
No stumbling block, Troll Boy. Using set theory, you construct
integers as ordered pairs natural numbers, then construct rational
numbers as ordered pairs of integers.
Realy? Who does that, apart from you?
https://coq.inria.fr/library/Coq.QArith.QArith_base.html
same in Isabelle/HOL system (read the source!)
afaik, almost EVERY theorem prover in the world defines constructively
rationals that way.
You don't know much about how real software formal provers works,
do you Peter?
I know nothing about how such things work. I was asking Dan to cite
some people who construct integers as ordered pairs natural numbers, and
then construct rational numbers as ordered pairs of integers. The
reason I was asking is that I am familiar (well, you know, more or less)
with the definition of integer as being an equivalence class of pairs of
natural numbers, and the definition of rational number as being an
equivalence class of pairs of integers. Such is the extent of my
ignorance that I do not even know if Dan's "construct" means "define".
You are definitely weird Peter. Somewhat insane.
Peter Percival
2016-08-22 14:19:25 UTC
Permalink
Post by Python
Post by Peter Percival
Post by Python
Post by Peter Percival
Post by Dan Christensen
The first major stumbling block...
No stumbling block, Troll Boy. Using set theory, you construct
integers as ordered pairs natural numbers, then construct rational
numbers as ordered pairs of integers.
Realy? Who does that, apart from you?
https://coq.inria.fr/library/Coq.QArith.QArith_base.html
same in Isabelle/HOL system (read the source!)
afaik, almost EVERY theorem prover in the world defines constructively
rationals that way.
You don't know much about how real software formal provers works,
do you Peter?
I know nothing about how such things work. I was asking Dan to cite
some people who construct integers as ordered pairs natural numbers, and
then construct rational numbers as ordered pairs of integers. The
reason I was asking is that I am familiar (well, you know, more or less)
with the definition of integer as being an equivalence class of pairs of
natural numbers, and the definition of rational number as being an
equivalence class of pairs of integers. Such is the extent of my
ignorance that I do not even know if Dan's "construct" means "define".
You are definitely weird Peter. Somewhat insane.
How does that relate to the matter being discussed? Dan is very unfond
of sticking to the subject, I hope you're not the same. So tell me how
does the question of whether an integer is a pair of natural numbers or
an equivalence class of pairs of natural numbers (in the context of
defined ("constructing" if you like) integers in PA) relate to me
being--acording to you--definitely weird and somewhat insane?
--
I have had a tremor of bliss, a wink of heaven, a whisper,
And I would no longer be denied; all things
Proceed to a joyful consummation.
Becket through the pen of Eliot, /Murder in the Cathedral/
Python
2016-08-22 14:28:26 UTC
Permalink
...
Post by Peter Percival
Post by Python
You are definitely weird Peter. Somewhat insane.
How does that relate to the matter being discussed? Dan is very unfond
of sticking to the subject, I hope you're not the same. So tell me how
does the question of whether an integer is a pair of natural numbers or
an equivalence class of pairs of natural numbers (in the context of
defined ("constructing" if you like) integers in PA) relate to me
being--acording to you--definitely weird and somewhat insane?
Post by Python
No stumbling block, Troll Boy. Using set theory, you construct
integers as ordered pairs natural numbers, then construct rational
numbers as ordered pairs of integers.
Realy? Who does that, apart from you?
I am familiar (well, you know, more or less)
with the definition of integer as being an equivalence class of pairs of
natural numbers, and the definition of rational number as being an
equivalence class of pairs of integers.
If you cannot see the kind of mental insanity you are showing, nobody
can help you Mr Percival.
Peter Percival
2016-08-22 16:24:46 UTC
Permalink
Post by Python
...
Post by Peter Percival
Post by Python
You are definitely weird Peter. Somewhat insane.
How does that relate to the matter being discussed? Dan is very unfond
of sticking to the subject, I hope you're not the same. So tell me how
does the question of whether an integer is a pair of natural numbers or
an equivalence class of pairs of natural numbers (in the context of
defined ("constructing" if you like) integers in PA) relate to me
being--acording to you--definitely weird and somewhat insane?
Post by Python
No stumbling block, Troll Boy. Using set theory, you construct
integers as ordered pairs natural numbers, then construct rational
numbers as ordered pairs of integers.
Realy? Who does that, apart from you?
I am familiar (well, you know, more or less)
with the definition of integer as being an equivalence class of pairs of
natural numbers, and the definition of rational number as being an
equivalence class of pairs of integers.
If you cannot see the kind of mental insanity you are showing, nobody
can help you Mr Percival.
I wasn't asking about what I can see, nor am I seeking help, I was
asking about the relevance of me being weird and somewhat insane (as
claimed by you) to Dan's claim about integers and rational numbers.

Incidentally, I didn't write "(as claimed by you)" as a half-hearted
attempt at denying that I am weird and somewhat insane. I put it there
for the benefit of anyone reading this thread in the middle and
wondering where that claim came from.
--
I have had a tremor of bliss, a wink of heaven, a whisper,
And I would no longer be denied; all things
Proceed to a joyful consummation.
Becket through the pen of Eliot, /Murder in the Cathedral/
John Gabriel
2016-08-22 14:29:52 UTC
Permalink
Post by Peter Percival
Post by Python
Post by Peter Percival
Post by Python
Post by Peter Percival
Post by Dan Christensen
The first major stumbling block...
No stumbling block, Troll Boy. Using set theory, you construct
integers as ordered pairs natural numbers, then construct rational
numbers as ordered pairs of integers.
Realy? Who does that, apart from you?
https://coq.inria.fr/library/Coq.QArith.QArith_base.html
same in Isabelle/HOL system (read the source!)
afaik, almost EVERY theorem prover in the world defines constructively
rationals that way.
You don't know much about how real software formal provers works,
do you Peter?
I know nothing about how such things work. I was asking Dan to cite
some people who construct integers as ordered pairs natural numbers, and
then construct rational numbers as ordered pairs of integers. The
reason I was asking is that I am familiar (well, you know, more or less)
with the definition of integer as being an equivalence class of pairs of
natural numbers, and the definition of rational number as being an
equivalence class of pairs of integers. Such is the extent of my
ignorance that I do not even know if Dan's "construct" means "define".
You are definitely weird Peter. Somewhat insane.
How does that relate to the matter being discussed? Dan is very unfond
of sticking to the subject, I hope you're not the same. So tell me how
does the question of whether an integer is a pair of natural numbers or
an equivalence class of pairs of natural numbers (in the context of
defined ("constructing" if you like) integers in PA) relate to me
being--acording to you--definitely weird and somewhat insane?
It's insane because you have gone against the decree of the mainstream orangutans and questioned "standard knowledge".

You are henceforth excommunicated! An integer is NOT a pair of natural numbers, it is a SIGNED or UNSIGNED natural number.

A natural number is a RATIO of two magnitudes p:q where q is the chosen unit and p is a multiple of q.

A rational number is a ratio of integers or in long form, a rational number is a ratio of ratios of magnitudes that are unit multiples.

My article explains the perfect derivation:

https://www.linkedin.com/pulse/how-we-got-numbers-john-gabriel?trk=seokp_posts_primary_cluster_res_photo
Post by Peter Percival
--
I have had a tremor of bliss, a wink of heaven, a whisper,
And I would no longer be denied; all things
Proceed to a joyful consummation.
Becket through the pen of Eliot, /Murder in the Cathedral/
Peter Percival
2016-08-22 17:27:03 UTC
Permalink
Post by Peter Percival
Post by Python
Post by Peter Percival
Post by Python
Post by Peter Percival
Post by Dan Christensen
The first major stumbling block...
No stumbling block, Troll Boy. Using set theory, you construct
integers as ordered pairs natural numbers, then construct rational
numbers as ordered pairs of integers.
Realy? Who does that, apart from you?
https://coq.inria.fr/library/Coq.QArith.QArith_base.html
same in Isabelle/HOL system (read the source!)
afaik, almost EVERY theorem prover in the world defines constructively
rationals that way.
You don't know much about how real software formal provers works,
do you Peter?
I know nothing about how such things work. I was asking Dan to cite
some people who construct integers as ordered pairs natural numbers, and
then construct rational numbers as ordered pairs of integers. The
reason I was asking is that I am familiar (well, you know, more or less)
with the definition of integer as being an equivalence class of pairs of
natural numbers, and the definition of rational number as being an
equivalence class of pairs of integers. Such is the extent of my
ignorance that I do not even know if Dan's "construct" means "define".
You are definitely weird Peter. Somewhat insane.
How does that relate to the matter being discussed? Dan is very unfond
of sticking to the subject, I hope you're not the same. So tell me how
does the question of whether an integer is a pair of natural numbers or
an equivalence class of pairs of natural numbers (in the context of
defined ("constructing" if you like) integers in PA)
Should be

(in the context of defining ("constructing" if you like) integers in PA)

my apologies.
Post by Peter Percival
relate to me
being--acording to you--definitely weird and somewhat insane?
--
I have had a tremor of bliss, a wink of heaven, a whisper,
And I would no longer be denied; all things
Proceed to a joyful consummation.
Becket through the pen of Eliot, /Murder in the Cathedral/
Dan Christensen
2016-08-22 14:11:45 UTC
Permalink
Post by Peter Percival
Such is the extent of my
ignorance that I do not even know if Dan's "construct" means "define".
This actually explains a lot. You are probably not alone in this here, Peter.


Example 1: If we have a set A, we can infer the existence of (i.e. "construct") the power set of A using the Power Set Axiom of whatever set theory you may prefer. (I think this is a common usage of the word. Perhaps a holdover from Euclidean geometry?)

Example 2: If we have sets A and B, we can infer the existence of (i.e. "construct") the union of A and B using the Union Axiom.

I hope this helps.


Dan

Download my DC Proof 2.0 software at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com
WM
2016-08-22 15:12:56 UTC
Permalink
Post by Dan Christensen
Example 1: If we have a set A, we can infer the existence of (i.e. "construct") the power set of A using the Power Set Axiom of whatever set theory you may prefer.
Not in set theory. The power set is not absolute. You cannot construct an uncountable power set of |N.

See: The relativeness of the power set in
https://www.hs-augsburg.de/~mueckenh/Transfinity/Transfinity/pdf

Regards, WM
Dan Christensen
2016-08-22 15:29:37 UTC
Permalink
Post by WM
Post by Dan Christensen
Example 1: If we have a set A, we can infer the existence of (i.e. "construct") the power set of A using the Power Set Axiom of whatever set theory you may prefer.
Not in set theory. The power set is not absolute. You cannot construct an uncountable power set of |N.
Wrong again, Mucke. Here is my formal proof that the power set of N is uncountable:

http://www.dcproof.com/Countable.htm

Let me know if you have any questions about.


Dan

Download my DC Proof 2.0 software at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com
Peter Percival
2016-08-22 17:05:16 UTC
Permalink
Post by Dan Christensen
Post by WM
Post by Dan Christensen
Example 1: If we have a set A, we can infer the existence of (i.e. "construct") the power set of A using the Power Set Axiom of whatever set theory you may prefer.
Not in set theory. The power set is not absolute. You cannot construct an uncountable power set of |N.
Wrong again, Mucke.
All constructible sets are countable.
Post by Dan Christensen
http://www.dcproof.com/Countable.htm
Let me know if you have any questions about.
Dan
Download my DC Proof 2.0 software at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com
--
I have had a tremor of bliss, a wink of heaven, a whisper,
And I would no longer be denied; all things
Proceed to a joyful consummation.
Becket through the pen of Eliot, /Murder in the Cathedral/
Dan Christensen
2016-08-22 17:34:10 UTC
Permalink
Post by Peter Percival
Post by Dan Christensen
Post by WM
Post by Dan Christensen
Example 1: If we have a set A, we can infer the existence of (i.e. "construct") the power set of A using the Power Set Axiom of whatever set theory you may prefer.
Not in set theory. The power set is not absolute. You cannot construct an uncountable power set of |N.
Wrong again, Mucke.
All constructible sets are countable.
Not sure what you mean by "constructible", but you can see my formal proof that the power set of the set of natural numbers is uncountable at http://www.dcproof.com/Countable.htm

Dan
Download my DC Proof 2.0 software at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com
Peter Percival
2016-08-22 17:45:02 UTC
Permalink
Post by Dan Christensen
Post by Peter Percival
Post by Dan Christensen
Post by WM
Post by Dan Christensen
Example 1: If we have a set A, we can infer the existence of (i.e. "construct") the power set of A using the Power Set Axiom of whatever set theory you may prefer.
Not in set theory. The power set is not absolute. You cannot construct an uncountable power set of |N.
Wrong again, Mucke.
All constructible sets are countable.
Not sure what you mean by "constructible",
Nor WM's "The power set is not absolute."?
Post by Dan Christensen
but you can see my formal proof that the power set of the set of natural numbers is uncountable at http://www.dcproof.com/Countable.htm
Dan
Download my DC Proof 2.0 software at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com
--
I have had a tremor of bliss, a wink of heaven, a whisper,
And I would no longer be denied; all things
Proceed to a joyful consummation.
Becket through the pen of Eliot, /Murder in the Cathedral/
WM
2016-08-23 12:28:05 UTC
Permalink
Post by Dan Christensen
Post by Peter Percival
Post by Dan Christensen
Post by WM
Post by Dan Christensen
Example 1: If we have a set A, we can infer the existence of (i.e. "construct") the power set of A using the Power Set Axiom of whatever set theory you may prefer.
Not in set theory. The power set is not absolute. You cannot construct an uncountable power set of |N.
Wrong again, Mucke.
All constructible sets are countable.
Not sure what you mean by "constructible",
Your example 1. You often use words the meaning of which you don't know?
Post by Dan Christensen
but you can see my formal proof that the power set of the set of natural numbers is uncountable at http://www.dcproof.com/Countable.htm
That has nothing to do with constructing it.

Regards, WM
John Gabriel
2016-08-23 13:56:45 UTC
Permalink
Post by Dan Christensen
Post by Peter Percival
Post by Dan Christensen
Post by WM
Post by Dan Christensen
Example 1: If we have a set A, we can infer the existence of (i.e. "construct") the power set of A using the Power Set Axiom of whatever set theory you may prefer.
Not in set theory. The power set is not absolute. You cannot construct an uncountable power set of |N.
Wrong again, Mucke.
All constructible sets are countable.
Not sure what you mean by "constructible",
Your example 1. You often use words the meaning of which you don't know?'s
That's the least of the troll worries, a power set has nothing to do with the topic at hand, but how can such an imbecile know?
Post by Dan Christensen
but you can see my formal proof that the power set of the set of natural numbers is uncountable at http://www.dcproof.com/Countable.htm
That has nothing to do with constructing it.
Regards, WM
Virgil
2016-08-23 18:27:58 UTC
Permalink
Post by WM
Post by Dan Christensen
Post by Peter Percival
Post by Dan Christensen
Post by WM
Post by Dan Christensen
Example 1: If we have a set A, we can infer the existence of (i.e.
"construct") the power set of A using the Power Set Axiom of whatever
set theory you may prefer.
Not in set theory. The power set is not absolute. You cannot construct
an uncountable power set of |N.
Wrong again, Mucke.
All constructible sets are countable.
Not sure what you mean by "constructible",
Your example 1. You often use words the meaning of which you don't know?
It is WM's own use of the word that is unclear, rather than anyone
else's.

The same lacks of clarity corrupt all WM's posts!

In Mathematics, Cantor is provably right,
proving both Card(Q) = Card(N) and Card(N) < Card(R)
So Card(Q) < Card(R), with fewer rationals than reals

In WM's weird WMytheology, WM falsely claims Cantor is wrong,
WM claiming Card(Q) > Card(N) and Card(N) = Card(R)
So Card(Q) > Card(R), with more rationals than reals.

But everywhere outside of WM's wierd WMytheology there are more reals
than rationals.
--
Virgil
"Mit der Dummheit kampfen Gotter selbst vergebens." (Schiller)
Vinicius Claudino Ferraz
2016-08-23 20:58:08 UTC
Permalink
Post by Virgil
In Mathematics, Cantor is provably right,
proving both Card(Q) = Card(N) and Card(N) < Card(R)
So Card(Q) < Card(R), with fewer rationals than reals
In WM's weird WMytheology, WM falsely claims Cantor is wrong,
WM claiming Card(Q) > Card(N) and Card(N) = Card(R)
So Card(Q) > Card(R), with more rationals than reals.
But everywhere outside of WM's wierd WMytheology there are more reals
than rationals.
--
Virgil
"Mit der Dummheit kampfen Gotter selbst vergebens." (Schiller)
AMEM.

My Today's thesis is that sci.math has a liturgy.
Virgil always prays the same.
J. Gabriel is always nazi.
And...
Fermat is always Fermat. : - )
He did his last move before dying.

Therefore, suppose like Virgil that |N| = 0 and |R| = 1.

Loading Image...:large

Vinicius

twitter.com/mathspiritual

But there's more!

Dialog between intuicionist i and classical logic L:
- yes, exists pi.
- no, there is no pi.
- yes, pi has infinite digits.
- no, there is no infinity.
- i construct sqrt 2 using ruler and compass.
- what is The Last Digit of sqrt 2?
- no, there is no last digit.

And so on.
Virgil
2016-08-23 23:02:56 UTC
Permalink
Post by Vinicius Claudino Ferraz
Post by Virgil
In Mathematics, Cantor is provably right,
proving both Card(Q) = Card(N) and Card(N) < Card(R)
So Card(Q) < Card(R), with fewer rationals than reals
In WM's weird WMytheology, WM falsely claims Cantor is wrong,
WM claiming Card(Q) > Card(N) and Card(N) = Card(R)
So Card(Q) > Card(R), with more rationals than reals.
But everywhere outside of WM's wierd WMytheology there are more reals
than rationals.
--
Virgil
Therefore, suppose like Virgil that |N| = 0 and |R| = 1.
But I do not now, and never previously have, supposed either of those
idiocies.

So Vinicius Claudino Ferraz is wrong in supposing I have supposed them.

I have supposed such things as 0.999... = 1
--
Virgil
"Mit der Dummheit kampfen Gotter selbst vergebens." (Schiller)
Vinicius Claudino Ferraz
2016-08-24 02:40:26 UTC
Permalink
Post by Virgil
So Vinicius Claudino Ferraz is wrong in supposing I have supposed them.
I have supposed such things as 0.999... = 1
Then 0.11111111111111111... = 1/9 ~ [ 1 + 9i ] * k
k integer
What's the problem of 1 * 9 = 9 infinitely many times?
Virgil
2016-08-24 03:49:03 UTC
Permalink
Post by Vinicius Claudino Ferraz
Post by Virgil
So Vinicius Claudino Ferraz is wrong in supposing I have supposed them.
I have supposed such things as 0.999... = 1
Then 0.11111111111111111... = 1/9 ~ [ 1 + 9i ] * k
k integer
NOT "1/9 ~ [ 1 + 9i ] * k, k integer " in my world!
--
Virgil
"Mit der Dummheit kampfen Gotter selbst vergebens." (Schiller)
Vinicius Claudino Ferraz
2016-08-24 21:30:57 UTC
Permalink
Virgil,

this is my relation R
(a + bi) R (ak + bki)
R is reflexive, symmetric and transitive.

z ~ z
z ~ w ==> w ~ z
z ~ w ~ x ==> z ~ x

this is my isomorphism f : Q --> C[Z]/R
f(p/q) = {p/g k + q/g k i ; k \neq 0, k \in Z, g = gcd(p, q)}

f is surjective
f is injective
f(a + b) = f(a) + f(b)
f(ab) = f(a)f(b)

Vinicius
twitter.com/mathspiritual

Have you reincluded the excluded middle?
Post by Virgil
Post by Vinicius Claudino Ferraz
Post by Virgil
So Vinicius Claudino Ferraz is wrong in supposing I have supposed them.
I have supposed such things as 0.999... = 1
Then 0.11111111111111111... = 1/9 ~ [ 1 + 9i ] * k
k integer
NOT "1/9 ~ [ 1 + 9i ] * k, k integer " in my world!
--
Virgil
"Mit der Dummheit kampfen Gotter selbst vergebens." (Schiller)
Virgil
2016-08-24 22:11:26 UTC
Permalink
In article <22387e9e-a68c-429c-a093-***@googlegroups.com>,
Vinicius Claudino Ferraz <***@gmail.com> wrote:


A bunch of garbage!
--
Virgil
"Mit der Dummheit kampfen Gotter selbst vergebens." (Schiller)
Michael F. Stemper
2016-08-24 22:57:40 UTC
Permalink
Post by Vinicius Claudino Ferraz
this is my relation R
(a + bi) R (ak + bki)
R is reflexive, symmetric and transitive.
If 0 is in the domain of this relation, it is not transitive.
--
Michael F. Stemper
Indians scattered on dawn's highway bleeding;
Ghosts crowd the young child's fragile eggshell mind.
Vinicius Claudino Ferraz
2016-08-25 02:43:28 UTC
Permalink
Hell_o, Stemper.

The class of equivalence of 0 is [0]_R = {0 + ki} = ( Z - {0} ) \cdot i.

f(0/q) = {0/g k + q/g k i ; k \neq 0, k \in Z, g = gcd(0, q)}

Well, i meant f(0/q) = [0]_R, so q/g = 1 and therefore gcd(0, q) = q.

Paz e alegria,
Vinícius
twitter.com/mathspiritual
Post by Michael F. Stemper
Post by Vinicius Claudino Ferraz
this is my relation R
(a + bi) R (ak + bki)
R is reflexive, symmetric and transitive.
If 0 is in the domain of this relation, it is not transitive.
--
Michael F. Stemper
Indians scattered on dawn's highway bleeding;
Ghosts crowd the young child's fragile eggshell mind.
But I continue typing every thought.

(1)
Naquele tempo, dizia Riemann aos caipiras: uai, ocê num tá vendo que o trem é meio? Divida um em duas partes iguais. - supôs isso e seguiu.

(2)
Seja uma lemniscata L no plano xy,
Gire L até pi/2, obtenha L'.
Gire L' até estar contida no plano xz, obtenha L''.
Seja M := L'' U L.

(x² + y²)² = a²(x² - y²) <=> (x,y) ∈ L(a)

São tantas lemniscatas!
Estão falando que para todo plano gamma, para toda base e_i, para todo a, existe uma lemni L(gamma, e_i, a). @ufmgbr

(x,z) ∈ L'' <=> (z² + x²)² = a²(z² - x²)
Suponha agora duas variáveis complexas.

z = b + ci
x = d + ei

[(b + ci)² + (d + ei)²]² = a²[(b + ci)² - (d + ei)²]

(3)
Free courses. AE!
https://www.edx.org/school/mitx

(4)
o Brasil é um cátion. @Graffite Tem mais elétrons. Cotas para neutrinos.
Retwwet: @Leandro__Karnal
Sobre Igualdade, Isonomia: https://m.facebook.com/story.php?story_fbid=1747278918847806&id=1603132246595808

Sim, estão faltando elétrons.
- A seara é grande, mas os trabalhadores são poucos. Mateus 9, 37. @Pontifex

(5)
How has << Einstein's shoulder := Lagrange >>
discovered minimal action.
What is an action?
Why does Nature minimize action?
Behind the picture, there must be a painter. an Artist =: alpha_omega
John Gabriel
2016-08-23 23:19:32 UTC
Permalink
Post by Vinicius Claudino Ferraz
Post by Virgil
In Mathematics, Cantor is provably right,
proving both Card(Q) = Card(N) and Card(N) < Card(R)
So Card(Q) < Card(R), with fewer rationals than reals
In WM's weird WMytheology, WM falsely claims Cantor is wrong,
WM claiming Card(Q) > Card(N) and Card(N) = Card(R)
So Card(Q) > Card(R), with more rationals than reals.
But everywhere outside of WM's wierd WMytheology there are more reals
than rationals.
--
Virgil
"Mit der Dummheit kampfen Gotter selbst vergebens." (Schiller)
AMEM.
My Today's thesis is that sci.math has a liturgy.
Virgil always prays the same.
J. Gabriel is always nazi.
You are wrong about this. The nazi on this site is the local bully Dan Christensen who throws a tantrum (by reposting lies and libel about me) every time I ignore him.
Post by Vinicius Claudino Ferraz
And...
Fermat is always Fermat. : - )
He did his last move before dying.
Therefore, suppose like Virgil that |N| = 0 and |R| = 1.
https://pbs.twimg.com/media/Cqkio-cXgAAVTLE.jpg:large
Vinicius
twitter.com/mathspiritual
But there's more!
- yes, exists pi.
- no, there is no pi.
- yes, pi has infinite digits.
- no, there is no infinity.
- i construct sqrt 2 using ruler and compass.
- what is The Last Digit of sqrt 2?
- no, there is no last digit.
And so on.
Virgil
2016-08-22 18:46:31 UTC
Permalink
Post by WM
Post by Dan Christensen
Example 1: If we have a set A, we can infer the existence of (i.e.
"construct") the power set of A using the Power Set Axiom of whatever set
theory you may prefer.
Not in set theory. The power set is not absolute.
Can WM name a set that does not have a power set?
Post by WM
You cannot construct an
uncountable power set of |N.
I can define one! The set of all subset of |N.
Post by WM
See: The relativeness of the power set in
https://www.hs-augsburg.de/~mueckenh
Each and every of those "//www.hs-augsburg.de/~mueckenh" papers are
based on WM's witless worthless wacky world of WMytheology rather than
on any proper mathematics and thus are of no mathematical use or
importance at all, though some of them are unintentionally a bit
amusing.


In Mathematics, Cantor is provably right,
proving both Card(Q) = Card(N) and Card(N) < Card(R)
So Card(Q) < Card(R), with fewer rationals than reals

In WM's weird WMytheology, WM claims Cantor is wrong,
WM claiming Card(Q) > Card(N) and Card(N) = Card(R)
So Card(Q) > Card(R), with more rationals than reals.

But everywhere outside of WM's wierd WMytheology there are more reals
than rationals.

Every rational is also a real but not every real is also a rational
--
Virgil
"Mit der Dummheit kampfen Gotter selbst vergebens." (Schiller)
Me
2016-08-22 14:14:41 UTC
Permalink
Post by Peter Percival
I was asking Dan to cite
some people who construct integers as ordered pairs natural numbers, and
then construct rational numbers as ordered pairs of integers. The
reason I was asking is that I am familiar (well, you know, more or less)
with the definition of integer as being an equivalence class of pairs of
natural numbers, and the definition of rational number as being an
equivalence class of pairs of integers.
Well, I get your point, Peter. On the other hand, I guess we may safely assume that this is what Dan had in mind when claiming "using set theory, you construct integers as ordered pairs natural numbers, then construct rational numbers as ordered pairs of integers."

Of course your formulation is superior from a technical point of view.

I'm sure it's absolutely essential when dealing with a crank like JG to explicitly state these technical details! (Otherwise he might not get the point.)
John Gabriel
2016-08-22 14:21:26 UTC
Permalink
Post by Me
Post by Peter Percival
I was asking Dan to cite
some people who construct integers as ordered pairs natural numbers, and
then construct rational numbers as ordered pairs of integers. The
reason I was asking is that I am familiar (well, you know, more or less)
with the definition of integer as being an equivalence class of pairs of
natural numbers, and the definition of rational number as being an
equivalence class of pairs of integers.
Well, I get your point, Peter. On the other hand, I guess we may safely assume that this is what Dan had in mind when claiming "using set theory, you construct integers as ordered pairs natural numbers, then construct rational numbers as ordered pairs of integers."
Of course your formulation is superior from a technical point of view.
I'm sure it's absolutely essential when dealing with a crank like JG to explicitly state these technical details! (Otherwise he might not get the point.)
What is really cranky is you moron, who understand nothing.

The point of my OP is missed by you and others like you. The natural numbers are RATIOS of magnitudes. These are assumed to be established in the failed derivation of rational numbers using set theory.

You can't argue against this in any rational way. As we've seen, from your past comments, you are an insignificant nobody. No one with respect uses the handle "Me", unless he knows he is an absolute moron and has much to lose by revealing his identity.

So, shut up crank. Shut up.
WM
2016-08-22 15:25:20 UTC
Permalink
Post by Me
I'm sure it's absolutely essential when dealing with a crank like JG to explicitly state these technical details! (Otherwise he might not get the point.)
Cranks are people who never answer questions (like you): Do you believe in one of the following points?
There exist undefinable "real" numbers.
Well-ordering of objects that cannot be distinguished is possible.
After omega unions in vain the union omega + 1 reaches the aim.
There are strictly increasing series that contain their limit.
Some things turn to the contrary "at finished infinity".
Fractions can become irrational at infinity.
Diverging sequences of sets can have empty limits.

Regards, WM
Dan Christensen
2016-08-22 15:37:37 UTC
Permalink
Post by WM
Post by Me
I'm sure it's absolutely essential when dealing with a crank like JG to explicitly state these technical details! (Otherwise he might not get the point.)
Cranks are people who never answer questions (like you): Do you believe in one of the following points?
There exist undefinable "real" numbers.
Well-ordering of objects that cannot be distinguished is possible.
After omega unions in vain the union omega + 1 reaches the aim.
There are strictly increasing series that contain their limit.
Some things turn to the contrary "at finished infinity".
Fractions can become irrational at infinity.
Diverging sequences of sets can have empty limits.
**********

More absurd quotes from Wolfgang Muckenheim (WM):

“In my system, two different numbers can have the same value.”
-- sci.math, 2014/10/16

“1+2 and 2+1 are different numbers.”
-- sci.math, 2014/10/20

“1/9 has no decimal representation.”
-- sci.math, 2015/09/22

"0.999... is not 1."
-- sci.logic 2015/11/25

“Axioms are rubbish!”
-- sci.math, 2014/11/19

“No set is countable, not even |N.”
-- sci.logic, 2015/08/05

“Countable is an inconsistent notion.”
-- sci.math, 2015/12/05

“A [natural] number with aleph_0 digits is not less than aleph_0.”
-- sci.math, 2015/08/12

“The notion of aleph_0 is not meaningful.”
-- sci.math, 2015/08/28


Slipping ever more deeply into madness...

“There is no actually infinite set |N.”
-- sci.math, 2015/10/26

“|N is not covered by the set of natural numbers.”
-- sci.math, 2015/10/26

“The set of all rationals can be shown not to exist.”
--sci.math, 2015/11/28

“Everything is in the list of everything and therefore everything belongs to a not uncountable set.”
-- sci.math, 2015/11/30

"'Not equal' and 'equal can mean the same.”
-- sci.math, 2016/06/09



A special word of caution to students: Do not attempt to use WM's “system” (MuckeMath) in any course work in any high school, college or university on the planet. You will fail miserably. MuckeMath is certainly no shortcut to success in mathematics.

Using WM's “axioms” for the natural numbers, he cannot prove that 1=/=2 or the existence of even a single number. 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
Me
2016-08-22 15:38:02 UTC
Permalink
Post by WM
Cranks are people who never answer questions
A rather idiosyncratic definition of /crank/.

I'll stick to

"A crank is defined as a man who cannot be turned."

— Nature, 8 Nov 1906, 25/2
b***@gmail.com
2016-08-22 18:27:33 UTC
Permalink
Post by Me
Post by WM
Cranks are people who never answer questions
A rather idiosyncratic definition of /crank/.
I'll stick to
"A crank is defined as a man who cannot be turned."
— Nature, 8 Nov 1906, 25/2
Or look no further than yourself?
Virgil
2016-08-22 18:37:33 UTC
Permalink
Post by WM
Post by Me
I'm sure it's absolutely essential when dealing with a crank like JG to
explicitly state these technical details! (Otherwise he might not get the
point.)
Cranks are people who never answer questions (like you): Do you believe in
one of the following points?
There exist undefinable "real" numbers.
There certainly "exist" far more real numbers
than definitions for them.
Post by WM
Well-ordering of objects that cannot be distinguished is possible.
Unless one can distinguish their order, obviously not.
Post by WM
After omega unions in vain the union omega + 1 reaches the aim.
After omega unions, only in WMytheology is there yet another.
Post by WM
There are strictly increasing series that contain their limit.
That only occurs in outre systems like WMytheology, not in proper math!
Post by WM
Some things turn to the contrary "at finished infinity".
Which direction is "contrary"?
Post by WM
Fractions can become irrational at infinity.
Fractions don't change, but a sequence of fractions can have an
irrational limit.
Post by WM
Diverging sequences of sets can have empty limits.
Diverging sequences of sets can fail to have any limit set at all.


In Mathematics, Cantor is provably right,
proving both Card(Q) = Card(N) and Card(N) < Card(R)
So Card(Q) < Card(R), with fewer rationals than reals

In WM's weird WMytheology, WM claims Cantor is wrong,
WM claiming Card(Q) > Card(N) and Card(N) = Card(R)
So Card(Q) > Card(R), with more rationals than reals.

But everywhere outside of WM's wierd WMytheology there are more reals
than rationals.
--
Virgil
"Mit der Dummheit kampfen Gotter selbst vergebens." (Schiller)
Me
2016-08-22 14:05:39 UTC
Permalink
Post by Dan Christensen
The first major stumbling block...
No stumbling block, Troll Boy. Using set theory, you construct
integers as ordered pairs [of] natural numbers, then construct
rational numbers as ordered pairs of integers.
Really? Who does that, apart from you?
Edmund Landau in Foundations of Analysis (1930)?

Arnold Oberschelp in Aufbau des Zahlensystems (1968)?

Friedhelm Padberg, Rainer Danckwerts and Martin Stein in Zahlbereiche (1995)?
Peter Percival
2016-08-22 16:10:15 UTC
Permalink
Post by Me
Post by Dan Christensen
The first major stumbling block...
No stumbling block, Troll Boy. Using set theory, you construct
integers as ordered pairs [of] natural numbers, then construct
rational numbers as ordered pairs of integers.
Really? Who does that, apart from you?
Edmund Landau in Foundations of Analysis (1930)?
Landau, I can comment on. The two works you cite below, I cannot.

Definition 16 right at the start of section 5, chapter II, reads

By a rational number, we mean the set of all fractions
which are equivalent to some fixed fraction.

Definition 7 right at the start of section 1, chapter II, reads

By a fraction $\frac{x_1}{x_2}$ (read "x_1 over x_2") is meant
the pair of natural numbers x_1, x_2 (in this order).

I.e., Landau's $\frac{x_1}{x_2}$ is what, in more modern notation, would
be written (x_1,x_2) or $\langle x_1,x_2\rangle$.

Landau doesn't introduce negative numbers until he discusses real
numbers (ch IV, sect 1). Though this seems a little contrary to logic,
it means fewer cases need to be considered when discussion the
arithmetic of real number. Anyway, that is why I have commented on his
definition of rational numbers, rather than that of integers.

The edition of Landau to which I refer is the third Chelsea edition of
/Grundlagen der Analysis/ as translated into English by Steinhardt.
Post by Me
Arnold Oberschelp in Aufbau des Zahlensystems (1968)?
Friedhelm Padberg, Rainer Danckwerts and Martin Stein in Zahlbereiche (1995)?
--
I have had a tremor of bliss, a wink of heaven, a whisper,
And I would no longer be denied; all things
Proceed to a joyful consummation.
Becket through the pen of Eliot, /Murder in the Cathedral/
John Gabriel
2016-08-22 04:05:20 UTC
Permalink
Post by John Gabriel
The first major stumbling block is that in order to define rational numbers using set theory, we already need to know how to "count". Did you get that?
That's right, you need to be able to compute the cardinality of a given set. Unless you are one of Cantor's delusional followers, cardinal value means NUMBER, not bijective cardinality myths involving sets whose members are not distinct, that is, the illusion of infinitely many points. Wake up you fucking morons!
Now, do you have any clue what effort went into deriving the machinery of counting numbers which came long after ratios of MAGNITUDES ???
Of course you don't. Chances are good you're a retard who has been brainwashed to believe in the bullshit that you do.
https://www.linkedin.com/pulse/how-we-got-numbers-john-gabriel?trk=seokp_posts_primary_cluster_res_photo
After reading that article, ask yourself O moron, does set theory require the natural numbers to be in place? Hint: YES
Does the von Neumann ordinal approach make any sense at all? Hint: NO
http://youtu.be/qkSE6NoOptQ
Is there any valid construction of irrational number? Hint: NO
https://drive.google.com/open?id=0B-mOEooW03iLSTROakNyVXlQUEU
Since there is no valid construction of irrational number, can there be any valid mathematical concept for real number? Hint: NO
8/21/16 - Refreshed due to deep trolling by DC.
John Gabriel
2016-08-22 04:06:43 UTC
Permalink
Post by John Gabriel
The first major stumbling block is that in order to define rational numbers using set theory, we already need to know how to "count". Did you get that?
That's right, you need to be able to compute the cardinality of a given set. Unless you are one of Cantor's delusional followers, cardinal value means NUMBER, not bijective cardinality myths involving sets whose members are not distinct, that is, the illusion of infinitely many points. Wake up you fucking morons!
Now, do you have any clue what effort went into deriving the machinery of counting numbers which came long after ratios of MAGNITUDES ???
Of course you don't. Chances are good you're a retard who has been brainwashed to believe in the bullshit that you do.
https://www.linkedin.com/pulse/how-we-got-numbers-john-gabriel?trk=seokp_posts_primary_cluster_res_photo
After reading that article, ask yourself O moron, does set theory require the natural numbers to be in place? Hint: YES
Does the von Neumann ordinal approach make any sense at all? Hint: NO
http://youtu.be/qkSE6NoOptQ
Is there any valid construction of irrational number? Hint: NO
https://drive.google.com/open?id=0B-mOEooW03iLSTROakNyVXlQUEU
Since there is no valid construction of irrational number, can there be any valid mathematical concept for real number? Hint: NO
Refreshed due to deep trolling by DC - 8/21/16
John Gabriel
2016-08-23 02:01:05 UTC
Permalink
Post by John Gabriel
The first major stumbling block is that in order to define rational numbers using set theory, we already need to know how to "count". Did you get that?
That's right, you need to be able to compute the cardinality of a given set. Unless you are one of Cantor's delusional followers, cardinal value means NUMBER, not bijective cardinality myths involving sets whose members are not distinct, that is, the illusion of infinitely many points. Wake up you fucking morons!
Now, do you have any clue what effort went into deriving the machinery of counting numbers which came long after ratios of MAGNITUDES ???
Of course you don't. Chances are good you're a retard who has been brainwashed to believe in the bullshit that you do.
https://www.linkedin.com/pulse/how-we-got-numbers-john-gabriel?trk=seokp_posts_primary_cluster_res_photo
After reading that article, ask yourself O moron, does set theory require the natural numbers to be in place? Hint: YES
Does the von Neumann ordinal approach make any sense at all? Hint: NO
http://youtu.be/qkSE6NoOptQ
Is there any valid construction of irrational number? Hint: NO
https://drive.google.com/open?id=0B-mOEooW03iLSTROakNyVXlQUEU
Since there is no valid construction of irrational number, can there be any valid mathematical concept for real number? Hint: NO
8/22/2016
John Gabriel
2016-08-24 04:01:10 UTC
Permalink
Post by John Gabriel
The first major stumbling block is that in order to define rational numbers using set theory, we already need to know how to "count". Did you get that?
That's right, you need to be able to compute the cardinality of a given set. Unless you are one of Cantor's delusional followers, cardinal value means NUMBER, not bijective cardinality myths involving sets whose members are not distinct, that is, the illusion of infinitely many points. Wake up you fucking morons!
Now, do you have any clue what effort went into deriving the machinery of counting numbers which came long after ratios of MAGNITUDES ???
Of course you don't. Chances are good you're a retard who has been brainwashed to believe in the bullshit that you do.
https://www.linkedin.com/pulse/how-we-got-numbers-john-gabriel?trk=seokp_posts_primary_cluster_res_photo
After reading that article, ask yourself O moron, does set theory require the natural numbers to be in place? Hint: YES
Does the von Neumann ordinal approach make any sense at all? Hint: NO
http://youtu.be/qkSE6NoOptQ
Is there any valid construction of irrational number? Hint: NO
https://drive.google.com/open?id=0B-mOEooW03iLSTROakNyVXlQUEU
Since there is no valid construction of irrational number, can there be any valid mathematical concept for real number? Hint: NO
8/23/16
John Gabriel
2016-08-25 09:25:42 UTC
Permalink
Post by John Gabriel
The first major stumbling block is that in order to define rational numbers using set theory, we already need to know how to "count". Did you get that?
That's right, you need to be able to compute the cardinality of a given set. Unless you are one of Cantor's delusional followers, cardinal value means NUMBER, not bijective cardinality myths involving sets whose members are not distinct, that is, the illusion of infinitely many points. Wake up you fucking morons!
Now, do you have any clue what effort went into deriving the machinery of counting numbers which came long after ratios of MAGNITUDES ???
Of course you don't. Chances are good you're a retard who has been brainwashed to believe in the bullshit that you do.
https://www.linkedin.com/pulse/how-we-got-numbers-john-gabriel?trk=seokp_posts_primary_cluster_res_photo
After reading that article, ask yourself O moron, does set theory require the natural numbers to be in place? Hint: YES
Does the von Neumann ordinal approach make any sense at all? Hint: NO
http://youtu.be/qkSE6NoOptQ
Is there any valid construction of irrational number? Hint: NO
https://drive.google.com/open?id=0B-mOEooW03iLSTROakNyVXlQUEU
Since there is no valid construction of irrational number, can there be any valid mathematical concept for real number? Hint: NO
8/25/16
John Gabriel
2016-08-27 20:43:45 UTC
Permalink
Post by John Gabriel
The first major stumbling block is that in order to define rational numbers using set theory, we already need to know how to "count". Did you get that?
That's right, you need to be able to compute the cardinality of a given set. Unless you are one of Cantor's delusional followers, cardinal value means NUMBER, not bijective cardinality myths involving sets whose members are not distinct, that is, the illusion of infinitely many points. Wake up you fucking morons!
Now, do you have any clue what effort went into deriving the machinery of counting numbers which came long after ratios of MAGNITUDES ???
Of course you don't. Chances are good you're a retard who has been brainwashed to believe in the bullshit that you do.
https://www.linkedin.com/pulse/how-we-got-numbers-john-gabriel?trk=seokp_posts_primary_cluster_res_photo
After reading that article, ask yourself O moron, does set theory require the natural numbers to be in place? Hint: YES
Does the von Neumann ordinal approach make any sense at all? Hint: NO
http://youtu.be/qkSE6NoOptQ
Is there any valid construction of irrational number? Hint: NO
https://drive.google.com/open?id=0B-mOEooW03iLSTROakNyVXlQUEU
Since there is no valid construction of irrational number, can there be any valid mathematical concept for real number? Hint: NO
8/27/16

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