FredJeffries schrieb am Freitag, 27. August 2021 um 22:54:28 UTC+2:
> On Friday, August 27, 2021 at 12:11:15 PM UTC-7, William wrote:

> An interval is NOT 'only its points'.
>
> An interval is an ORDERED SET.

If it were completely ordered, then a next point to 0 would exist.
>
> That requires a SET of points

Sets are not required other than helping to abbreviate descriptions of objects which exist without sets as well. It is the fools of matheology only who try to spread the nonsense that a set is more than its elements.

Regards, WM

FredJeffries schrieb am Freitag, 27. August 2021 um 21:42:50 UTC+2:
> 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

This insistence is in vain because there is no uncoubtable infinity. My proof shows that there is no countable set.

> 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.

All definable natural numbers can be analyzed item by item. Try to find one that cannot. Fail. Recognize that you have been fooled.

Regards, WM
>

Jim Burns schrieb am Freitag, 27. August 2021 um 22:03:37 UTC+2:
> 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] t

99.9 % are not indexed. If you fail to apply percentage calculation, then look at the square matrix with its zigzag covering precisely as many fractions less than 1 as fractions larger than 1. If you fail this too, then EOD.

Regards, WM

On Friday, August 27, 2021 at 6:00:05 PM UTC-3, WM wrote:
> 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.

Nope. There is neither a gap nor a point closest to zero. This is a simple consequence of the set |N_F having no last element.

--
William Hughes

William schrieb am Freitag, 27. August 2021 um 23:11:13 UTC+2:
> On Friday, August 27, 2021 at 6:00:05 PM UTC-3, WM wrote:
> > 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.
> Nope. There is neither a gap nor a point closest to zero. This is a simple consequence of the set |N_F having no last element.
>
There is a gap or not a gap next to zero. This is a consequence of bivalent logic.

Regards, WM

On 8/27/2021 5:10 PM, WM wrote:
> Jim Burns schrieb
> am Freitag, 27. August 2021 um 22:03:37 UTC+2:
>> 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] t
>
> 99.9 % are not indexed.

All rationals in (1000,1001] are indexed.
All rationals in Q+ are indexed.

For each rational x in Q+, p',q' in N+ exist, p'/q' = x.
For each p',q' in N+, p,q in N+ exist, p'/q' = p/q in lowest terms.
For each p,q in N+, q*q*p*p/rad(p) in N+ exists.

If q*q*p*p/rad(p) = s*s*r*r/rad(r), then p/q = r/s,

All rationals in Q+ are indexed.
All rationals in (1000,1001] are indexed.

> If you fail to apply percentage calculation,
> then look at the square matrix with its zigzag covering
> precisely as many fractions less than 1
> as fractions larger than 1.
> If you fail this too, then EOD.

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.

On Friday, August 27, 2021 at 6:23:45 PM UTC-3, WM wrote:
> William schrieb am Freitag, 27. August 2021 um 23:11:13 UTC+2:
> > Nope. There is neither a gap nor a point closest to zero. This is a simple consequence of the set |N_F having no last element.
> >
> There is a gap or not a gap next to zero. This is a consequence of bivalent logic.

Correct. There is not a gap next to zero. There is a point or not a point next to 0. This is a consequence of bivalent logic. There is no a point next to 0. It is not true that there must be a gap next to zero, or a point next to zero. This is a simple consequence of the set |N_F having no last element.

--
William Hughes

On Friday, August 27, 2021 at 9:11:15 PM UTC+2, William wrote:
> On Friday, August 27, 2021 at 4:02:30 PM UTC-3, WM wrote:
> >
> > The interval is only its points.
> >
> Correct

Nope. If this were true than [a, a] = {a} would have to be /a/; but that's not the case in the context of ZF(C).

There {a} =/= a for any set a.

On 8/27/2021 4:32 PM, William wrote:
> On Friday, August 27, 2021 at 6:23:45 PM UTC-3, WM wrote:
>> William schrieb am Freitag, 27. August 2021 um 23:11:13 UTC+2:
>>> Nope. There is neither a gap nor a point closest to zero. This is a simple consequence of the set |N_F having no last element.
>>>
>> There is a gap or not a gap next to zero. This is a consequence of bivalent logic.
>
> Correct. There is not a gap next to zero. There is a point or not a point next to 0. This is a consequence of bivalent logic. There is no a point next to 0. It is not true that there must be a gap next to zero, or a point next to zero. This is a simple consequence of the set |N_F having no last element.
>

identically the same as what is 'next to' infinity (1,2,...,oo)

WMs "next to" is meaningless in Reals or Complex numbers, you can construct cases with counting numbers, what is next to 3 ? 2 and 4...

Crank Wolfgang Mueckenheim, aka WM wrote:
> 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.

This is complete insanity Crank Wolfgang Mueckenheim, from Hochschule
Augsburg.

Crank Wolfgang Mueckenheim, from Hochschule Augsburg, have you
considered looking from some help from a psychiatrist?

Crank Wolfgang Mueckenheim, aka WM wrote:
> 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.

When it comes to build bijections, symmetry arguments are not the only
ones, Crank Wolfgang Mueckenheim from Hochschule Augsburg.

YOU ARE MENTALLY INSANE CRANK.

Crank Wolfgang Mueckenheim, aka WM a écrit :
....
> Arithmetic is correct. Set theory is not.

Arithmetic AND Set Theory are correct, Crank Wolfgang Mueckenheim,
from Hochschule Augsburg. YOU are NOT.

on 8/27/2021, WM supposed :
> FredJeffries schrieb am Freitag, 27. August 2021 um 22:54:28 UTC+2:
>> On Friday, August 27, 2021 at 12:11:15 PM UTC-7, William wrote:
>
>> An interval is NOT 'only its points'.
>>
>> An interval is an ORDERED SET.
>
> If it were completely ordered, then a next point to 0 would exist.
>>
>> That requires a SET of points
>
> Sets are not required other than helping to abbreviate descriptions of
> objects which exist without sets as well. It is the fools of matheology only
> who try to spread the nonsense that a set is more than its elements.

It was you was it not who earlier said that all sets had to have order
else they could not be compared to find their intersections? We had to
convince you that being a set does not enforce order IIRC.

I could be wrong, it might have been another crank.

On 8/27/2021 3:52 PM, Serg io wrote:
> 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).
>

MENTALLY INSANE CRANK ANTS

On 8/27/2021 4:06 PM, WM wrote:
> FredJeffries schrieb am Freitag, 27. August 2021 um 21:42:50 UTC+2:
>> 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
>
> This insistence is in vain because there is no uncoubtable infinity. My proof shows that there is no countable set.

Your spoof is poof.
Cantors Enumeration of rationals, simple and obvious, counts ALL of them.

Your matrix, plain, diagonal, are all diversions.

You must accept Cantors Enumeration of rationals as being 100% correct, and that you are wrong.

>> 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.
>
> All definable natural numbers can be analyzed item by item. Try to find one that cannot. Fail. Recognize that you have been fooled.

fooled by a fool.... nope! gotcha.

>
> Regards, WM
>>

Serg io wrote:

>> This insistence is in vain because there is no uncoubtable infinity. My
>> proof shows that there is no countable set.
>
> Your spoof is poof.
> Cantors Enumeration of rationals, simple and obvious, counts ALL of
> them.

honestly, I never saw the hitler's nazis beating and arresting people the
way the capitalist pigs are doing all the places today. Nor that hitler
pushed his propaganda apparatus to forcefully convince people getting
toxic pseudo-experimental lethal injections into their bodies "for the
sake of the others"!!

I am forced to conclude, based on hard evidences, that the nazis were
angels when compared to these capitalist corporate *pigs*.

Some Pigs Beating Up An Old Man
https://153news.net/watch_video.php?v=7D987W6567K5

On 8/27/2021 4:00 PM, FredJeffries wrote:
> 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.
>

then WM could be a bot, or someone could bot-tize him.

a finite subject area, same set of words and phrases, perhaps 500 or so max

easily done.

same results too!

On Friday, August 27, 2021 at 5:40:14 PM UTC-7, Serg io wrote:
> On 8/27/2021 4:00 PM, FredJeffries wrote:
> > 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.
> >
> then WM could be a bot, or someone could bot-tize him.
>
> a finite subject area, same set of words and phrases, perhaps 500 or so max
>
> easily done.
>
> same results too!

We ALL might as well be bots. The same 'arguments' are offered as twenty years ago. NOTHING has been accomplished. No one has learned ANYTHING over these tens of thousands of posts.

William schrieb am Freitag, 27. August 2021 um 23:32:34 UTC+2:

> Correct. There is not a gap next to zero.

The alternative is a point.

> There is a point or not a point next to 0. This is a consequence of bivalent logic.

So it is.

> There is no a point next to 0. It is not true that there must be a gap next to zero, or a point next to zero.

Either there is a definable point next to zero or there is no definable point next to zero. Do you agree?

Regards, WM

Greg Cunt schrieb am Freitag, 27. August 2021 um 23:34:14 UTC+2:
> On Friday, August 27, 2021 at 9:11:15 PM UTC+2, William wrote:
> > On Friday, August 27, 2021 at 4:02:30 PM UTC-3, WM wrote:
> > >
> > > The interval is only its points.
> > >
> > Correct
> Nope. If this were true than [a, a] = {a} would have to be /a/; but that's not the case in the context of ZF(C).
>
Who cares? We do mathematics.

Regards, WM

On Saturday, August 28, 2021 at 8:49:58 PM UTC+2, WM wrote:
> GC wrote:
> >
> > If this were true than [a, a] = {a} would have to be /a/; but that's not the case in the context of ZF(C).
> >
> Who cares?

Anyone who pretends to talk about "set theory".

FredJeffries schrieb am Samstag, 28. August 2021 um 03:31:01 UTC+2:

> The same 'arguments' are offered as twenty years ago. NOTHING has been accomplished. No one has learned ANYTHING over these tens of thousands of posts.

That is wrong. I have learnt a lot over the years, laid down here: https://www.hs-augsburg.de/~mueckenh/Transfinity/Transfinity/pdf. For instance I have realized only in 2015 that Cantor indexes the different unit intervals irregularly. I have never found any literature noting or explaining let alone defending this. Meanwhile I have found many colleagues suspecting Cantor's enumeration. That's a lot beeing accomplished.

Regards, WM

On Saturday, August 28, 2021 at 8:47:34 PM UTC+2, WM wrote:

> Either there is a definable point next to zero or there is no definable point next to zero.

What is a /definable point/? Could you please define that notion?

On Saturday, August 28, 2021 at 9:01:59 PM UTC+2, WM wrote:

> I have never found any literature noting or explaining [...] this.

Maybe the reason for this is that there's nothing to see?

Greg Cunt schrieb am Samstag, 28. August 2021 um 21:02:44 UTC+2:
> On Saturday, August 28, 2021 at 8:47:34 PM UTC+2, WM wrote:
>
> > Either there is a definable point next to zero or there is no definable point next to zero.
> What is a /definable point/? Could you please define that notion?

Well, that is not immediately clear for real numbers. "The point next to zero" is already a definition. But what I meant is this, only defined for natural numbers or unit fractions:

1/n is a definable unit fraction if n is the last element of a FISON. Equivalently 1/n is a definable unit fraction if n has a decimal representation.

Regards, WM