The cursor runs from 1 to 0. Every passed accessible unit fraction has infinitely many smaller unit fractions as successors. When the cursor passes 0 all unit fractions have been passed. None remains, not even the infinitely many following upon every accessible unit fraction. They are not accessible.. They are dark.

Regards, WM

On Sunday, July 4, 2021 at 3:08:33 PM UTC+2, WM wrote:

> The cursor runs from 1 to 0. Every passed unit fraction has infinitely many smaller unit fractions as successors. When the cursor passes 0 all unit fractions have been passed. None remains, not even the infinitely many following upon every unit fraction.

Exactly. Well done, Mückenheim.

On Sunday, July 4, 2021 at 9:08:33 AM UTC-4, WM wrote:
> The cursor runs from 1 to 0.

You need to define and formalize what you mean by a mathematical "cursor." Is it some kind of function on the real or rational numbers?

> Every passed accessible unit fraction has infinitely many smaller unit fractions as successors.

So you have the infinite sequence: 1, 1/2, 1/3, 1/4, 1/5, ...

> When the cursor passes 0 all unit fractions have been passed.

You also need to define what you mean "cursor passes 0."

> None remains,

What do you mean by "none remains" in this context?

> not even the infinitely many following upon every accessible unit fraction.

What do you mean by "accessible unit fraction" in this case. The above sequence eventually gets to (or in some sense "accesses") every unit fraction in [0, 1], i.e. given any unit fraction 1/n in [0, 1], it is the nth term in that sequence.

> They are not accessible. They are dark.
>

More gibberish. This proves nothing, Mucke.

Try again, making sure to define and formalize ALL of your terminology.

Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com

On Sunday, July 4, 2021 at 9:08:33 AM UTC-4, WM wrote:
> The cursor runs from 1 to 0.

And passes a set of points with no last element. If the cursor moves at all it must pass a set if points with no last element. There is neither a first nor a last point that the cursor passes, A stepwise method is of no use in describing the movement of the cursor.

--
William Hughes

Dan Christensen schrieb am Sonntag, 4. Juli 2021 um 17:13:27 UTC+2:
> On Sunday, July 4, 2021 at 9:08:33 AM UTC-4, WM wrote:
> > The cursor runs from 1 to 0.

> You need to define and formalize what you mean by a mathematical "cursor." Is it some kind of function on the real or rational numbers?

A mathematician would know it. See the other answers.

> > Every passed accessible unit fraction has infinitely many smaller unit fractions as successors.
> So you have the infinite sequence: 1, 1/2, 1/3, 1/4, 1/5, ...
> > When the cursor passes 0 all unit fractions have been passed.
> You also need to define what you mean "cursor passes 0."

A mathematician would know it. See the other answers.
>
> > None remains,
>
> What do you mean by "none remains" in this context?

A mathematician would know it. See the other answers.

Regards, WM

William schrieb am Sonntag, 4. Juli 2021 um 17:22:27 UTC+2:
> On Sunday, July 4, 2021 at 9:08:33 AM UTC-4, WM wrote:
> > The cursor runs from 1 to 0.
> And passes a set of points with no last element. If the cursor moves at all it must pass a set if points with no last element. There is neither a first nor a last point that the cursor passes,

The first point is 1/1, the second is 1/2, the nth is 1/n.

> A stepwise method is of no use in describing the movement of the cursor.

The cursor runs with constant velocity. It does not move stepwise. But it shows that not every unit fraction has aleph_0 successors, because then aleph_0 unit fractions would permanently exist between the cursor and zero and could never be passed. This is contradicted by the fact that the cursor arrives at zero.

Regards, WM

On 7/4/2021 8:08 AM, WM wrote:
> The cursor runs from 1 to 0. Every passed accessible unit fraction has infinitely many smaller unit fractions as successors. When the cursor passes 0 all unit fractions have been passed. None remains, not even the infinitely many following upon every accessible unit fraction. They are not accessible. They are dark.
>
> Regards, WM
>

Wrong.

Stop your cursor at any point k, between 1 to 0, that point is defined
as the cursor is on it.

so for all k between 1 and 0, the point k is defined, and not dark.

the following constructs/terms are totally unnecessary
unit fractions
successors
direction
being passed
remains
Following
accessible
dark

Greg Cunt schrieb am Sonntag, 4. Juli 2021 um 15:21:05 UTC+2:
> On Sunday, July 4, 2021 at 3:08:33 PM UTC+2, WM wrote:
>
> > The cursor runs from 1 to 0. Every passed unit fraction has infinitely many smaller unit fractions as successors. When the cursor passes 0 all unit fractions have been passed. None remains, not even the infinitely many following upon every unit fraction.
>
> Exactly. Well done, Mückenheim.

Thank you. Note: If every unit fraction had aleph_0 successors, then there would permanently exist aleph_0 successors between the cursor and zero. This is contradicted by the final arrival of the cursor.

Regards, WM

On 7/4/2021 11:02 AM, Transfinity wrote:
> William schrieb am Sonntag, 4. Juli 2021 um 17:22:27 UTC+2:
>> On Sunday, July 4, 2021 at 9:08:33 AM UTC-4, WM wrote:
>>> The cursor runs from 1 to 0.
>> And passes a set of points with no last element. If the cursor moves at all it must pass a set if points with no last element. There is neither a first nor a last point that the cursor passes,
>
> The first point is 1/1, the second is 1/2, the nth is 1/n.
>
>> A stepwise method is of no use in describing the movement of the cursor.
>
> The cursor runs with constant velocity. It does not move stepwise. But it shows that not every unit fraction has aleph_0 successors, because then aleph_0 unit fractions would permanently exist between the cursor and zero and could never be passed. This is contradicted by the fact that the cursor arrives at zero.

wrong.

between the cursor and 1 are aleph_0 points, and between the cursor and
0 there are aleph_0 points.

the cursor is simply a point k in the 1 to 0 interval of real numbers.

forget your useless unit fractions, they are diversion

>
> Regards, WM
>
>

Sergio schrieb am Sonntag, 4. Juli 2021 um 18:04:41 UTC+2:
> On 7/4/2021 8:08 AM, WM wrote:
> > The cursor runs from 1 to 0. Every passed accessible unit fraction has infinitely many smaller unit fractions as successors. When the cursor passes 0 all unit fractions have been passed. None remains, not even the infinitely many following upon every accessible unit fraction. They are not accessible. They are dark.

> Stop your cursor at any point k, between 1 to 0, that point is defined
> as the cursor is on it.

Of course. Nevertheless, if every unit fractions has aleph_0 successors, then the cursor cannot arrive at zero because there are aleph_0 unit fractions between the cursor and zero. But the cursor finally arrives.

Regards, WM

On 7/4/2021 10:13 AM, Dan Christensen wrote:
> On Sunday, July 4, 2021 at 9:08:33 AM UTC-4, WM wrote:
>> The cursor runs from 1 to 0.
>
> You need to define and formalize what you mean by a mathematical "cursor." Is it some kind of function on the real or rational numbers?

I assume it is a point, k, that moves across the interval. It assumes
the value of each point it passes, which is all points in the interval.

>
>> Every passed accessible unit fraction has infinitely many smaller unit fractions as successors.
>
> So you have the infinite sequence: 1, 1/2, 1/3, 1/4, 1/5, ...
>
>> When the cursor passes 0 all unit fractions have been passed.
>
> You also need to define what you mean "cursor passes 0."
>
>> None remains,
>
> What do you mean by "none remains" in this context?
>
>> not even the infinitely many following upon every accessible unit fraction.
>
> What do you mean by "accessible unit fraction" in this case. The above sequence eventually gets to (or in some sense "accesses") every unit fraction in [0, 1], i.e. given any unit fraction 1/n in [0, 1], it is the nth term in that sequence.
>
>> They are not accessible. They are dark.
>>
>
> More gibberish. This proves nothing, Mucke.
>
> Try again, making sure to define and formalize ALL of your terminology.
>
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com
>
>

On 7/4/2021 11:09 AM, Transfinity wrote:
> Sergio schrieb am Sonntag, 4. Juli 2021 um 18:04:41 UTC+2:
>> On 7/4/2021 8:08 AM, WM wrote:
>>> The cursor runs from 1 to 0. Every passed accessible unit fraction has infinitely many smaller unit fractions as successors. When the cursor passes 0 all unit fractions have been passed. None remains, not even the infinitely many following upon every accessible unit fraction. They are not accessible. They are dark.
>
>> Stop your cursor at any point k, between 1 to 0, that point is defined
>> as the cursor is on it.
>
> Of course. Nevertheless, if every unit fractions has aleph_0 successors, then the cursor cannot arrive at zero

wrong.

you need to show that it cannot arrive at 0

> because there are aleph_0 unit fractions between the cursor and zero.

so what? between any two numbers, there is an infinity of numbers.

> But the cursor finally arrives.

no, you mean Achilles.

>
> Regards, WM
>

On Sunday, July 4, 2021 at 9:08:33 AM UTC-4, WM wrote:
> The cursor runs from 1 to 0. Every passed accessible unit fraction has infinitely many smaller unit fractions as successors. When the cursor passes 0 all unit fractions have been passed.

Yes, all accessible/definable/addressable/visable/term de jour unit fractions (all the unit fractions that can be written down) have been passed. As have the unit fractions of the form 1/m where m is an element of |N_F (not all of these can be written down, but none are dark) and the putative dark unit fractions. (Note that no stepwise method is appropriate as you start with an element of |N_F and every element of |N_F has a successor that is an element of |N_F so there is no step that is not at 1/m where m is an element of |N_F.}

--
Willliam Hughes

On 7/4/2021 11:06 AM, Transfinity wrote:
> Greg Cunt schrieb am Sonntag, 4. Juli 2021 um 15:21:05 UTC+2:
>> On Sunday, July 4, 2021 at 3:08:33 PM UTC+2, WM wrote:
>>
>>> The cursor runs from 1 to 0. Every passed unit fraction has infinitely many smaller unit fractions as successors. When the cursor passes 0 all unit fractions have been passed. None remains, not even the infinitely many following upon every unit fraction.
>>
>> Exactly. Well done, Mückenheim.
>
> Thank you. Note: If every unit fraction had aleph_0 successors, then there would permanently exist aleph_0 successors between the cursor and zero. This is contradicted by the final arrival of the cursor.

wrong.

you assume it takes time for the cursor to pass an infinity of numbers,
it does not take any time at all.

>
> Regards, WM
>

On Sunday, July 4, 2021 at 11:57:53 AM UTC-4, Transfinity wrote:
> Dan Christensen schrieb am Sonntag, 4. Juli 2021 um 17:13:27 UTC+2:
> > On Sunday, July 4, 2021 at 9:08:33 AM UTC-4, WM wrote:
> > > The cursor runs from 1 to 0.
>

> > You need to define and formalize what you mean by a mathematical "cursor." Is it some kind of function on the real or rational numbers?

> A mathematician would know it.

Very evasive, Mucke. Without a formalization notion of a cursor, your "proof" goes nowhere.

*******************************************
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

“Formal definitions have lead to worthless crap like undefinable numbers.”
-- sci.math 2017/02/05

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

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

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

“The set of numbers will get empty after all have numbers been used..”
-- sci.math, 2016/08/24

“I need no set theory.”
-- sci.math, 2016/09/01

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 even prove that 1=/=2. His goofy little system 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

On Sunday, July 4, 2021 at 12:02:34 PM UTC-4, Transfinity wrote:
> William schrieb am Sonntag, 4. Juli 2021 um 17:22:27 UTC+2:
> > On Sunday, July 4, 2021 at 9:08:33 AM UTC-4, WM wrote:
> > > The cursor runs from 1 to 0.
> > And passes a set of points with no last element. If the cursor moves at all it must pass a set if points with no last element. There is neither a first nor a last point that the cursor passes,
> The first point is 1/1, the second is 1/2, the nth is 1/n.

Nope, these are only the unit fractions. There are points which are not unit fractions. There is a first unit fraction but there is no last 1/m where m is an element of |N_F

> > A stepwise method is of no use in describing the movement of the cursor.
> The cursor runs with constant velocity. It does not move stepwise.

Correct. The movement of the cursor cannot be described by a stepwise process.

> But it shows that not every unit fraction has aleph_0 successors, because then aleph_0 unit fractions would permanently exist between the cursor and zero and > could never be passed.

No, they could not be passed stepwise. Recall, the movement of the cursor cannot be described by a stepwise process.

--
William Hughes

On Sunday, July 4, 2021 at 12:10:24 PM UTC-4, Sergio wrote:
> On 7/4/2021 10:13 AM, Dan Christensen wrote:
> > On Sunday, July 4, 2021 at 9:08:33 AM UTC-4, WM wrote:
> >> The cursor runs from 1 to 0.
> >
> > You need to define and formalize what you mean by a mathematical "cursor." Is it some kind of function on the real or rational numbers?
> I assume it is a point, k, that moves across the interval. It assumes
> the value of each point it passes, which is all points in the interval.

So, maybe it's the identity function f(x)=x? How would that advance his "proof?" What then could he mean by "cursor PASSES 0?" A limit of some kind?

Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com

On Sunday, 4 July 2021 at 09:08:33 UTC-4, WM wrote:
> The cursor runs from 1 to 0. Every passed accessible unit fraction has infinitely many smaller unit fractions as successors. When the cursor passes 0 all unit fractions have been passed. None remains, not even the infinitely many following upon every accessible unit fraction. They are not accessible. They are dark.

Set theorists love mythology. What good is set theory without infinity? :)

"From the paradise, that Cantor created for us, no-one shall be able to expel us." - David Moron Hilbert

LMAO.

You know, if someone said something similar today, he would be considered a crank by the mainstream.

>
> Regards, WM

On Sunday, 4 July 2021 at 13:12:30 UTC-4, Eram semper recta wrote:
> On Sunday, 4 July 2021 at 09:08:33 UTC-4, WM wrote:
> > The cursor runs from 1 to 0. Every passed accessible unit fraction has infinitely many smaller unit fractions as successors. When the cursor passes 0 all unit fractions have been passed. None remains, not even the infinitely many following upon every accessible unit fraction. They are not accessible. They are dark.
> Set theorists love mythology. What good is set theory without infinity? :)
>
> "From the paradise, that Cantor created for us, no-one shall be able to expel us." - David Moron Hilbert

Fact is that set theory is a sewer and the last thing we want is for these fools to be expelled. Nay, we want to seal them all in and put several layers of concrete on the top, so that it might even withstand a nuclear explosion.

Trump states are experiencing rising numbers in Covid infections because the morons refuse to be vaccinated, and so the alarms are being sounded by Biden administration. I can't understand why. Let them all die and rot, I say..

>
> LMAO.
>
> You know, if someone said something similar today, he would be considered a crank by the mainstream.
>
> >
> > Regards, WM

On Sunday, 4 July 2021 at 13:15:58 UTC-4, Eram semper recta wrote:
> On Sunday, 4 July 2021 at 13:12:30 UTC-4, Eram semper recta wrote:
> > On Sunday, 4 July 2021 at 09:08:33 UTC-4, WM wrote:
> > > The cursor runs from 1 to 0. Every passed accessible unit fraction has infinitely many smaller unit fractions as successors. When the cursor passes 0 all unit fractions have been passed. None remains, not even the infinitely many following upon every accessible unit fraction. They are not accessible. They are dark.
> > Set theorists love mythology. What good is set theory without infinity? :)
> >
> > "From the paradise, that Cantor created for us, no-one shall be able to expel us." - David Moron Hilbert
> Fact is that set theory is a sewer and the last thing we want is for these fools to be expelled. Nay, we want to seal them all in and put several layers of concrete on the top, so that it might even withstand a nuclear explosion.
>
> Trump states are experiencing rising numbers in Covid infections because the morons refuse to be vaccinated, and so the alarms are being sounded by Biden administration. I can't understand why. Let them all die and rot, I say.

S = Lim S!! Long Live Euler!!! Euler Oagbar! Euler Oagbar! He is the one! S = Lim S!

Euler's S = Lim S is a major blight on his accomplishments and those who follow him will go down with him.

Euler wrote:

Daher ist uns Bruch 1/(1+a) {Lim S} gleich dieser unendlichen Reihe 1 - a + aa - aaa + ...&c {S}.

Therefore is our fraction 1/(1+a) {Lim S} equal this unending series 1 - a + aa - aaa + ...&c {S}.

Because 1/(1+a) = Lim S and S = 1 - a + aa - aaa + ...&c

All else is hand waving bullshit.

> >
> > LMAO.
> >
> > You know, if someone said something similar today, he would be considered a crank by the mainstream.
> >
> > >
> > > Regards, WM

On Sunday, July 4, 2021 at 6:30:22 PM UTC+2, Dan Christensen wrote:
> On Sunday, July 4, 2021 at 12:10:24 PM UTC-4, Sergio wrote:
> > >
> > > You need to define and formalize what you mean by a mathematical "cursor." Is it some kind of function on the real or rational numbers?

The "cursor" is part of a "semi-physical" "Gedankenexperiment". (A moving "something", where the point of it's linear path may be related with the real number in the "usual" way. The beginn of it's path is related with 1. The speed of this something is -1 unit per second. Hence after 1 second it arrives at the point which is related to 0.)

We might describe its "path" with a function: x(t) = 1 + v * t (0 <= t <= 1), where v = -1 is the "constant" speed of the "cursor".

The cursor "passes" a point x0 if there is a t e [0, 1] such that x0 = x(t).

And it "passes" a point x0 at time t0 if x0 = x(t0).

> So, maybe it's the identity function f(x)=x? How would that advance his "proof?" What then could he mean by "cursor PASSES 0?"

That x(1) = 0 .

It's just a variant of one of Zeno's "paradoxes".

On Sunday, July 4, 2021 at 6:30:22 PM UTC+2, Dan Christensen wrote:
> On Sunday, July 4, 2021 at 12:10:24 PM UTC-4, Sergio wrote:
> > >
> > > You need to define and formalize what you mean by a mathematical "cursor." Is it some kind of function on the real or rational numbers?

The "cursor" is part of a "semi-physical" "Gedankenexperiment". (A moving (pointlike) "something", where the points of it's linear path may be related with the real numbers in the "usual" way. The begin of it's path is related with 1. The speed of this something is -1 unit per second. Hence after 1 second it arrives at the point which is related to 0.)

We might describe its "path" with a function: x(t) = 1 + v * t (0 <= t <= 1), where v = -1 is the "constant" speed of the "cursor".

The cursor "passes" a point x0 if there is a t e [0, 1] such that x0 = x(t).

And it "passes" a point x0 at time t0 if x0 = x(t0).

> So, maybe it's the identity function f(x)=x? How would that advance his "proof?" What then could he mean by "cursor PASSES 0?"

That x(1) = 0 .

It's just a variant of one of Zeno's "paradoxes".

On 7/4/2021 11:30 AM, Dan Christensen wrote:
> On Sunday, July 4, 2021 at 12:10:24 PM UTC-4, Sergio wrote:
>> On 7/4/2021 10:13 AM, Dan Christensen wrote:
>>> On Sunday, July 4, 2021 at 9:08:33 AM UTC-4, WM wrote:
>>>> The cursor runs from 1 to 0.
>>>
>>> You need to define and formalize what you mean by a mathematical "cursor." Is it some kind of function on the real or rational numbers?
>> I assume it is a point, k, that moves across the interval. It assumes
>> the value of each point it passes, which is all points in the interval.
>
> So, maybe it's the identity function f(x)=x? How would that advance his "proof?" What then could he mean by "cursor PASSES 0?" A limit of some kind?
>

cursor is just x, no functions at all, no limits.

just read out values on the real line, like on a radio dial.

WM does not do proofs, + has stated such.

cursor passes 0, WM thinks there is a problem using words, has not shown
any math to back it up.

WM depends upon an implied amount of time to get past an infinity of
numbers. He is wrong. He tries to tie the sequence to being dependent
upon the cursor

WM tries to attach the cursor to the sequence, but there is no
attachment of any kind.

He did the same with Achilles and frames, etc, a one trick pony so far.

> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com
>

On Sunday, July 4, 2021 at 7:28:16 PM UTC+2, Greg Cunt wrote:
> On Sunday, July 4, 2021 at 6:30:22 PM UTC+2, Dan Christensen wrote:
> > On Sunday, July 4, 2021 at 12:10:24 PM UTC-4, Sergio wrote:
> > > >
> > > > You need to define and formalize what you mean by a mathematical "cursor." Is it some kind of function on the real or rational numbers?

> The "cursor" is part of a "semi-physical" "Gedankenexperiment". (A moving (pointlike) "something", where the points of it's linear path may be related with the real numbers in the "usual" way. The begin of it's path is related with 1. The speed of this something is -1 unit per second. Hence after 1 second it arrives at the point which is related to 0.)
>
> We might describe its "path" with a function: x(t) = 1 + v * t (0 <= t <= 1), where v = -1 is the "constant" speed of the "cursor".
>
> The cursor "passes" a point x0 if there is a t e [0, 1] such that x0 = x(t).
>
> And it "passes" a point x0 at time t0 if x0 = x(t0).

> > So, maybe it's the identity function f(x)=x? How would that advance his "proof?" What then could he mean by "cursor PASSES 0?"

> That x(1) = 0 .

Hence imho the following is a quite appropriate description of what's "going on":

"The cursor runs from 1 to 0. Every passed unit fraction has infinitely many smaller unit fractions as successors. When the cursor passes 0 all unit fractions have been passed. None remains [unpassed], not even the infinitely many following upon every unit fraction." (WM)

On Sunday, July 4, 2021 at 7:29:02 PM UTC+2, Sergio wrote:

> cursor is just x

I'd say the the cursor has a position x(t) at time t.

You see: Imho, the "cursor" is part of a "semi-physical" "Gedankenexperiment". (A moving (pointlike) "something", where the points of it's linear path are related with the real numbers in the "usual" way. The begin of it's path is identified with 1. The speed of this something is -1 unit per second. Hence after 1 second it arrives at the point which is identified with 0.)

We might describe its "path" with a function: x(t) = 1 + v * t (0 <= t <= 1), where v = -1 is the "constant" speed of the "cursor".

> cursor passes 0

x(1) = 0.

> WM tries to attach the cursor to the sequence, but there is no attachment of any kind.

Indeed!

> He did the same with Achilles and frames, etc, a one trick pony so far.

Right.