WM laid this down on his screen :
> mitchr...@gmail.com schrieb am Sonntag, 19. Februar 2023 um 03:04:10 UTC+1:
>
>> There is No infinity that is countable.
>
> Correct. But nevertheless it is called countable infinity in oder to
> distinguish it from uncountable infinity.

Wrong, you just don't understand what countable means.

FromTheRafters schrieb am Sonntag, 19. Februar 2023 um 12:58:51 UTC+1:
> WM pretended :
> > FromTheRafters schrieb am Sonntag, 19. Februar 2023 um 00:08:26 UTC+1:
> >> WM wrote on 2/18/2023 :
> >>> FromTheRafters schrieb am Samstag, 18. Februar 2023 um 21:27:25 UTC+1:
> >>>> WM formulated the question :
> >>>
> >>>>> Without dark parts every unit fractions could be detected.
> >>>> They can anyway.
> >>>
> >>> No, the many last unit fractions cannot be detected. But they are existing
> >>> because before zero, there are many, while beyond zero there is none. And
> >>> all are at different places.
> >>>
> >>>>> Note that the all sit at different positions.
> >>>> How can you tell without detecting them?
> >>>
> >>> It is the virtue of mathematics to prove that all existing unit fractions
> >>> differ. It is the virtue of set theory to prove that all unit fractions are
> >>> existing.
> >> What do those two statements mean?
> >
> > They mean that the set of unit fractions consists of a fixed number of
> > well-distinguished points, such that every point, including the last point,
> There is no last point.

If the cursor passes a fixed number of distinct points and after a while no further point follows, then it has passed a last one. There is no alternative.

Regards, WM

FromTheRafters schrieb am Sonntag, 19. Februar 2023 um 13:00:33 UTC+1:
> WM laid this down on his screen :
> > mitchr...@gmail.com schrieb am Sonntag, 19. Februar 2023 um 03:04:10 UTC+1:
> >
> >> There is No infinity that is countable.
> >
> > Correct. But nevertheless it is called countable infinity in oder to
> > distinguish it from uncountable infinity.
> Wrong, you just don't understand what countable means.

Countable means a bijection with ℕ. But since most elements of infinite sets cannot be discerned, there is no bijection possible.

Regards, WM

WM was thinking very hard :
> FromTheRafters schrieb am Sonntag, 19. Februar 2023 um 12:58:51 UTC+1:
>> WM pretended :
>>> FromTheRafters schrieb am Sonntag, 19. Februar 2023 um 00:08:26 UTC+1:
>>>> WM wrote on 2/18/2023 :
>>>>> FromTheRafters schrieb am Samstag, 18. Februar 2023 um 21:27:25 UTC+1:
>>>>>> WM formulated the question :
>>>>>>> Without dark parts every unit fractions could be detected.
>>>>>> They can anyway.
>>>>>
>>>>> No, the many last unit fractions cannot be detected. But they are
>>>>> existing because before zero, there are many, while beyond zero there is
>>>>> none. And all are at different places.
>>>>>
>>>>>>> Note that the all sit at different positions.
>>>>>> How can you tell without detecting them?
>>>>>
>>>>> It is the virtue of mathematics to prove that all existing unit fractions
>>>>> differ. It is the virtue of set theory to prove that all unit fractions
>>>>> are existing.
>>>> What do those two statements mean?
>>>
>>> They mean that the set of unit fractions consists of a fixed number of
>>> well-distinguished points, such that every point, including the last point,
>> There is no last point.
>
> If the cursor passes a fixed number of distinct points and after a while no
> further point follows, then it has passed a last one. There is no
> alternative.

Are you suggesting that the reals can be swept over in increments? What
measure does your increment have?

It happens that WM formulated :
> FromTheRafters schrieb am Sonntag, 19. Februar 2023 um 13:00:33 UTC+1:
>> WM laid this down on his screen :
>>> mitchr...@gmail.com schrieb am Sonntag, 19. Februar 2023 um 03:04:10 UTC+1:
>>>
>>>> There is No infinity that is countable.
>>>
>>> Correct. But nevertheless it is called countable infinity in oder to
>>> distinguish it from uncountable infinity.
>> Wrong, you just don't understand what countable means.
>
> Countable means a bijection with ℕ.

No, it doesn't.

> But since most elements of infinite sets cannot be discerned, there is no
> bijection possible.

Yes, there is.

On Sunday, February 19, 2023 at 3:58:51 AM UTC-8, FromTheRafters wrote:
> WM pretended :
> > FromTheRafters schrieb am Sonntag, 19. Februar 2023 um 00:08:26 UTC+1:
> >> WM wrote on 2/18/2023 :
> >>> FromTheRafters schrieb am Samstag, 18. Februar 2023 um 21:27:25 UTC+1:
> >>>> WM formulated the question :
> >>>
> >>>>> Without dark parts every unit fractions could be detected.
> >>>> They can anyway.
> >>>
> >>> No, the many last unit fractions cannot be detected. But they are existing
> >>> because before zero, there are many, while beyond zero there is none. And
> >>> all are at different places.
> >>>
> >>>>> Note that the all sit at different positions.
> >>>> How can you tell without detecting them?
> >>>
> >>> It is the virtue of mathematics to prove that all existing unit fractions
> >>> differ. It is the virtue of set theory to prove that all unit fractions are
> >>> existing.
> >> What do those two statements mean?
> >
> > They mean that the set of unit fractions consists of a fixed number of
> > well-distinguished points, such that every point, including the last point,
> There is no last point.

What about .999 repeating ending at the last infinitesimal?

FromTheRafters schrieb am Sonntag, 19. Februar 2023 um 18:01:19 UTC+1:
> WM was thinking very hard :

> >>> They mean that the set of unit fractions consists of a fixed number of
> >>> well-distinguished points, such that every point, including the last point,
> >> There is no last point.
> >
> > If the cursor passes a fixed number of distinct points and after a while no
> > further point follows, then it has passed a last one. There is no
> > alternative.
> Are you suggesting that the reals can be swept over in increments? What
> measure does your increment have?

I am adhering to this basic principle of geometrical logic: If there are points, which are separated from each other by non-zero distances, on a line which has an end, then there is a last point before this end.

Regards, WM

crank Wolfgang Mückenheim, aka WM wrote:
> FromTheRafters schrieb am Sonntag, 19. Februar 2023 um 18:01:19 UTC+1:
>> WM was thinking very hard :
>
>>>>> They mean that the set of unit fractions consists of a fixed number of
>>>>> well-distinguished points, such that every point, including the last point,
>>>> There is no last point.
>>>
>>> If the cursor passes a fixed number of distinct points and after a while no
>>> further point follows, then it has passed a last one. There is no
>>> alternative.
>> Are you suggesting that the reals can be swept over in increments? What
>> measure does your increment have?
>
> I am adhering to this basic principle of geometrical logic: If there are points, which are separated from each other by non-zero distances, on a line which has an end, then there is a last point before this end.

More dementia than ever from Wolfgang Mückenheim, from Hochschule
Augsburg!

On 2/19/2023 12:27 PM, mitchr...@gmail.com wrote:
> On Sunday, February 19, 2023 at 3:58:51 AM UTC-8, FromTheRafters wrote:
>> WM pretended :
>>> FromTheRafters schrieb am Sonntag, 19. Februar 2023 um 00:08:26 UTC+1:
>>>> WM wrote on 2/18/2023 :
>>>>> FromTheRafters schrieb am Samstag, 18. Februar 2023 um 21:27:25 UTC+1:
>>>>>> WM formulated the question :
>>>>>
>>>>>>> Without dark parts every unit fractions could be detected.
>>>>>> They can anyway.
>>>>>
>>>>> No, the many last unit fractions cannot be detected. But they are existing
>>>>> because before zero, there are many, while beyond zero there is none. And
>>>>> all are at different places.
>>>>>
>>>>>>> Note that the all sit at different positions.
>>>>>> How can you tell without detecting them?
>>>>>
>>>>> It is the virtue of mathematics to prove that all existing unit fractions
>>>>> differ. It is the virtue of set theory to prove that all unit fractions are
>>>>> existing.
>>>> What do those two statements mean?
>>>
>>> They mean that the set of unit fractions consists of a fixed number of
>>> well-distinguished points, such that every point, including the last point,
>> There is no last point.
>
> What about .999 repeating ending at the last infinitesimal?

Roy, .999... never ends. There is no last point.

WM explained on 2/19/2023 :
> FromTheRafters schrieb am Sonntag, 19. Februar 2023 um 18:01:19 UTC+1:
>> WM was thinking very hard :
>
>>>>> They mean that the set of unit fractions consists of a fixed number of
>>>>> well-distinguished points, such that every point, including the last
>>>>> point,
>>>> There is no last point.
>>>
>>> If the cursor passes a fixed number of distinct points and after a while no
>>> further point follows, then it has passed a last one. There is no
>>> alternative.
>> Are you suggesting that the reals can be swept over in increments? What
>> measure does your increment have?
>
> I am adhering to this basic principle of geometrical logic: If there are
> points, which are separated from each other by non-zero distances, on a line
> which has an end, then there is a last point before this end.

But that statement is false. You forget that the language is adapted to
our use, not the other way around.

What is the first real number greater than zero? What is the first unit
fraction greater than zero?

Which is larger?

On Sunday, February 19, 2023 at 3:25:50 PM UTC-8, FromTheRafters wrote:
> WM explained on 2/19/2023 :
> > FromTheRafters schrieb am Sonntag, 19. Februar 2023 um 18:01:19 UTC+1:
> >> WM was thinking very hard :
> >
> >>>>> They mean that the set of unit fractions consists of a fixed number of
> >>>>> well-distinguished points, such that every point, including the last
> >>>>> point,
> >>>> There is no last point.
> >>>
> >>> If the cursor passes a fixed number of distinct points and after a while no
> >>> further point follows, then it has passed a last one. There is no
> >>> alternative.
> >> Are you suggesting that the reals can be swept over in increments? What
> >> measure does your increment have?
> >
> > I am adhering to this basic principle of geometrical logic: If there are
> > points, which are separated from each other by non-zero distances, on a line
> > which has an end, then there is a last point before this end.
> But that statement is false. You forget that the language is adapted to
> our use, not the other way around.
>
> What is the first real number greater than zero? What is the first unit
> fraction greater than zero?

1 divided by infinity. There is a first non zero...
>
> Which is larger?

They are the same.

Python schrieb am Sonntag, 19. Februar 2023 um 23:17:52 UTC+1:
> Wolfgang Mückenheim, aka WM wrote:
> > I am adhering to this basic principle of geometrical logic: If there are points, which are separated from each other by non-zero distances, on a line which has an end, then there is a last point before this end.

> More

With pleasure: If there are ℵo unit fractions to the left-hand side of every point that you can chose, then these ℵo unit fractions cannot be chosen.

Regards, WM

FromTheRafters schrieb am Montag, 20. Februar 2023 um 00:25:50 UTC+1:
> WM explained on 2/19/2023 :

> > I am adhering to this basic principle of geometrical logic: If there are
> > points, which are separated from each other by non-zero distances, on a line
> > which has an end, then there is a last point before this end.
> But that statement is false.

No this statement is basic.

> You forget that the language is adapted to
> our use, not the other way around.

If there are ℵo unit fractions to the left-hand side of every point that you can chose, then these ℵo unit fractions cannot be chosen.
>
> What is the first real number greater than zero? What is the first unit
> fraction greater than zero?

They are dark, not in a discernible order. Therefore this question cannot be answered.

Regards, WM

On 2/20/2023 4:01 AM, WM wrote:
> FromTheRafters schrieb am Montag,
> 20. Februar 2023 um 00:25:50 UTC+1:
>> WM explained on 2/19/2023 :

>>> I am adhering to this basic principle of
>>> geometrical logic: If there are points,
>>> which are separated from each other by
>>> non-zero distances, on a line which has an end,
>>> then there is a last point before this end.
>>
>> But that statement is false.
>
> No this statement is basic.

https://www.youtube.com/watch?v=8PcE_pzA9eU
Construction 05 - Midpoint Construction (0.51)

Jim Burns schrieb am Montag, 20. Februar 2023 um 18:48:11 UTC+1:
> On 2/20/2023 4:01 AM, WM wrote:
> > FromTheRafters schrieb am Montag,
> > 20. Februar 2023 um 00:25:50 UTC+1:
> >> WM explained on 2/19/2023 :
>
> >>> I am adhering to this basic principle of
> >>> geometrical logic: If there are points,
> >>> which are separated from each other by
> >>> non-zero distances, on a line which has an end,
> >>> then there is a last point before this end.
> >>
> >> But that statement is false.
> >
> > No this statement is basic.
> https://www.youtube.com/watch?v=8PcE_pzA9eU
> Construction 05 - Midpoint Construction (0.51)

There are all unit fractions existing in actual infinity. None is constructed. Only such can be chosen, which have infinitely many dark unit fractions at their LHS. Hence infinitely many cannot be chosen.

Regards, WM

On 2/21/2023 3:23 AM, WM wrote:
> Jim Burns schrieb am Montag,
> 20. Februar 2023 um 18:48:11 UTC+1:
>> On 2/20/2023 4:01 AM, WM wrote:
>>> FromTheRafters schrieb am Montag,
>>> 20. Februar 2023 um 00:25:50 UTC+1:
>>>> WM explained on 2/19/2023 :

>>>>> I am adhering to this basic principle of
>>>>> geometrical logic: If there are points,
>>>>> which are separated from each other by
>>>>> non-zero distances, on a line which has an end,
>>>>> then there is a last point before this end.
>>>>
>>>> But that statement is false.
>>>
>>> No this statement is basic.
>>
>> https://www.youtube.com/watch?v=8PcE_pzA9eU
>> Construction 05 - Midpoint Construction (0.51)
>
> There are all unit fractions existing
> in actual infinity. None is constructed.

Midpoints are not _built_ in the video.
"Construction" is being used with a technical
meaning different from "build (a house)"

> Only such can be chosen,
> which have infinitely many dark unit fractions
> at their LHS.

Each unit fraction has infinitely-many
unit fractions at its LHS,
none of which _do not_ have infinitely-many
unit fractions at their LHS's

If
any dark unit fraction exists,
then
some dark unit fraction one step from
a visible unit fraction exists.

Almost all
visible infinitely-many unit fractions
are near 0.

> Hence infinitely many cannot be chosen.

If motion is possible,
motion past infinitely-many points
is possible.

Motion is not a finite list of points.

Jim Burns schrieb am Dienstag, 21. Februar 2023 um 16:35:01 UTC+1:
> On 2/21/2023 3:23 AM, WM wrote:

> > There are all unit fractions existing
> > in actual infinity. None is constructed.
> Midpoints are not _built_ in the video.

I don't look videos.

> > Only such can be chosen,
> > which have infinitely many dark unit fractions
> > at their LHS.
> Each unit fraction has infinitely-many
> unit fractions at its LHS,
> none of which _do not_ have infinitely-many
> unit fractions at their LHS's

Wrong. All unit fractions have finite distances from each other. Therefore in every not dark case the one closer to zero can be determined. Therefore your statement proves dark unit fractions.

Since the interval (0, 1] has not even one point distance from zero, it contains real points x > 0 which are closer to zero than even finitely many unit fraction and their internal distances would span. One point is less than 50000 points with internals distances of infinitely many points.
>
> If
> any dark unit fraction exists,
> then
> some dark unit fraction one step from
> a visible unit fraction exists.

I know that this is difficult to understand. Nevertheless it is true, because otherwise your non-conservation would ruin all of mathematics.

> > Hence infinitely many cannot be chosen.
> If motion is possible,
> motion past infinitely-many points
> is possible.
>
Of course. Between any two real numbers there are infinitely many undefined real numbers infinitely many of them are undefinable.

Regards, WM

On 2/21/2023 3:02 PM, WM wrote:
> Jim Burns schrieb am Dienstag,
> 21. Februar 2023 um 16:35:01 UTC+1:
>> On 2/21/2023 3:23 AM, WM wrote:

>>> There are all unit fractions existing
>>> in actual infinity. None is constructed.
>>
>> Midpoints are not _built_ in the video.
>
> I don't look videos.

What you would have seen:
For any two points, a midpoint is between them.
No two points are _next to_ each other.

>>> Only such can be chosen,
>>> which have infinitely many dark unit fractions
>>> at their LHS.
>>
>> Each unit fraction has infinitely-many
>> unit fractions at its LHS,
>> none of which _do not_ have infinitely-many
>> unit fractions at their LHS's
>
> Wrong.

For each 1/n in (0,1]
there is a point in (0,1] which
1/n is NOT to the LHS of.
| | 1/n ∉ (0,1/n⁺⁺]

For each 1/n in (0,1]
there is its own unit fraction (1/n)/mₓ
to the LHS of x in (0,1]
| | 1/k ≠ 1/n ⇒ (1/k)/mₓ ≠ (1/n)/mₓ
| | mₓ = ⌈1/x⌉

Bob is not conserved.

Infinity is not
a reallyreallyreallyreallyreallyreally large
natural number.

On Tuesday, February 21, 2023 at 1:19:56 PM UTC-8, Jim Burns wrote:
> On 2/21/2023 3:02 PM, WM wrote:
> > Jim Burns schrieb am Dienstag,
> > 21. Februar 2023 um 16:35:01 UTC+1:
> >> On 2/21/2023 3:23 AM, WM wrote:
>
> >>> There are all unit fractions existing
> >>> in actual infinity. None is constructed.
> >>
> >> Midpoints are not _built_ in the video.
> >
> > I don't look videos.
> What you would have seen:
> For any two points, a midpoint is between them.
> No two points are _next to_ each other.
> >>> Only such can be chosen,
> >>> which have infinitely many dark unit fractions
> >>> at their LHS.
> >>
> >> Each unit fraction has infinitely-many
> >> unit fractions at its LHS,
> >> none of which _do not_ have infinitely-many
> >> unit fractions at their LHS's
> >
> > Wrong.
> For each 1/n in (0,1]
> there is a point in (0,1] which
> 1/n is NOT to the LHS of.
> |
> | 1/n ∉ (0,1/n⁺⁺]
>
> For each 1/n in (0,1]
> there is its own unit fraction (1/n)/mₓ
> to the LHS of x in (0,1]
> |
> | 1/k ≠ 1/n ⇒ (1/k)/mₓ ≠ (1/n)/mₓ
> |
> | mₓ = ⌈1/x⌉
>
> Bob is not conserved.
>
> Infinity is not
> a reallyreallyreallyreallyreallyreally large
> natural number.

Distance and age will never be infinite.
If the universe was infinite why would the stars be young?

Jim Burns schrieb am Dienstag, 21. Februar 2023 um 22:19:56 UTC+1:
> On 2/21/2023 3:02 PM, WM wrote:

> > I don't look videos.
> What you would have seen:
> For any two points, a midpoint is between them.

That is wrong, because points are fixed. Proof: Between 0 and (0, 1] nothing can be found. Alas (0, 1] is only collectively defined. In fact all _visible_ points have a distance of ℵo dark points between them. Therefore it is possible, to find always a point between them, and between them, and between them, ... Potential infinity,

> No two points are _next to_ each other.

No two visible points. Dark points are so close to each other that nothing fits in between. Otherwise new points had to be created. But that's impossible, if all are already existing.

> For each 1/n in (0,1]
> there is a point in (0,1] which
> 1/n is NOT to the LHS of.

But the points are fixed. They are not subject to if "if n". Don't you think so?

> Bob is not conserved.

But all counted fractions are conserved? Why??
>
> Infinity is not
> a reallyreallyreallyreallyreallyreally large
> natural number.

Between 0 and every x > 0 you have passed ℵo unit fractions already.. It is impossible to stop between them i.e., before so many have been passed, although they cover a considerable distance consisting of ℵo unit fractions and ℵo points between every pair of consecutive unit fractions. In total this is a finite distance because ℵo finite distances are added.

Can this finite distance vanish like Bob?

Regards, WM

On 2/22/2023 5:30 AM, WM wrote:
> Jim Burns schrieb am Dienstag,
> 21. Februar 2023 um 22:19:56 UTC+1:

>> No two points are _next to_ each other.
>
> No two visible points.

Then each point is visible.

No two visible points are next to each other.
No point is not visible.

> Dark points are so close to each other
> that nothing fits in between.

A description can exist of
something that does not exist.

> Otherwise new points had to be created.

There's a description.
The description is true of each thing described.
The description does not create.

> But that's impossible,

Right.
A description can exist of
something that does not exist.

> if all are already existing.

The description does not create points.

>> For each 1/n in (0,1]
>> there is a point in (0,1] which
>> 1/n is NOT to the LHS of.
>
> But the points are fixed.
> They are not subject to if "if n".
> Don't you think so?

I don't see what you're asking.
Maybe ask differently?
Maybe give examples?

>> Bob is not conserved.
>
> But all counted fractions are conserved?
> Why??

"Not conserved" means
all of a set can be matched to
less than all of that set.

Put X's on less-than-all,
put Bob on on non-X spot,
swap all the matches,
and it's 'bye Bob.

All of a _set_
"Conserved/not-conserved" is
a property of a _set_
not of any individual in the set.

Each FISON conserves its things.
Each FISON has that property,
like each red truck is red.

However,
the set of
all the things in all the FISONs
has a different definition.
Does it conserve its things?
We check.
No, that _set_ doesn't,
even though those other _sets_ do.

>> Infinity is not
>> a reallyreallyreallyreallyreallyreally large
>> natural number.
>
> Between 0 and every x > 0
> you have passed ℵo unit fractions already.
> It is impossible to stop between them

No, it's possible.
There's a midpoint.

> i.e., before so many have been passed,

That's a different question.
It's impossible
to move to a positive point without
passing |N| unit fractions.

Almost all unit fraction are near 0

Non-mathematically, "near" is a fuzzy word.
Are your feet near each other?
Put one foot on a chair.
Are they near each other now?
Are you near where you were born?
Fly to Mars.
Were you near where you were born before?

Mathematically,
no matter which neighborhood (-x,x) of 0
is "near 0"
almost all unit fractions are in (-x,x)

No one is shocked by that.
Between any two points, there is a point
between any two other points. Geometry.

Work your way down a list with an end.
The list has fewer and fewer items.
A line segment is not a list with an end.
Move down a line segment.
The number of points is the same. Geometry.

> although they cover a considerable distance
> consisting of ℵo unit fractions and
> ℵo points between every pair of consecutive
> unit fractions.
> In total this is a finite distance because
> ℵo finite distances are added.

What?!
No.
Finite or infinite, depending.
How can you not know this,
while allegedly knowing any physics?

> Can this finite distance vanish like Bob?

Match the points in [0,1] and [0,2]
Set Bob in (1,2]
Swap all matches.
'Bye, Bob.

Jim Burns schrieb am Mittwoch, 22. Februar 2023 um 18:12:55 UTC+1:

> Mathematically,
> no matter which neighborhood (-x,x) of 0
> is "near 0"
> almost all unit fractions are in (-x,x)

Alas you cannot remove any unit fraction which has ℵo unit fractions on the right-hand side. Why?

Regards, WM

On Thursday, February 16, 2023 at 10:17:04 PM UTC-5, mitchr...@gmail.com wrote:
> space does not contract. There is nothing about movement
> to contract the universe. The universe expands forever contained
> in the hypersphere boundary,
>
> Propulsion cannot end time. Neither can a black hole.
> If space time ended at the singularity how could a BH
> move? They are not still. So how can they be an end
> to space time?
>
> We are seeing look a likes that are not BHs.
> That is also why there are jets that can leave gravity.
> Supermassive neutron forms at the center
> of galaxies are real instead. Limited gravity
> allows jets to happen instead. Neutronium
> does not end space time. That is why we see
> it moving in the universe.
>
> Mitchell Raemsch

This is a long post for Mitch. I'm impressed that he's expounded this much. Here's hoping for more.
The thing is, as usual, it is just the title alone that draws me.
To not end time; you cannot end time; well, I'd say you almost can't even begin time.
The reasoning is purely mathematical, but it is via physical correspondence that the reasoning secures itself.
Firstly we generalize sign, and that's been done for maybe a couple of decades now.
Then we convince the status quo of the superiority of the polysign number system.
That's ongoing though, and to posit some troubling details on humanity now, well: that's already been done, too.
Yes, it is a big deal, and geometry is taken into the fold along with algebra when we generalize sign. I needn't even specify it here, for upon engaging in the process it all unfolds. Here though, for the time inference, We'll have to expose the basic property of the one-signed numbers:
- x = 0
and this goes in conjunction with the two-signed behavior:
- x + x = 0
which thencely exists in the three-signed form:
- x + x * x = 0
at which point the geometry and the algebra of the complex numers are recovered via the same rules which beget the real numbers as P2, and while the format is P3, we of course can go on to P4 and so forth. But just this moment we want to investigate the unidirectional P1; the one-signed numbers; for their correspondence to time is remarkable. Yet look at their geometry. Though you likely won't perceive it, the law of balance just posed requires a geometry in n signs of n rays emanating from an origin outward to the vertices of an n-verticed simplex. These sum to zero. They are the only ones that do this consistent with the algebra. That algebra is of course the familiar algebra of the real and complex numbers. P1 can do this algebra, though in a very limited form:
- 2 - 3 = - 5 [ a sum ]
( - 2 )( - 3 ) = - 6 [ a product ]
yet according to the geometry these P1 systems render to naught. Meanwhile they preserve this unidirectional quality. Such things occur in n-ary interpretations. It somewhat explains how we got P2 first, but our conventions have prevented the development of polysign as a result. Notational consistency will require the introduction of a zero sign, and until then the identity sign has to dance around; - in P1; + in P2; * in P3; and so forth. Of course these signs behave modulo-n under product, and so the equivalence of the zero sign '@' to these wraparound signs is not a problem.

So whether you like @1 for your one-signed value or -1 is not a material conflict. The treatment of the minus unity (MU) as a value of significance, as it capable generates the others, whereas the +1 of the real values (consistent with P2 still) is normally regarded as a primary value. Well, this discussion of even having a 'primary value' only really lights up when polysign is achieved. We have an arithmetic product that can march us through our spatial coordinates in polysign.

P1 : 0D
P2 : 1D
P3 : 2D
P4 : 3D
....
Pn : (n-1)D
Above we see the ordinary dimensional interpreation of Pn, and that terminology of dimension strangely does preserve some meaning, though this may not be the fully matured interpretation, for to rely upon P2 as a fundamental interpretation in an n-ary system cannot actually be a sensible interpertation; it is just an interpretation that allows our transitional state of progress to coexist for the moment. Yet as we absorb the ray as more fundamental than the line, then witness that ray collapsing to naught geometrically, we see a new behavior that seemingly requires an exception, and yet as we realize that the unidirectional nature of time carries very good correspondence to this P1 arithmetic construction then perhaps we can relax a bit.

Let's please consider the means by which we realize space as three dimensional. Here we have a first breach of theory as empirical, which is inherently conflicted. Still, we can go this route to arrive at our three dimensional interpretation of space; we shift an object around on a rectangular table top, discovering that its center of mass can be resolved to two values in direct correspondence to the sides of the table. Then, elevating the object, and let's say it's a small object, we arrive with a third dimension, and no further freedoms for the object (other than the rotation freedoms, which in my opinion do deserve more treatment) can be found. Now, introduce time as a fourth full dimension. Now place your object backward of forward in time. Can't do it? Well, then P1 does carry correspondence, doesn't it?

This view of the geometric ray as collapsing it's space can be brought into correspondence with the photon as well. Let's for the moment consider the photon particle as a little spaceship travelling at c. Thereby, in its own frame of reference, it ages exactly zero seconds in its transition and transmission from emission at position A to absorption at position B, and furthermore, the distance travelled by that photon in its own frame has collapsed to naught. Thus P1 correspondence shows itself entangled inside of relativity theory. Few bother to analyze the photon at this level, probably partly for the quagmire it seems to open, but regardless, such a simple-minded bit of interpretation is possible. To admit that not all is well here; this might be a mature statement, but then, to start out with the real number as your fundamental construction source has already been exposed here as dubious. That pure mathematics can say this much about physics in so few paragraphs with so little background really is remarkable, and so we await your own remarks here; in the open. No, it is not a terribly organized place. Whether it is even truly uncensored anymore deserves scrutiny, but by the degraded posts we see there is some proof that this place is uncensored. This ought to be taken as something of value especially in these days of extreme infiltration.

On 2/23/2023 10:16 AM, WM wrote:
> Jim Burns schrieb am Mittwoch,
> 22. Februar 2023 um 18:12:55 UTC+1:

>> Mathematically,
>> no matter which neighborhood (-x,x) of 0
>> is "near 0"
>> almost all unit fractions are in (-x,x)
>
> Alas
> you cannot remove any unit fraction which
> has ℵo unit fractions on the right-hand side.
> Why?

Each unit fraction ends a sequence from 1/1
such that, for each split between 1/1 and it,
some 1/i,1/i⁺⁺ is last-before,first-after.

Your description exists, but it describes
something which does not exist.

We cannot remove things which do not exist.

Jim Burns schrieb am Donnerstag, 23. Februar 2023 um 19:54:18 UTC+1:
> On 2/23/2023 10:16 AM, WM wrote:
> > Jim Burns schrieb am Mittwoch,
> > 22. Februar 2023 um 18:12:55 UTC+1:
>
> >> Mathematically,
> >> no matter which neighborhood (-x,x) of 0
> >> is "near 0"
> >> almost all unit fractions are in (-x,x)
> >
> > Alas
> > you cannot remove any unit fraction which
> > has ℵo unit fractions on the right-hand side.
> > Why?
> Each unit fraction ends a sequence from 1/1
> such that, for each split between 1/1 and it,
> some 1/i,1/i⁺⁺ is last-before,first-after.

That is potential infinity.
>
> Your description exists, but it describes
> something which does not exist.

So you deny the existence of ℵo real points on the real line.
If they existed at the RHS of 0, then they would cover a finite distance, part of which would cover less than ℵo real points on the real line together with their internal distances.

Regards, WM