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tech / sci.math / [0, 1] contains more unit fractions than can be discerned.

[0, 1] contains more unit fractions than can be discerned.

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Subject: [0, 1] contains more unit fractions than can be discerned.
From: askaske...@gmail.com (WM)
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by: WM - Thu, 9 Feb 2023 08:23 UTC

Re: [0, 1] contains more unit fractions than can be discerned.

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From: chris.m....@gmail.com (Chris M. Thomasson)
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Subject: Re: [0, 1] contains more unit fractions than can be discerned.
Date: Thu, 9 Feb 2023 00:43:03 -0800
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by: Chris M. Thomasson - Thu, 9 Feb 2023 08:43 UTC

On 2/9/2023 12:23 AM, WM wrote:
> Doesn't it?

Did you fry you brain on some sort of odd substance over the years?

0...1 contains infinite unit fractions...........

They are all there. Name one that is not there?

Re: [0, 1] contains more unit fractions than can be discerned.

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Subject: Re: [0, 1] contains more unit fractions than can be discerned.
From: franz.fr...@gmail.com (Fritz Feldhase)
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by: Fritz Feldhase - Thu, 9 Feb 2023 09:01 UTC

On Thursday, February 9, 2023 at 9:43:15 AM UTC+1, Chris M. Thomasson wrote:

> 0...1 contains infinite unit fractions...........

Nope. But there are _infinitely MANY_ unit fractions in [0, 1].

Please try to get that straight.

(Hint: For each and every number n: 0 < 1/n <= 1. Hence no unit fraction is "infinite". :-P)

Re: [0, 1] contains more unit fractions than can be discerned.

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by: JVR - Thu, 9 Feb 2023 09:01 UTC

On Thursday, February 9, 2023 at 9:23:17 AM UTC+1, WM wrote:
> Doesn't it?
>
> Regards, WM

Brilliant, Mücke. For this important insight you win the Archimides-Plutonicus Prize
for the decade. There will be a ceremony honoring you for this, as well as your many other
contributions, in the famous Burghölzli Institute in Zürich on February 29. Everybody is
cordially invited.

Re: [0, 1] contains more unit fractions than can be discerned.

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Subject: Re: [0, 1] contains more unit fractions than can be discerned.
From: askaske...@gmail.com (WM)
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by: WM - Thu, 9 Feb 2023 09:07 UTC

Fritz Feldhase schrieb am Donnerstag, 9. Februar 2023 um 10:01:59 UTC+1:
> But there are _infinitely MANY_ unit fractions in [0, 1].

Of course. ℵo.

> (Hint: For each and every number n: 0 < 1/n <= 1. Hence no unit fraction is "infinite". :-P)

But if there are always ℵo in front of the cursor, then will jolt about ℵo unit fractions all at once when crossing the border between (0, 1] and 0. That means they cannot be distinguished. We call them dark unit fractions.

Regards, WM

Re: [0, 1] contains more unit fractions than can be discerned.

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From: chris.m....@gmail.com (Chris M. Thomasson)
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Subject: Re: [0, 1] contains more unit fractions than can be discerned.
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by: Chris M. Thomasson - Thu, 9 Feb 2023 09:09 UTC

On 2/9/2023 1:01 AM, Fritz Feldhase wrote:
> On Thursday, February 9, 2023 at 9:43:15 AM UTC+1, Chris M. Thomasson wrote:
>
>> 0...1 contains infinite unit fractions...........
>
> Nope. But there are _infinitely MANY_ unit fractions in [0, 1].
>
> Please try to get that straight.

God damn it! I deserve a self slap. Sorry... It's a horrible habit of mine:

infinite unit fractions

infinitely _many_ unit fractions

damn! I meant the latter...

>
> (Hint: For each and every number n: 0 < 1/n <= 1. Hence no unit fraction is "infinite". :-P)

Got ya. Thanks. Btw, I will try to do better wrt being more precise in
my wording.

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Re: [0, 1] contains more unit fractions than can be discerned.

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by: JVR - Thu, 9 Feb 2023 09:22 UTC

On Thursday, February 9, 2023 at 10:07:31 AM UTC+1, WM wrote:
> Fritz Feldhase schrieb am Donnerstag, 9. Februar 2023 um 10:01:59 UTC+1:
> > But there are _infinitely MANY_ unit fractions in [0, 1].
> Of course. ℵo.
> > (Hint: For each and every number n: 0 < 1/n <= 1. Hence no unit fraction is "infinite". :-P)
> But if there are always ℵo in front of the cursor, then will jolt about ℵo unit fractions all at once when crossing the border between (0, 1] and 0. That means they cannot be distinguished. We call them dark unit fractions.
>
> Regards, WM

Indeed, ist a rough road and slow progress. But it it is not too great inconvenience in
view of the great rewards.

The cursor does 'jolt about', even though the bumps in the road are invisible?
I agree, that must be very scary.

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by: Eram semper recta - Thu, 9 Feb 2023 09:23 UTC

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Subject: Re: [0, 1] contains more unit fractions than can be discerned.
From: thenewca...@gmail.com (Eram semper recta)
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by: Eram semper recta - Thu, 9 Feb 2023 09:24 UTC

On Thursday, 9 February 2023 at 11:19:31 UTC+2, zelos...@gmail.com wrote:
> torsdag 9 februari 2023 kl. 09:23:17 UTC+1 skrev WM:
> > Doesn't it?
> >
> > Regards, WM
> wtf does "discerned" even mean?
Ты слишком тупой, чтобы понять. Возьмите урок английского языка.
Got Russian lessons? 🤣🤣🤣🤣
I bet you wished you had a US passport now, eh? I have one. Wooohooo.

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Subject: Re: [0, 1] contains more unit fractions than can be discerned.
From: thenewca...@gmail.com (Eram semper recta)
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by: Eram semper recta - Thu, 9 Feb 2023 09:27 UTC

On Thursday, 9 February 2023 at 11:19:31 UTC+2, zelos...@gmail.com wrote:
> torsdag 9 februari 2023 kl. 09:23:17 UTC+1 skrev WM:
> > Doesn't it?
> >
> > Regards, WM
> wtf does "discerned" even mean?

Да сэр!

Learn it! It is how you will address your new masters in the not-too-distant future. :-)

I suppose if you stick your tongue a little deeper up Türkiye's arse, maybe they'll let you join NATO?

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Subject: Re: [0, 1] contains more unit fractions than can be discerned.
From: franz.fr...@gmail.com (Fritz Feldhase)
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by: Fritz Feldhase - Thu, 9 Feb 2023 09:28 UTC

Re: [0, 1] contains more unit fractions than can be discerned.

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Subject: Re: [0, 1] contains more unit fractions than can be discerned.
From: thenewca...@gmail.com (Eram semper recta)
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by: Eram semper recta - Thu, 9 Feb 2023 09:29 UTC

On Thursday, 9 February 2023 at 11:24:52 UTC+2, Eram semper recta wrote:
> On Thursday, 9 February 2023 at 11:19:31 UTC+2, zelos...@gmail.com wrote:
> > torsdag 9 februari 2023 kl. 09:23:17 UTC+1 skrev WM:
> > > Doesn't it?
> > >
> > > Regards, WM
> > wtf does "discerned" even mean?
> Ты слишком тупой, чтобы понять. Возьмите урок английского языка.
>
> Got Russian lessons? 🤣🤣🤣🤣
>
> I bet you wished you had a US passport now, eh? I have one. Wooohooo.
On second thoughts, Türkiye might get an anal infection from your dirty germ infested tongue up their arses.

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Subject: Re: [0, 1] contains more unit fractions than can be discerned.
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by: Fritz Feldhase - Thu, 9 Feb 2023 09:36 UTC

Re: [0, 1] contains more unit fractions than can be discerned.

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by: Chris M. Thomasson - Thu, 9 Feb 2023 09:38 UTC

On 2/9/2023 1:29 AM, Eram semper recta wrote:
> On Thursday, 9 February 2023 at 11:24:52 UTC+2, Eram semper recta wrote:
>> On Thursday, 9 February 2023 at 11:19:31 UTC+2, zelos...@gmail.com wrote:
>>> torsdag 9 februari 2023 kl. 09:23:17 UTC+1 skrev WM:
>>>> Doesn't it?
>>>>
>>>> Regards, WM
>>> wtf does "discerned" even mean?
>> Ты слишком тупой, чтобы понять. Возьмите урок английского языка.
>>
>> Got Russian lessons? 🤣🤣🤣🤣
>>
>> I bet you wished you had a US passport now, eh? I have one. Wooohooo.
>
> On second thoughts, Türkiye might get an anal infection from your dirty germ infested tongue up their arses.

Why did your brain go there? wow. lol.

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Subject: Re: [0, 1] contains more unit fractions than can be discerned.
From: franz.fr...@gmail.com (Fritz Feldhase)
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by: Fritz Feldhase - Thu, 9 Feb 2023 09:44 UTC

On Thursday, February 9, 2023 at 10:39:09 AM UTC+1, Chris M. Thomasson wrote:
> On 2/9/2023 1:29 AM, Eram semper recta wrote:
> >
> > On second thoughts, Türkiye might get an anal infection from your dirty germ infested tongue up their arses.
> >
> Why did your brain go there? wow. lol.

"For the mouth speaks what the heart is full of."

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Subject: Re: [0, 1] contains more unit fractions than can be discerned.
From: askaske...@gmail.com (WM)
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by: WM - Thu, 9 Feb 2023 17:36 UTC

zelos...@gmail.com schrieb am Donnerstag, 9. Februar 2023 um 10:19:31 UTC+1:
> torsdag 9 februari 2023 kl. 09:23:17 UTC+1 skrev WM:
> > Doesn't it?

> wtf does "discerned" even mean?

Consult a dictionary.

Regards, WM

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Subject: Re: [0, 1] contains more unit fractions than can be discerned.
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by: WM - Thu, 9 Feb 2023 17:40 UTC

Fritz Feldhase schrieb am Donnerstag, 9. Februar 2023 um 10:29:05 UTC+1:
> On Thursday, February 9, 2023 at 10:23:10 AM UTC+1, Eram semper recta wrote:
> > On Thursday, 9 February 2023 at 10:23:17 UTC+2, WM wrote:
> > >
> > > Doesn't it?
> > >
> > Of course it does!!!!!
> Two graet minds join forces!

Are you not able to understand this simple truth?
Will you argue that every unit fraction has ℵo successors before zero?
If the cursor does not discern the last one, then there are dark unit fractions.

Regards, WM

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by: FromTheRafters - Thu, 9 Feb 2023 19:11 UTC

Re: [0, 1] contains more unit fractions than can be discerned.

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From: chris.m....@gmail.com (Chris M. Thomasson)
Newsgroups: sci.math
Subject: Re: [0, 1] contains more unit fractions than can be discerned.
Date: Thu, 9 Feb 2023 14:29:21 -0800
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by: Chris M. Thomasson - Thu, 9 Feb 2023 22:29 UTC

On 2/9/2023 1:44 AM, Fritz Feldhase wrote:
> On Thursday, February 9, 2023 at 10:39:09 AM UTC+1, Chris M. Thomasson wrote:
>> On 2/9/2023 1:29 AM, Eram semper recta wrote:
>>>
>>> On second thoughts, Türkiye might get an anal infection from your dirty germ infested tongue up their arses.
>>>
>> Why did your brain go there? wow. lol.
>
> "For the mouth speaks what the heart is full of."

No shit, Fritz! God damn. ;^o

Re: [0, 1] contains more unit fractions than can be discerned.

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Subject: Re: [0, 1] contains more unit fractions than can be discerned.
From: zelos.ma...@gmail.com (zelos...@gmail.com)
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by: zelos...@gmail.com - Fri, 10 Feb 2023 11:46 UTC

torsdag 9 februari 2023 kl. 10:30:40 UTC+1 skrev Eram semper recta:
> On Thursday, 9 February 2023 at 11:19:31 UTC+2, zelos...@gmail.com wrote:
> > torsdag 9 februari 2023 kl. 09:23:17 UTC+1 skrev WM:
> > > Doesn't it?
> > >
> > > Regards, WM
> > wtf does "discerned" even mean?
> Да сэр!
>
> Learn it! It is how you will address your new masters in the not-too-distant future. :-)
>
> I suppose if you stick your tongue a little deeper up Türkiye's arse, maybe they'll let you join NATO?

I see you are still just as evil as always

Re: [0, 1] contains more unit fractions than can be discerned.

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Subject: Re: [0, 1] contains more unit fractions than can be discerned.
From: zelos.ma...@gmail.com (zelos...@gmail.com)
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by: zelos...@gmail.com - Fri, 10 Feb 2023 11:47 UTC

torsdag 9 februari 2023 kl. 10:24:52 UTC+1 skrev Eram semper recta:
> On Thursday, 9 February 2023 at 11:19:31 UTC+2, zelos...@gmail.com wrote:
> > torsdag 9 februari 2023 kl. 09:23:17 UTC+1 skrev WM:
> > > Doesn't it?
> > >
> > > Regards, WM
> > wtf does "discerned" even mean?
> Ты слишком тупой, чтобы понять. Возьмите урок английского языка.
>
> Got Russian lessons? 🤣🤣🤣🤣
>
> I bet you wished you had a US passport now, eh? I have one. Wooohooo.
No, why would I want to live in that hell hole?

Why is it you want war and death to innocent people? Why do you support genocidal dictators?

Re: [0, 1] contains more unit fractions than can be discerned.

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Subject: Re: [0, 1] contains more unit fractions than can be discerned.
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by: zelos...@gmail.com - Fri, 10 Feb 2023 11:48 UTC

torsdag 9 februari 2023 kl. 18:36:15 UTC+1 skrev WM:
> zelos...@gmail.com schrieb am Donnerstag, 9. Februar 2023 um 10:19:31 UTC+1:
> > torsdag 9 februari 2023 kl. 09:23:17 UTC+1 skrev WM:
> > > Doesn't it?
> > wtf does "discerned" even mean?
> Consult a dictionary.
>
> Regards, WM

I want a mathematical meaning, clearly defined. A dictionary reports usage, not definitions.

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Subject: Re: [0, 1] contains more unit fractions than can be discerned.
From: franz.fr...@gmail.com (Fritz Feldhase)
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by: Fritz Feldhase - Fri, 10 Feb 2023 14:40 UTC

On Thursday, February 9, 2023 at 6:40:23 PM UTC+1, WM wrote:

> Will you [claim] that every unit fraction has ℵo successors before zero?

Indeed!

Hint: Let U := {1/n : n e IN}.

Then for each and every u e U: card({v e U : 0 < v < u}) = ℵo

Hint: For each and every natural number n: 1/n > 1/(n+1) > 1/(n+2) > ... > 0

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Subject: Re: [0, 1] contains more unit fractions than can be discerned.
From: franz.fr...@gmail.com (Fritz Feldhase)
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by: Fritz Feldhase - Fri, 10 Feb 2023 14:42 UTC

On Thursday, February 9, 2023 at 6:40:23 PM UTC+1, WM wrote:

> If the cursor does not discern the last one, then there are dark unit fractions.

Because you say so?

Hint: "[Mückenheim's] conclusions are based on the sloppiness of his notions, his inability of giving precise definitions, his fundamental misunderstanding of elementary mathematical concepts, and sometimes, as the late Dik Winter remarked [...], on nothing at all."

Subject	Author
[0, 1] contains more unit fractions than can be discerned.	WM
Re: [0, 1] contains more unit fractions than can be discerned.	Chris M. Thomasson
Re: [0, 1] contains more unit fractions than can be discerned.	Fritz Feldhase
Re: [0, 1] contains more unit fractions than can be discerned.	WM
Re: [0, 1] contains more unit fractions than can be discerned.	JVR
Re: [0, 1] contains more unit fractions than can be discerned.	Chris M. Thomasson
Re: [0, 1] contains more unit fractions than can be discerned.	JVR
Re: [0, 1] contains more unit fractions than can be discerned.	zelos...@gmail.com
Re: [0, 1] contains more unit fractions than can be discerned.	Eram semper recta
Re: [0, 1] contains more unit fractions than can be discerned.	Eram semper recta
Re: [0, 1] contains more unit fractions than can be discerned.	Chris M. Thomasson
Re: [0, 1] contains more unit fractions than can be discerned.	Fritz Feldhase
Re: [0, 1] contains more unit fractions than can be discerned.	Chris M. Thomasson
Re: [0, 1] contains more unit fractions than can be discerned.	zelos...@gmail.com
Re: [0, 1] contains more unit fractions than can be discerned.	Eram semper recta
Re: [0, 1] contains more unit fractions than can be discerned.	zelos...@gmail.com
Re: [0, 1] contains more unit fractions than can be discerned.	Fritz Feldhase
Re: [0, 1] contains more unit fractions than can be discerned.	WM
Re: [0, 1] contains more unit fractions than can be discerned.	zelos...@gmail.com
Re: [0, 1] contains more unit fractions than can be discerned.	WM
Re: [0, 1] contains more unit fractions than can be discerned.	FromTheRafters
Re: [0, 1] contains more unit fractions than can be discerned.	Fritz Feldhase
Re: [0, 1] contains more unit fractions than can be discerned.	FromTheRafters
Re: [0, 1] contains more unit fractions than can be discerned.	Eram semper recta
Re: [0, 1] contains more unit fractions than can be discerned.	Fritz Feldhase
Re: [0, 1] contains more unit fractions than can be discerned.	WM
Re: [0, 1] contains more unit fractions than can be discerned.	Fritz Feldhase
Re: [0, 1] contains more unit fractions than can be discerned.	WM
Re: [0, 1] contains more unit fractions than can be discerned.	Fritz Feldhase
Re: [0, 1] contains more unit fractions than can be discerned.	WM
Re: [0, 1] contains more unit fractions than can be discerned.	Fritz Feldhase
Re: [0, 1] contains more unit fractions than can be discerned.	WM