Crank Wolfgang Mueckenheim, aka WM wrote:
> Greg Cunt schrieb am Donnerstag, 26. August 2021 um 23:35:51 UTC+2:
>
>> Hint: "In mathematics, the cardinality of a set is a measure of the "number of elements" of the set." (Wikipedia, Cardinality)
>>
> Fact: If we have an infinite matrix or plane, then its entries or points above the diagonal are precisely as many as below.

There is also as much entries in the first line than in the whole
matrix, would you say that they are "half" of entries in the first
line, Crank Wolfgang Mueckenheim, from Hochschule Augsburg?

Crank Wolfgang Mueckenheim, aka WM wrote:
> Serg io schrieb am Freitag, 27. August 2021 um 16:18:14 UTC+2:
>> Cantor enumerates all rationals.
>
> Why doesn't he start with all fractions n/1?

Beause it wouldn't work, Crank Wolfgang Mueckenheim, from Hochschule
Augsburg. That a bijection exist does not mean that all functions are
bijectives. Something far beyond your (mis)understandings, Crank
Wolfgang Mueckenheim, from Hochschule Augsburg.

On 8/27/2021 9:23 AM, WM wrote:
> Serg io schrieb am Freitag, 27. August 2021 um 16:18:14 UTC+2:
>> Cantor enumerates all rationals.
>
> Why doesn't he start with all fractions n/1?
>
> Regards, WM
>

you can propose your own newer better enumeration, the Mueckenheim Enumeration, instead of that old stale simplistic Cantor enumeration.

On Thursday, August 26, 2021 at 11:56:56 AM UTC-7, William wrote:
> On Thursday, August 26, 2021 at 3:52:44 PM UTC-3, WM wrote:
> > William schrieb am Donnerstag, 26. August 2021 um 20:31:13 UTC+2:
> > > On Thursday, August 26, 2021 at 3:21:03 PM UTC-3, WM wrote:
> > > > William schrieb am Donnerstag, 26. August 2021 um 17:26:38 UTC+2:
> > > > > On Thursday, August 26, 2021 at 9:50:32 AM UTC-3, WM wrote:
> > > > > > William schrieb am Donnerstag, 26. August 2021 um 01:12:57 UTC+2:
> > > > > >
> > > > > > > "Number of points" is nonsense when you try to apply it to sets with infinite cardinality.
> > > > > > Cardinality is nonsense.
> > > > > Nope, As you note there is a bijection between the rationals in (0,1] and the rationals in (1000,1001]. So the two sets have the same cardinality. It is nonsense to say that the range of the bijection has "more points] in (0,1] than in (1000,1001].
> > > > My bijection f(q) = q + 1000 shows same number
> > > "same number" is nonsense when talking about infinite cardinalities.
> > This is not cardinality but identity of number.
> Saying "identity of number" instead of "same number" is still nonsense.

On the contrary, it is the SAYING which is all-important.

You must remember that in our Professor's magic kingdom, mathematics is based on the magical Law of Names. If you give an item the same name as something else, the latter acquires properties of the former. And if you change somethings name (e.g. 'Cardinality' to 'Identity of number') you thereby change that item's properties. No matter how similar (or identical) the definitions look, it is henceforth different. And since YOU changed the name, YOU have all power over that object.

https://www.themystica.com/law-of-names/
https://en.wikipedia.org/wiki/True_name

On Friday, August 27, 2021 at 5:47:06 PM UTC+2, FredJeffries wrote:

> [...] And since YOU changed the name, YOU have all power over that object.

Exactly. Just consider his masterful handling of /dark/ numbers!

On 8/27/2021 11:08 AM, Greg Cunt wrote:
> On Friday, August 27, 2021 at 5:47:06 PM UTC+2, FredJeffries wrote:
>
>> [...] And since YOU changed the name, YOU have all power over that object.
>
> Exactly. Just consider his masterful handling of /dark/ numbers!
>

yes, and once you don't see them, you don't see them everywhere!

On 8/27/2021 7:14 AM, WM wrote:
> Jim Burns schrieb
> am Donnerstag, 26. August 2021 um 23:17:48 UTC+2:
>> On 8/26/2021 4:52 PM, WM wrote:

>>>> I can prove it exists, that thing I say exists.
>>>
>>> In an inconsistent theory everything can be proved.
>>
>> If you can prove arithmetic is inconsistent, go ahead.
>
> Arithmetic is consistent.

I'll take "WM knows what that means" as a working assumption.

<JB>
>>
>>> But Cantor does not enumerates all fractions.
>>
>> Cantor enumerates all rationals.
>
> In (1000, 1001] he misses about 99.9 %. That is fact.

For each p'/q' in (1000,1001] there is a unique p/q = p'/q'
in lowest terms. gcd(p,q) = 1.
For each p/q in lowest terms, there is a unique q*q*p*p/rad(p).
Define the index of p'/q' in (1000,1001] to be q*q*p*p/rad(p)

For each rational p'/q' in (1000,1001], there is
a unique index. None are missed.

> Conjuration of

There is no conjuration.
I can prove it exists, that thing I say exists.
It's not difficult to do.

</JB>

I amend my claim.
It's not challenging to prove but it's very tedious.

What part of the quote do you deny?
That there is a unique p/q in lowest terms?
That there is a unique q*q*p*p/rad(p)?

> Set theory is inconsistent

Let's go back to _crowds_

| For each predicate P(x) on individual x,
| a _crowd_ pp exists such that, forall x, x in pp iff P(x).
| | For crowds pp, qq,
| ( pp = qq ) iff ( forall x, x in pp iff x in qq )
| | Crowds are not individuals. "pp in qq" is not well-formed.

> because if we have an infinite matrix or plane,
> then its entries or points above the diagonal are
> precisely as many as below.
> This shows that Cantor's enumeration is incomplete,
> no bijection, no valid measure of infinite sets.

Matching the elements of a set to one of its proper subsets
shows that it is an infinite set. A _Dedekind infinite_ set.

>> "Inconsistent result" and "unwanted result"
>> aren't the same thing.
>
> Unwanted is the result that in an infinite matrix or plane,
> the entries or points above the diagonal are precisely
> as many as below. That is basic and consistent.

The rationals in Q+ = (0, +inf) are precisely as many as
the rationals in (1, +inf).
Match (p,q) where q = p+1

The rationals in Q+ = (1, +inf) are precisely as many as
the rationals in (0, 1).
Match (p,q) where q = 1/p

The rationals in Q+ = (0, 1) are precisely as many as
the rationals in (r, r+s), for rationals r,s.
Match (p,q) where q = r + s*p

Therefore,
the rationals in Q+ = (0, +inf) are precisely as many as
the rationals in (r, r+s) for rationals r,s.

Arithmetic giving you unwanted results.
You could give up arithmetic.
You could decide you wanted the wrong results.
Or you could bullshit.

I wonder which you'll do.

On Friday, August 27, 2021 at 9:45:30 AM UTC-3, WM wrote:
> William schrieb am Freitag, 27. August 2021 um 14:21:45 UTC+2:

> > There is no "last one that is there". You cannot put a real number between the set U and 0.
> There is no real number between 0 and (0, 1]. That proves that the interval is next to 0

Indeed, and not because there is a point in (0,1] next to 0. The set (0,1] only contains real numbers ( in particular it does not contain "dark real numbers" whatever they are) and there is no real number "next to" 0. The set (0,1] is next to zero because it does not contain an element which is closest to 0.

--
William Hughes

Python schrieb am Freitag, 27. August 2021 um 16:45:42 UTC+2:
> Wolfgang Mueckenheim, aka WM wrote:
> > Greg Cunt schrieb am Donnerstag, 26. August 2021 um 23:35:51 UTC+2:
> >
> >> Hint: "In mathematics, the cardinality of a set is a measure of the "number of elements" of the set." (Wikipedia, Cardinality)
> >>
> > Fact: If we have an infinite matrix or plane, then its entries or points above the diagonal are precisely as many as below.
> There is also as much entries in the first line than in the whole
> matrix,

No symmetry argument will support this nonsense.

Regards, WM

Python schrieb am Freitag, 27. August 2021 um 16:47:28 UTC+2:
> Wolfgang Mueckenheim, aka WM wrote:
> > Serg io schrieb am Freitag, 27. August 2021 um 16:18:14 UTC+2:
> >> Cantor enumerates all rationals.
> >
> > Why doesn't he start with all fractions n/1?
> Beause it wouldn't work,

So it is.

> That a bijection exist does not mean that all functions are
> bijectives.

If there was really a bijection where all elements existed with their partners, then it would work. Then no transposition could destroy the bijection.

Regards, WM

Serg io schrieb am Freitag, 27. August 2021 um 16:48:50 UTC+2:
> On 8/27/2021 9:23 AM, WM wrote:
> > Serg io schrieb am Freitag, 27. August 2021 um 16:18:14 UTC+2:
> >> Cantor enumerates all rationals.
> >
> > Why doesn't he start with all fractions n/1?
> >
> you can propose your own newer better enumeration,

There is no enumertion possible! Cantor is a trickster paying debts with future income. My proposal shows this to everybody not yet brain-damaged by too much set theory.

Regards, WM

FredJeffries schrieb am Freitag, 27. August 2021 um 17:47:06 UTC+2:

> > Saying "identity of number" instead of "same number" is still nonsense.
>
> On the contrary, it is the SAYING which is all-important.

Saying and distinguishing: Cantor is a trickster who pays debts by future income. Identity of number is unerring: If we have an infinite matrix or plane, then its entries or points above the diagonal are precisely as many as below . That is honest and clear - not Cantor's nonsense.

Regards, WM

Jim Burns schrieb am Freitag, 27. August 2021 um 20:12:49 UTC+2:
> On 8/27/2021 7:14 AM, WM wrote:

> >>> But Cantor does not enumerates all fractions.
> >>
> >> Cantor enumerates all rationals.
> >
> > In (1000, 1001] he misses about 99.9 %. That is fact.
>
> For each p'/q' in (1000,1001] there is a unique p/q = p'/q'
> in lowest terms. gcd(p,q) = 1.

That assumes that all fractions can be chosen. This is refuted by the 99.9 % missing indices.

This is my basic rule: If we have an infinite matrix or plane, then its entries or points above the diagonal are precisely as many as below. If you deny this simple truth then we have no common basis.

> What part of the quote do you deny?
> That there is a unique p/q in lowest terms?
> That there is a unique q*q*p*p/rad(p)?

You cannot choose dark numbers. See above.
>
> Let's go back to _crowds_

Same. You cannot choose dark numbers.

> > Unwanted is the result that in an infinite matrix or plane,
> > the entries or points above the diagonal are precisely
> > as many as below. That is basic and consistent.
> The rationals in Q+ = (0, +inf) are precisely as many as
> the rationals in (1, +inf).
> Match (p,q) where q = p+1

No. This again pays debts by future income. Here it is not so obvious as in Cantor's enumeration of the rationals. There it becomes clear immediately, if we first enumerate the fractions n/1. Then his trick fails.

> Arithmetic giving you unwanted results.
> You could give up arithmetic.

Arithmetic is correct. Set theory is not.

Regards, WM

William schrieb am Freitag, 27. August 2021 um 20:29:17 UTC+2:
> On Friday, August 27, 2021 at 9:45:30 AM UTC-3, WM wrote:
> > William schrieb am Freitag, 27. August 2021 um 14:21:45 UTC+2:
>
> > > There is no "last one that is there". You cannot put a real number between the set U and 0.
> > There is no real number between 0 and (0, 1]. That proves that the interval is next to 0
> Indeed, and not because there is a point in (0,1] next to 0.

Otherwise it would be impossible. The interval is only its points.

Regards, WM

On Friday, August 27, 2021 at 4:02:30 PM UTC-3, WM wrote:
> William schrieb am Freitag, 27. August 2021 um 20:29:17 UTC+2:
> > On Friday, August 27, 2021 at 9:45:30 AM UTC-3, WM wrote:
> > > William schrieb am Freitag, 27. August 2021 um 14:21:45 UTC+2:
> >
> > > > There is no "last one that is there". You cannot put a real number between the set U and 0.
> > > There is no real number between 0 and (0, 1]. That proves that the interval is next to 0
> > Indeed, and not because there is a point in (0,1] next to 0.
> Otherwise it would be impossible.

Nope. You don't need a point next to 0, you need no closest point to 0.

> The interval is only its points.

Correct and no point is the closest point to 0.

--
William Hughes

On Friday, August 27, 2021 at 9:02:30 PM UTC+2, WM wrote:

> The interval is only its points.

You fucking idiot, we are talking SET THEORY here, not MEREOLOGY.

Holy shit!

Hint: [a, a] =/= a (for any a e IR).

On Friday, August 27, 2021 at 11:51:33 AM UTC-7, WM wrote:
> FredJeffries schrieb am Freitag, 27. August 2021 um 17:47:06 UTC+2:
>
>
> > > Saying "identity of number" instead of "same number" is still nonsense.
> >
> > On the contrary, it is the SAYING which is all-important.
> Saying and distinguishing: Cantor is a trickster who pays debts by future income. Identity of number is unerring: If we have an infinite matrix or plane, then its entries or points above the diagonal are precisely as many as below . That is honest and clear - not Cantor's nonsense.

On the contrary, Cantor and modern set theories clearly and distinctly insist on the necessity for the second method of number generation and the Axiom of Infinity in the creation of the bijections and explicitly point out that the sets and functions CANNOT be created item-by-item as you insist in your farce.

These facts have been pointed out to you for decades. You insist on ignoring them.

It is YOU who are the fraud, the huckster, the carnival side-show promoter, the dishonest shell-game operator.

EOD

On 8/27/2021 3:00 PM, WM wrote:
> Jim Burns schrieb
> am Freitag, 27. August 2021 um 20:12:49 UTC+2:
>> On 8/27/2021 7:14 AM, WM wrote:

>>>>> But Cantor does not enumerates all fractions.
>>>>
>>>> Cantor enumerates all rationals.
>>>
>>> In (1000, 1001] he misses about 99.9 %. That is fact.
>>
>> For each p'/q' in (1000,1001] there is a unique p/q = p'/q'
>> in lowest terms. gcd(p,q) = 1.
>
> That assumes that all fractions can be chosen.

That assumes that, for rational x in Q+,
there are naturals p' and q' in N+ such that p'/q' = x.
Anything without such p', q' are not in Q+.

Also, that assumes that, for p',q' in N+,
there are {1,...,p'}, {1,...,q'} sub N+ such that,
for each split B,A, there is a crossing-pair i,j
such that j = i+1.

Also also, that assumes that,
for each k in N+, exists k+1 in N+,
not exists k in N+, k+1 = 1
for each j,k in N+, (j = k) iff (j+1 = k+1)

> This is refuted by the 99.9 % missing indices.

You can match the elements of a set to one of its
proper subsets. Good for you.
That means it's a Dedekind infinite set.

> This is my basic rule:
> If we have an infinite matrix or plane, then its entries
> or points above the diagonal are precisely as many as below.
> If you deny this simple truth then we have no common basis.

This is my basic rule:

Elements in Q+ equal p'/q' for some p',q' in N+.

Elements p',q' in N+ have steppable {1,...,p'}, {1,...,q'}
with adjacent i,j = i+1.

for each k in N+, exists k+1 in N+,
not exists k in N+, k+1 = 1
for each j,k in N+, (j = k) iff (j+1 = k+1)

If you deny these simple truths then we have no common basis.

>> What part of the quote do you deny?
>> That there is a unique p/q in lowest terms?
>> That there is a unique q*q*p*p/rad(p)?
>
> You cannot choose dark numbers. See above.
>
>> Let's go back to _crowds_
>
> Same. You cannot choose dark numbers.

Then I won't choose them.
If x is in Q+, then there are p',q' in N+, p'/q' = x.
If p',q' are in N+, then there are {1,...,p'},
{1,...,q'} sub N+ as described.

No choosing.

>> Arithmetic giving you unwanted results.
>> You could give up arithmetic.
>
> Arithmetic is correct. Set theory is not.

For each lowest-terms p/q, unique q*q*p*/rad(p) exists.

WM explained on 8/27/2021 :
> Serg io schrieb am Freitag, 27. August 2021 um 16:18:14 UTC+2:
>> Cantor enumerates all rationals.
>
> Why doesn't he start with all fractions n/1?

Because it is a subset. More obviously the same size (cardinality).

On 8/27/2021 10:47 AM, FredJeffries wrote:
> On Thursday, August 26, 2021 at 11:56:56 AM UTC-7, William wrote:
>> On Thursday, August 26, 2021 at 3:52:44 PM UTC-3, WM wrote:
>>> William schrieb am Donnerstag, 26. August 2021 um 20:31:13 UTC+2:
>>>> On Thursday, August 26, 2021 at 3:21:03 PM UTC-3, WM wrote:
>>>>> William schrieb am Donnerstag, 26. August 2021 um 17:26:38 UTC+2:
>>>>>> On Thursday, August 26, 2021 at 9:50:32 AM UTC-3, WM wrote:
>>>>>>> William schrieb am Donnerstag, 26. August 2021 um 01:12:57 UTC+2:
>>>>>>>
>>>>>>>> "Number of points" is nonsense when you try to apply it to sets with infinite cardinality.
>>>>>>> Cardinality is nonsense.
>>>>>> Nope, As you note there is a bijection between the rationals in (0,1] and the rationals in (1000,1001]. So the two sets have the same cardinality. It is nonsense to say that the range of the bijection has "more points] in (0,1] than in (1000,1001].
>>>>> My bijection f(q) = q + 1000 shows same number
>>>> "same number" is nonsense when talking about infinite cardinalities.
>>> This is not cardinality but identity of number.
>> Saying "identity of number" instead of "same number" is still nonsense.
>
> On the contrary, it is the SAYING which is all-important.
>
> You must remember that in our Professor's magic kingdom, mathematics is based on the magical Law of Names. If you give an item the same name as something else, the latter acquires properties of the former. And if you change somethings name (e.g. 'Cardinality' to 'Identity of number') you thereby change that item's properties. No matter how similar (or identical) the definitions look, it is henceforth different. And since YOU changed the name, YOU have all power over that object.
>
> https://www.themystica.com/law-of-names/
> https://en.wikipedia.org/wiki/True_name
>

from the Ant List;

972 Switcharoo Ants
973 Switching Quantifier Ants

On 8/27/2021 1:51 PM, WM wrote:
> FredJeffries schrieb am Freitag, 27. August 2021 um 17:47:06 UTC+2:
>
>
>>> Saying "identity of number" instead of "same number" is still nonsense.
>>
>> On the contrary, it is the SAYING which is all-important.
>
> Saying and distinguishing: Cantor is a trickster who pays debts by future income. Identity of number is unerring: If we have an infinite matrix or plane, then its entries or points above the diagonal are precisely as many as below . That is honest and clear - not Cantor's nonsense.
>
> Regards, WM
>

more ANTS!!!

Honest Ants
Clear Ants
Honest Ants that are transparent
NonSense Ants
Trickster Ants who pays debts by future income
Identity of Ant is unerring
Infinite Matrix Ants
Infinite Plane Ants
Ants Above the Diagonal
Ants Below the Diagonal
Ants On the Diagonal
Entry to the Matrix Ants
Same Ants
Identity Ants
Still Nonsense Ants
schrieb am Freitag Ants
Fraud Ants,
The huckster Ants,
The carnival side-show promoter Ants,
The dishonest shell-game operator Ants.
insist on ignoring them Ants
Professor's magic kingdom Ants
The magical Law of Names Ants
support this nonsense Ants
Rejected bijection Ants
Impartially Blocked Brain Ants
Silly Ants
You fucking idiot Ants
MEREOLOGY Ants recovering from Brain Surgery
Hint Ants: [Ant, Ant] =/= Ant (for any Ant e IR).

On Friday, August 27, 2021 at 12:11:15 PM UTC-7, William wrote:
> On Friday, August 27, 2021 at 4:02:30 PM UTC-3, WM wrote:
> > William schrieb am Freitag, 27. August 2021 um 20:29:17 UTC+2:
> > > On Friday, August 27, 2021 at 9:45:30 AM UTC-3, WM wrote:
> > > > William schrieb am Freitag, 27. August 2021 um 14:21:45 UTC+2:
> > >
> > > > > There is no "last one that is there". You cannot put a real number between the set U and 0.
> > > > There is no real number between 0 and (0, 1]. That proves that the interval is next to 0
> > > Indeed, and not because there is a point in (0,1] next to 0.
> > Otherwise it would be impossible.
> Nope. You don't need a point next to 0, you need no closest point to 0.
> > The interval is only its points.
> Correct and no point is the closest point to 0.

Oh, come on!

An interval is NOT 'only its points'.

An interval is an ORDERED SET.

That requires a SET of points (NOT merely (all) its points) AND an ordering. Without the ordering, how do you tell what is and isn't in the set.

Our beloved Professor has been living on the lacks of discrimination between SETs and ORDERED SETs and between a SET and the elements of that set for over two decades now. Discriminations that those who have been fruitlessly arguing with him for these two decades also lack -- suckers for his shell game.

Greg Cunt schrieb am Freitag, 27. August 2021 um 21:31:55 UTC+2:
> On Friday, August 27, 2021 at 9:02:30 PM UTC+2, WM wrote:
>
> > The interval is only its points.
> we are talking SET THEORY here, not MEREOLOGY.
>
Here we are talking mathematics, not nonsense.

Regards, WM

William schrieb am Freitag, 27. August 2021 um 21:11:15 UTC+2:
> On Friday, August 27, 2021 at 4:02:30 PM UTC-3, WM wrote:
> > William schrieb am Freitag, 27. August 2021 um 20:29:17 UTC+2:
> > > On Friday, August 27, 2021 at 9:45:30 AM UTC-3, WM wrote:
> > > > William schrieb am Freitag, 27. August 2021 um 14:21:45 UTC+2:
> > >
> > > > > There is no "last one that is there". You cannot put a real number between the set U and 0.
> > > > There is no real number between 0 and (0, 1]. That proves that the interval is next to 0
> > > Indeed, and not because there is a point in (0,1] next to 0.
> > Otherwise it would be impossible.
> Nope. You don't need a point next to 0, you need no closest point to 0.

Closest to 0 is either a point or a gap. No other alternative is possible.
> > The interval is only its points.
> Correct

Nice that you understand this at least.

> and no point is the closest point to 0.

BUT: If all points were visible, then a closest point must exist by the linearity of the real line. It does not. At least it cannot be found.

Regards, WM

On Friday, August 27, 2021 at 7:18:14 AM UTC-7, Serg io wrote:
> wrong. Cantor enumerates all rationals.

Wrong. Cantor enumerates the SET of rationals.

You are playing our Professor's dishonest shell game. If that's what you want to do, it's your life.... But you won't win -- he's been getting away with it for over 20 years now.

As Einstein never said 'Insanity is doing the same thing over and over again and expecting different results.' Our Professor has been demonstrating the 'insanity' of his interlocutors for over 20 years.