On Sunday, July 4, 2021 at 6:08:33 AM UTC-7, 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

The dark is zero and first quantity.
sub finite is the dark math...

On Sunday, July 4, 2021 at 7:41:37 PM UTC+2, Greg Cunt wrote:

> You see: Imho, the "cursor" is part of a "semi-physical" "Gedankenexperiment". (A moving (pointlike) "something",

See: https://en.wikipedia.org/wiki/Point_particle

> 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".

On Sunday, 4 July 2021 at 10:08:33 UTC-3, 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.

Whatever "remains" might mean in this context. If you means "that none remains to be passed" because all have been passed, then, congratulations, you have finally figured out motion.

However, in this context your argument about dark objects is even less tenable than with the natural numbers. By the time the cursor gets to 0, every blessed one will have been illuminated, albeit for a shorter and shorter time interval. And as far as I can tell about your mathematical delusions, even you admit that once illuminated, always illuminated.

On 7/4/2021 12:34 PM, Greg Cunt wrote:
> 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)
>

this stuff is trivial.

between any two points on the real line, there is an infinity of points.

WM tries to obscure that fact, and WM using discrete steps in an
infinite process to create confusion. WM uses turtles, frames,
Achilles, cursors, endsegments, on and on.

from what I can tell, WM's math is of no value.

On Sunday, July 4, 2021 at 1:28:16 PM UTC-4, 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.)
>

I get it. Here, WM introduces the physical notions of a point particle, time and events in space-time. In this case, an event is just the point particle in question arriving at a point x in [0, 1] at a given time t. He then wrongly assumes that infinitely many events cannot occur in a finite time interval, thus obtaining his long sought-after "contradiction" in set theory. Really quite pathetic.

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 8:26:57 PM UTC+2, Dan Christensen wrote:

> I get it. Here, WM introduces the physical notions of a point particle, time and events in space-time. In this case, an event is just the point particle in question arriving at a point x in [0, 1] at a given time t. He then wrongly assumes that infinitely many events cannot occur in a finite time interval, thus obtaining his long sought-after "contradiction" in set theory. Really quite pathetic.

Yes, it is.

He appears like Bozo the Clown, stumbling over Zeno's paradoxes.

William schrieb am Sonntag, 4. Juli 2021 um 18:13:15 UTC+2:
> 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.}

But the claim that every unit fraction has aleph_0 successors (smaller unit fractions) is disproved. If every unit fraction had aleph_0 successors, then there would be aleph_0 unit fractions between cursor and zero forever. The physical movement would be hampered. That's impossible. Therefore a last unit fraction has been passed by the cursor when reaching zero. But it is dark and cannot be identified or put in an order.

Regards, WM

On Sunday, July 4, 2021 at 8:25:58 PM UTC+2, Sergio wrote:

> this stuff is trivial.

Sort of.

> between any two points on the real line, there is an infinity of points.
>
> WM tries to obscure that fact, and WM using discrete steps in an
> infinite process to create confusion. WM uses turtles, frames,
> Achilles, cursors, endsegments, on and on.

Right. Actually, he appears like Bozo the Clown, stumbling over Zeno's paradoxes. :-P

Sergio schrieb am Sonntag, 4. Juli 2021 um 18:13:16 UTC+2:
> On 7/4/2021 11:09 AM, Transfinity wrote:

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

Between any two definable numbers.

Regards, WM

On Sunday, July 4, 2021 at 9:57:12 PM UTC+2, WM wrote:

> [bla bla]
>
> The physical movement would be hampered.

Exactly! The arrow does not move [in this case]. Zeno knew that already!

On Sunday, July 4, 2021 at 9:59:53 PM UTC+2, WM wrote:
> Sergio schrieb am Sonntag, 4. Juli 2021 um 18:13:16 UTC+2:
> >
> > between any two numbers, there is an infinity of numbers.
> >
> Between any two definable numbers.

Eat shit, man!

William schrieb am Sonntag, 4. Juli 2021 um 18:21:23 UTC+2:
> 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.

They are irrelevant for this problem.

> There is a first unit fraction but there is no last 1/m where m is an element of |N_F

No, the last unit fraction is dark, like aleph_0 of its predecessors.

> > 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.

So it is. But it can be proved that it passes a last unit fraction. Otherwise it would never bridge the gap of aleph_0 unit fractions between itself and zero.

Regards, WM

Greg Cunt schrieb am Sonntag, 4. Juli 2021 um 19:28:16 UTC+2:

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

No. The cursor arrives at zero. Only if all unit fractions had aleph_0 successors, then the cursor could never get to zero because in every case aleph_0 unit fractions would be in between. Of course the cursor arrives in time.

Regards WM

On Sunday, July 4, 2021 at 3:57:12 PM UTC-4, WM wrote:
> William schrieb am Sonntag, 4. Juli 2021 um 18:13:15 UTC+2:
> > 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.}
> But the claim that every unit fraction has aleph_0 successors (smaller unit fractions) is disproved. If every unit fraction had aleph_0 successors, then there would be aleph_0 unit fractions between cursor and zero forever.

Nope, it does not take forever for the cursor to pass aleph_0 points. Why should it?

--
William Hughes

On Sunday, July 4, 2021 at 4:03:06 PM UTC-4, WM wrote:
> William schrieb am Sonntag, 4. Juli 2021 um 18:21:23 UTC+2:
> > 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.
> They are irrelevant for this problem.
> > There is a first unit fraction but there is no last 1/m where m is an element of |N_F
> No, the last unit fraction is dark, like aleph_0 of its predecessors.

No 1/m where m is an element of |N_F is dark. However, there is no last 1/m where m is an element of |N_F.
Your putative "dark unit fractions" must come after aleph_0 1/m where m is an element of |N_F.

--
William Hughes

Gus Gassmann schrieb am Sonntag, 4. Juli 2021 um 20:12:13 UTC+2:

> By the time the cursor gets to 0, every blessed one will have been illuminated, albeit for a shorter and shorter time interval.

If every unit fraction had aleph_0 successors, then the cursor could never pass all. The set would simply not decrease.

Regards, WM

Dan Christensen schrieb am Sonntag, 4. Juli 2021 um 20:26:57 UTC+2:

> I get it. Here, WM introduces the physical notions of a point particle, time and events in space-time. In this case, an event is just the point particle in question arriving at a point x in [0, 1] at a given time t. He then wrongly assumes that infinitely many events cannot occur in a finite time interval,

You didn't get it. This is the argument: If every unit fraction had aleph_0 successors, then the set between cursor and zero could not disappear. The cursor could not reach zero. The physical motion would be hampered by this infinity.

Regards, WM

Greg Cunt schrieb am Sonntag, 4. Juli 2021 um 22:00:05 UTC+2:
> On Sunday, July 4, 2021 at 9:57:12 PM UTC+2, WM wrote:

> > The physical movement would be hampered.
> Exactly! The arrow does not move [in this case]. Zeno knew that already!

He did not know how to solve it.

Regards, WM

William schrieb am Sonntag, 4. Juli 2021 um 22:30:15 UTC+2:
> On Sunday, July 4, 2021 at 3:57:12 PM UTC-4, WM wrote:

> > But the claim that every unit fraction has aleph_0 successors (smaller unit fractions) is disproved. If every unit fraction had aleph_0 successors, then there would be aleph_0 unit fractions between cursor and zero forever.
> Nope, it does not take forever for the cursor to pass aleph_0 points. Why should it?

Because never less than aleph_0 unit fractions were between the cursor and zero.

Regards, WM

On Sunday, 4 July 2021 at 17:03:06 UTC-3, WM wrote:
> William schrieb am Sonntag, 4. Juli 2021 um 18:21:23 UTC+2:
> > 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.
> They are irrelevant for this problem.
> > There is a first unit fraction but there is no last 1/m where m is an element of |N_F
> No, the last unit fraction is dark, like aleph_0 of its predecessors.

The cursor illuminates it, you moron. (Just in case the cursor doesn't, I'll do the cursing instead.) Presumably the movement is at a constant speed, so it doesn't fucking matter whether the stuff it passes is illuminated, previously dark and lit by the cursor, unit fraction, rational, irrational. It gets lit, and, by your own *FUCKING ADMISSION* it will stay lit, you moron. You are now disavowing not just Cantor's mathematics but 2500 years of development in math AND physics. You are certifiably demented.

William schrieb am Sonntag, 4. Juli 2021 um 22:43:15 UTC+2:
> On Sunday, July 4, 2021 at 4:03:06 PM UTC-4, WM wrote:
> > No, the last unit fraction is dark, like aleph_0 of its predecessors.
> No 1/m where m is an element of |N_F is dark. However, there is no last 1/m where m is an element of |N_F.
> Your putative "dark unit fractions" must come after aleph_0 1/m where m is an element of |N_F.

They come after all your 1/m. In a linear problem where never two or more unit fractions are passed simultaneously, there is a last one passed, when all have been passed. But that cannot be one of your elements of |N_F.

Regards, WM

On Sunday, July 4, 2021 at 5:17:49 PM UTC-4, WM wrote:
> William schrieb am Sonntag, 4. Juli 2021 um 22:30:15 UTC+2:
> > On Sunday, July 4, 2021 at 3:57:12 PM UTC-4, WM wrote:
>
> > > But the claim that every unit fraction has aleph_0 successors (smaller unit fractions) is disproved. If every unit fraction had aleph_0 successors, then there would be aleph_0 unit fractions between cursor and zero forever.
> > Nope, it does not take forever for the cursor to pass aleph_0 points. Why should it?
> Because never less than aleph_0 unit fractions were between the cursor and zero

Not true, For a finite amount of time, [t_0,t_1) there are aleph_0 1/m where m is an element of |N_F between the cursor and 0. For any t>=t_1, (hardly "never") there are no 1/m where m is an element of |N_F between 0 and the cursor.

--
William Hughes

Greg Cunt formulated the question :
> On Sunday, July 4, 2021 at 9:59:53 PM UTC+2, WM wrote:
>> Sergio schrieb am Sonntag, 4. Juli 2021 um 18:13:16 UTC+2:
>>>
>>> between any two numbers, there is an infinity of numbers.
>>>
>> Between any two definable numbers.
>
> Eat shit, man!

You'll have to put that into a step by step process else he'll never
get started. Have him eat half of it, then half of what's left, half of
what's left, half of what's left, until it is *all* gone. You may have
to explain many many times what *all* means though, good luck.

On Sunday, July 4, 2021 at 5:21:14 PM UTC-4, WM wrote:
> William schrieb am Sonntag, 4. Juli 2021 um 22:43:15 UTC+2:
> > On Sunday, July 4, 2021 at 4:03:06 PM UTC-4, WM wrote:
>
> > > No, the last unit fraction is dark, like aleph_0 of its predecessors.
> > No 1/m where m is an element of |N_F is dark. However, there is no last 1/m where m is an element of |N_F.
> > Your putative "dark unit fractions" must come after aleph_0 1/m where m is an element of |N_F.
> They come after all your 1/m.

Correct, Recall that the set,U_F (1/m where m is an element of |N_F) has cardinality aleph_0. Recall that no element of U_F is "dark"

> In a linear problem where never two or more [elements of U_F] are passed simultaneously, there is a last one passed,

Nope,. There is no last element of U_F to pass and no time at which a last element of U_F is passed. (This despite the fact that all element of U_F are passed This is clearly not possible for a stepwise process, however, one cannot describe the movement of the cursor using stepwise methods)

--
William Hughes

WM

On Sunday, July 4, 2021 at 11:45:58 PM UTC+2, FromTheRafters wrote:
> Greg Cunt formulated the request:
> >
> > Eat shit, man!
> >
> You'll have to put that into a step by step process else he'll never
> get started. Have him eat half of it, then half of what's left, half of
> what's left, half of what's left, until it is *all* gone. You may have
> to explain many many times what *all* means though, good luck.

Hmmm... Maybe it would be simpler to eat it myself?