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

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

On a hyper-sphere perhaps the black holes we observe are paths back to the origin, which we cannot observe.
This would somewhat then be a great attractor; a single singularity that is the origin of the observable universe.
Rather than the cold death it would be more like a return to naught.
If spacetime is thinning via black hole returns then perhaps the laws of electromagnetics are changing over time.
That there is a black hole at the center of most every galaxy might perhaps then help explain the galactic rotation puzzle better.
The puzzle of stability I think remains, and the raisins in the loaf of bread.
But while the yeast in the loaf is expanding pockets are deflating.
Nah; that bread analogy only goes so far...

Timothy Golden pretended :
> 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
>
> On a hyper-sphere perhaps the black holes we observe are paths back to the
> origin, which we cannot observe. This would somewhat then be a great
> attractor; a single singularity that is the origin of the observable
> universe.

Yes, especially the spiral galaxies with all the stars and stuff going
around as if they were actually going somewhere like down a drain into
nothingness.

> Rather than the cold death it would be more like a return to
> naught. If spacetime is thinning via black hole returns then perhaps the laws
> of electromagnetics are changing over time. That there is a black hole at the
> center of most every galaxy might perhaps then help explain the galactic
> rotation puzzle better. The puzzle of stability I think remains, and the
> raisins in the loaf of bread. But while the yeast in the loaf is expanding
> pockets are deflating. Nah; that bread analogy only goes so far...

No matter how you slice it.

On Friday, February 17, 2023 at 2:06:11 PM UTC-5, FromTheRafters wrote:
> Timothy Golden pretended :
> > 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
> >
> > On a hyper-sphere perhaps the black holes we observe are paths back to the
> > origin, which we cannot observe. This would somewhat then be a great
> > attractor; a single singularity that is the origin of the observable
> > universe.
> Yes, especially the spiral galaxies with all the stars and stuff going
> around as if they were actually going somewhere like down a drain into
> nothingness.

Well, in terms of conservation of energy, it would sort of complete the thing.
The whole multiverse concept as well could take its place as our universe is but one happenstance clap.
We can thank the continuum of time for giving us our miniscule slice of existence in the breath of a clap of some exotic (and likely static in our frame) reference. Fresh bread is nice, too. And then there is toast.

> > Rather than the cold death it would be more like a return to
> > naught. If spacetime is thinning via black hole returns then perhaps the laws
> > of electromagnetics are changing over time. That there is a black hole at the
> > center of most every galaxy might perhaps then help explain the galactic
> > rotation puzzle better. The puzzle of stability I think remains, and the
> > raisins in the loaf of bread. But while the yeast in the loaf is expanding
> > pockets are deflating. Nah; that bread analogy only goes so far...
> No matter how you slice it.

Darn. We've been scooped:

https://www.livescience.com/monster-black-holes-could-be-the-source-of-dark-energy-driving-the-accelerating-expansion-of-the-universe-study-suggests

I promise not to end time.

However, the ultimate fate of the universe
remains to be seen.

https://en.wikipedia.org/wiki/Big_Rip
| ... the Big Rip is a hypothetical cosmological
| model ... and even spacetime itself,
| is progressively torn apart by the expansion
| of the universe at a certain time in
| the future, ...

On 2/16/2023 10:17 PM, 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.

On Friday, February 17, 2023 at 1:31:04 PM UTC-8, Jim Burns wrote:
> I promise not to end time.
>
> However, the ultimate fate of the universe
> remains to be seen.

We already know it. The stars die.
If our universe dies does the multiverse?

>
> https://en.wikipedia.org/wiki/Big_Rip
> | ... the Big Rip is a hypothetical cosmological
> | model ... and even spacetime itself,
> | is progressively torn apart by the expansion
> | of the universe at a certain time in
> | the future, ...

You mean island universes would be created if space
expands forever. If it is expanding faster how could it ever contract?
Astronomical measurement is for a faster expansion.

Mitchell Raemsch

> On 2/16/2023 10:17 PM, 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.

On 2/17/2023 4:51 PM, mitchr...@gmail.com wrote:
> On Friday, February 17, 2023
> at 1:31:04 PM UTC-8, Jim Burns wrote:

>> I promise not to end time.
>>
>> However, the ultimate fate of the universe
>> remains to be seen.
>
> We already know it. The stars die.

Stars dying and time ending are different.

Time ending is a possibility in the very distant
future, for all we know today.
We have no time to waste.

> If our universe dies does the multiverse?

I don't see why the multiverse would.
You understand that me not seeing something
is not that much of an indication, right?

On 2/17/23 14:18, Jim Burns wrote:
> On 2/17/2023 4:51 PM, mitchr...@gmail.com wrote:
>> On Friday, February 17, 2023
>> at 1:31:04 PM UTC-8, Jim Burns wrote:
>
>>> I promise not to end time.
>>>
>>> However, the ultimate fate of the universe
>>> remains to be seen.
>>
>> We already know it. The stars die.
>
> Stars dying and time ending are different.
>
> Time ending is a possibility in the very distant
> future, for all we know today.
> We have no time to waste.

Doesn't the word 'end' imply that before a point
in time something exists but after then it does
not exist?

Without time, however there may be no basis for
the word 'end'.

Why is the concept of 'time ending' not a logical
dichotomy? Are you not destroying the basis for
the word 'end' when you string those two words
together? If time does not exist then how can
'ending' exist?

>> If our universe dies does the multiverse?
>
> I don't see why the multiverse would.
> You understand that me not seeing something
> is not that much of an indication, right?
>
>

Trolidan7 was thinking very hard :
> On 2/17/23 14:18, Jim Burns wrote:
>> On 2/17/2023 4:51 PM, mitchr...@gmail.com wrote:
>>> On Friday, February 17, 2023
>>> at 1:31:04 PM UTC-8, Jim Burns wrote:
>>
>>>> I promise not to end time.
>>>>
>>>> However, the ultimate fate of the universe
>>>> remains to be seen.
>>>
>>> We already know it. The stars die.
>>
>> Stars dying and time ending are different.
>>
>> Time ending is a possibility in the very distant
>> future, for all we know today.
>> We have no time to waste.
>
> Doesn't the word 'end' imply that before a point
> in time something exists but after then it does
> not exist?

No, not generally, but in this established context 'time' and 'end' are
inextricable.

> Without time, however there may be no basis for
> the word 'end'.

Yes, in this context.

> Why is the concept of 'time ending' not a logical
> dichotomy?

It is IMO. Just like "What happened before the beginning of time?"
presupposes there was some measure of time for things to 'happen'
'before' time started.

That doesn't mean that there is no 'place' in 'spacetime' where time
becomes irrelevant.

> Are you not destroying the basis for
> the word 'end' when you string those two words
> together? If time does not exist then how can
> 'ending' exist?

Previous to its ending, it existed. :)

--
It will forever be missed

Trolidan7 schrieb am Samstag, 18. Februar 2023 um 09:34:25 UTC+1:

> Doesn't the word 'end' imply that before a point
> in time something exists but after then it does
> not exist?

Exactly. There are infinitely many positive unit fractions met by the cursor when moving from 1 to -1, but when the cursor arrives at 0, the unit fractions have ended.

Regards, WM

On 2/18/2023 3:34 AM, Trolidan7 wrote:
> On 2/17/23 14:18, Jim Burns wrote:
>> On 2/17/2023 4:51 PM, mitchr...@gmail.com wrote:
>>> On Friday, February 17, 2023
>>> at 1:31:04 PM UTC-8, Jim Burns wrote:

>>>> I promise not to end time.
>>>>
>>>> However, the ultimate fate of the universe
>>>> remains to be seen.
>>>
>>> We already know it. The stars die.
>>
>> Stars dying and time ending are different.
>>
>> Time ending is a possibility in the very distant
>> future, for all we know today.
>> We have no time to waste.
>
> Doesn't the word 'end' imply that before a point
> in time something exists but after then it does
> not exist?

Does it?

Does "spending time" with someone imply
that time is a form of money?
Maybe it does.
I don't think we should place too much
importance on that, though.

The paper I'm thinking of
(a paper I haven't read,
I've only read a non-technical summary)
plays out a scenario for our universe,
given certain cosmological values.

In this scenario, over a long period of time,
the expansion of the universe accelerates.
The horizon of our observable universe
draws closer.

By horizon, I mean the expansion of space
between _there_ and _here_ gives _there_
an apparent motion away from _here_ at
the speed of light, red-shifted to c=1.
And, farther away, faster than that.

Over a long period of time,
the most distant galaxies become no longer
observable. Then, less distant galaxies.
Then, all all other galaxies, Andromeda last.

All the other stars in this galaxy
red-shift to 1.
The rest of our solar system.
The rest of Earth.
At the end(?), for each particle,
every other particle is moving away from it
at faster than the speed of light.

That's what I'm calling the end of time,
each particle in its own observable universe.

You don't need to call it that,
if you don't want to. I think
that it's a reasonable interpretation by me
of the use by someone else of "end of time".

> Without time, however there may be no basis
> for the word 'end'.

"Without time" is inaccurate.
You have time. I have time. Time is.

The notion of time embedded in the playing out
of the scenario is different from the notion
of time we use when we soft-boil an egg.

To that notion, the Big Bang, 13.8 billion
years ago, and soft-boiling your egg are
equally "present".

It's a notion closer to:
Here is a sheet of paper,
here is what's written on it.

Perhaps there is no more paper beyond
a certain point.

> Why is the concept of 'time ending' not
> a logical dichotomy? Are you not destroying
> the basis for the word 'end' when
> you string those two words together?
> If time does not exist then
> how can 'ending' exist?

It's not a logical requirement
that time continue.
It's been our experience
that time continues.

It sounds absurd to say "Time ends".
I have no doubt that the absurdness grows
from intuitions distilled from experience.

However, as important as intuition is
as a guide in so many ways, it's not perfect.
It becomes less perfect, the farther away
we get from the experiences from which
it rose.

The observable universe shrunk down to
a single particle? What could be farther
away from your and my experience?
I would give very little trust to
my intuition for this.

WM submitted this idea :
> Trolidan7 schrieb am Samstag, 18. Februar 2023 um 09:34:25 UTC+1:
>
>> Doesn't the word 'end' imply that before a point
>> in time something exists but after then it does
>> not exist?
>
> Exactly. There are infinitely many positive unit fractions met by the cursor
> when moving from 1 to -1, but when the cursor arrives at 0, the unit
> fractions have ended.

Of course, since the rate of encounter has increased toward countable
infinity. Unless, of course, you further stipulate that the cursor
adjust its speed of motion to counteract this problem with your setup
exactly.

Then, there will be another problem.

On Saturday, February 18, 2023 at 9:05:41 AM UTC-8, FromTheRafters wrote:
> WM submitted this idea :
> > Trolidan7 schrieb am Samstag, 18. Februar 2023 um 09:34:25 UTC+1:
> >
> >> Doesn't the word 'end' imply that before a point
> >> in time something exists but after then it does
> >> not exist?
> >
> > Exactly. There are infinitely many positive unit fractions met by the cursor
> > when moving from 1 to -1, but when the cursor arrives at 0, the unit
> > fractions have ended.
> Of course, since the rate of encounter has increased toward countable
> infinity. Unless, of course, you further stipulate that the cursor
> adjust its speed of motion to counteract this problem with your setup
> exactly.
>
> Then, there will be another problem.

Time slows down by motion and gravity but they cannot stop it.
You cannot jump from finite slow to the infinite time slow...
Gamma math demonstrates it.

FromTheRafters schrieb am Samstag, 18. Februar 2023 um 18:05:41 UTC+1:
> WM submitted this idea :
> > Trolidan7 schrieb am Samstag, 18. Februar 2023 um 09:34:25 UTC+1:
> >
> >> Doesn't the word 'end' imply that before a point
> >> in time something exists but after then it does
> >> not exist?
> >
> > Exactly. There are infinitely many positive unit fractions met by the cursor
> > when moving from 1 to -1, but when the cursor arrives at 0, the unit
> > fractions have ended.
> Of course, since the rate of encounter has increased toward countable
> infinity.

Without dark pars every unit fractions could be detected. Note that the all sit at different positions.

Regards, WM

On 2/18/2023 2:20 PM, WM wrote:
> FromTheRafters schrieb am Samstag,
> 18. Februar 2023 um 18:05:41 UTC+1:
>> WM submitted this idea :

>>> There are infinitely many positive unit fractions
>>> met by the cursor when moving from 1 to -1,
>>> but when the cursor arrives at 0,
>>> the unit fractions have ended.
>>
>> Of course, since the rate of encounter
>> has increased toward countable infinity.
>
> Without dark pars every unit fractions
> could be detected.
> Note that the all sit at different positions.

n cannot be detectable without
more being detectable.

If
a sequence ⟨ 0 ... n ⟩ exists
from 0 to n such that,
for each split of ⟨ 0 ... n ⟩
some i,i⁺⁺ is last-before,first-after

then
a sequence ⟨ 0 ... n n⁺⁺ ⟩ exists
from 0 to n⁺⁺ such that,
for each split of ⟨ 0 ... n n++ ⟩
some i,i⁺⁺ is last-before,first-after

If
n is detectable

then
n⁺⁺ is detectable
and so
more than those in ⟨ 0 ... n ⟩
are detectable.

WM formulated the question :
> FromTheRafters schrieb am Samstag, 18. Februar 2023 um 18:05:41 UTC+1:
>> WM submitted this idea :
>>> Trolidan7 schrieb am Samstag, 18. Februar 2023 um 09:34:25 UTC+1:
>>>
>>>> Doesn't the word 'end' imply that before a point
>>>> in time something exists but after then it does
>>>> not exist?
>>>
>>> Exactly. There are infinitely many positive unit fractions met by the
>>> cursor when moving from 1 to -1, but when the cursor arrives at 0, the
>>> unit fractions have ended.
>> Of course, since the rate of encounter has increased toward countable
>> infinity.
>
> Without dark pars every unit fractions could be detected.

They can anyway.

> Note that the all sit at different positions.

How can you tell without detecting them? Maybe they piggyback on
illuminated numbers.

Jim Burns schrieb am Samstag, 18. Februar 2023 um 20:58:54 UTC+1:
> On 2/18/2023 2:20 PM, WM wrote:

> > Without dark parts every unit fractions
> > could be detected.
> > Note that the all sit at different positions.
> n cannot be detectable without
> more being detectable.

Correct. But beyond the detectable there are the undetectable.
All unit fractions are points on the real axis with finite distances between them. Hence there is an invarable number.

> If
> n is detectable
>
> then
> n⁺⁺ is detectable
> and so
> more than those in ⟨ 0 ... n ⟩
> are detectable.

Of course. There is no last detectable, nevertheless there is a last existing before zero.
There are many existing before zero but none beyond.

Regards, WM

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.

Regards, WM

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 don't seem to have anything to
do with things which are undetected.

On 2/18/2023 5:07 PM, WM wrote:
> Jim Burns schrieb am Samstag,
> 18. Februar 2023 um 20:58:54 UTC+1:
>> On 2/18/2023 2:20 PM, WM wrote:

>>> Without dark parts every unit fractions
>>> could be detected.
>>> Note that the all sit at different positions.
>>
>> n cannot be detectable without
>> more being detectable.
>
> Correct.
> But beyond the detectable
> there are the undetectable.

For each detectable, there are _more_ detectable

Those _more_ detectable
(which are less than all)
can match _all_ all detectable

Matching less than all detectable
to all detectable
is how Bob disappears.

Each 1/n in (0,1]
has its own 1/(mₓn) in (0,x]
where mₓ = ⌈1/x⌉

If Bob is on a unit fraction other than 1/(mₓn)
all the swaps 1/(mₓn):1/n replace detectable Bob
with detectable non-Bobs

On Saturday, February 18, 2023 at 11:20:30 AM UTC-8, WM wrote:
> FromTheRafters schrieb am Samstag, 18. Februar 2023 um 18:05:41 UTC+1:
> > WM submitted this idea :
> > > Trolidan7 schrieb am Samstag, 18. Februar 2023 um 09:34:25 UTC+1:
> > >
> > >> Doesn't the word 'end' imply that before a point
> > >> in time something exists but after then it does
> > >> not exist?

Yes. According to that time cannot cease to exist....

> > >
> > > Exactly. There are infinitely many positive unit fractions met by the cursor
> > > when moving from 1 to -1, but when the cursor arrives at 0, the unit
> > > fractions have ended.
> > Of course, since the rate of encounter has increased toward countable
> > infinity.

There is No infinity that is countable.

Jim Burns schrieb am Sonntag, 19. Februar 2023 um 02:23:37 UTC+1:
> On 2/18/2023 5:07 PM, WM wrote:
> > Jim Burns schrieb am Samstag,
> > 18. Februar 2023 um 20:58:54 UTC+1:
> >> On 2/18/2023 2:20 PM, WM wrote:
>
> >>> Without dark parts every unit fractions
> >>> could be detected.
> >>> Note that the all sit at different positions.
> >>
> >> n cannot be detectable without
> >> more being detectable.
> >
> > Correct.
> > But beyond the detectable
> > there are the undetectable.
> For each detectable, there are _more_ detectable

Yes. But when the cursor arrives at zero, there is no more detectable. This is fact. Already before the cursor has arrived at zero there are no detectable unit fractions because if all were detectable, the last one would be detectable too. If only the last one was undetectable, the one before the last one was detectable. And so on. Therefor the last one together with ℵo of its colleagues is undetectable.

> Those _more_ detectable
> (which are less than all)
> can match _all_ all detectable

Yes. That is correct. The bijection with a subset is possible in potential infinity. For every n we can find n^n^n and biject them.
>
> Matching less than all detectable
> to all detectable
> is how Bob disappears.

No. There is no disappearance. The stock is big enough. There are ℵo remaining in any case.
>
> Each 1/n in (0,1]
> has its own 1/(mₓn) in (0,x]
> where mₓ = ⌈1/x⌉
>
> If Bob is on a unit fraction other than 1/(mₓn)
> all the swaps 1/(mₓn):1/n replace detectable Bob
> with detectable non-Bobs

Detectable points can be created and extinguished. But when claiming this for all points, you go astray. Every unit fraction is occupying one and only one point on the real axis. This is a bijection. It is impossible that any of these points vanishes. It is as impossible as that an O vanishes in my matrix proof. It is impossible to biject |ℕ| to |ℕ| - 1. Proof by the reality of real points.

As long as you claim such a loss of reality, further discussion is useless because I do not accept that.

Regards, WM

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, can be passed by a cursor. Hence there is a last point. This cannot be observed. It is dark, together with ℵo of its colleagues.

Regards, WM

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. In fact there is no infinity countable and therefore no infinity uncountable either, or better: every infinity is uncountable. But using that word would raise a wrong impression. Therefore it is better to use the notion actual infinity.

Regards, WM

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.