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tech / sci.math / Re: Dark unit fractions

SubjectAuthor
* Dark unit fractionsWM
+* Re: Dark unit fractionsGreg Cunt
|`* Re: Dark unit fractionsTransfinity
| `- Re: Dark unit fractionsSergio
+* Re: Dark unit fractionsDan Christensen
|+* Re: Dark unit fractionsTransfinity
||`- Re: Dark unit fractionsDan Christensen
|`* Re: Dark unit fractionsSergio
| `* Re: Dark unit fractionsDan Christensen
|  +- Re: Dark unit fractionsGreg Cunt
|  +* Re: Dark unit fractionsGreg Cunt
|  |+* Re: Dark unit fractionsGreg Cunt
|  ||`* Re: Dark unit fractionsSergio
|  || `- Re: Dark unit fractionsGreg Cunt
|  |+* Re: Dark unit fractionsDan Christensen
|  ||+- Re: Dark unit fractionsGreg Cunt
|  ||`* Re: Dark unit fractionsWM
|  || +- Re: Dark unit fractionsDan Christensen
|  || `- Re: Dark unit fractionsSergio
|  |`- Re: Dark unit fractionsWM
|  `* Re: Dark unit fractionsSergio
|   `* Re: Dark unit fractionsGreg Cunt
|    `- Re: Dark unit fractionsGreg Cunt
+* Re: Dark unit fractionsWilliam
|`* Re: Dark unit fractionsTransfinity
| +- Re: Dark unit fractionsSergio
| `* Re: Dark unit fractionsWilliam
|  `* Re: Dark unit fractionsWM
|   +* Re: Dark unit fractionsWilliam
|   |`* Re: Dark unit fractionsWM
|   | +* Re: Dark unit fractionsWilliam
|   | |`* Re: Dark unit fractionsWM
|   | | +* Re: Dark unit fractionsGreg Cunt
|   | | |`- Re: Dark unit fractionsWM
|   | | +- Re: Dark unit fractionsGreg Cunt
|   | | +* Re: Dark unit fractionsGreg Cunt
|   | | |`* Re: Dark unit fractionsWM
|   | | | `* Re: Dark unit fractionsGreg Cunt
|   | | |  `* Re: Dark unit fractionsWM
|   | | |   +* Re: Dark unit fractionsGreg Cunt
|   | | |   |`- Re: Dark unit fractionsWM
|   | | |   `- Re: Dark unit fractionsGreg Cunt
|   | | +- Re: Dark unit fractionsWilliam
|   | | `- Re: Dark unit fractionsWilliam
|   | `* Re: Dark unit fractionsWilliam
|   |  `* Re: Dark unit fractionsWM
|   |   +- Re: Dark unit fractionsGreg Cunt
|   |   +* Re: Dark unit fractionsWilliam
|   |   |`* Re: Dark unit fractionsWM
|   |   | `* Re: Dark unit fractionsWilliam
|   |   |  `* Re: Dark unit fractionsWM
|   |   |   `- Re: Dark unit fractionsWilliam
|   |   `* Re: Dark unit fractionsSergio
|   |    +* Re: Dark unit fractionsWilliam
|   |    |`* Re: Dark unit fractionsWM
|   |    | `* Re: Dark unit fractionsWilliam
|   |    |  `* Re: Dark unit fractionsWM
|   |    |   `* Re: Dark unit fractionsWilliam
|   |    |    `* Re: Dark unit fractionsWM
|   |    |     +* Re: Dark unit fractionsGreg Cunt
|   |    |     |`- Re: Dark unit fractionsWM
|   |    |     +* Re: Dark unit fractionsWilliam
|   |    |     |`* Re: Dark unit fractionsWM
|   |    |     | +- Re: Dark unit fractionsGreg Cunt
|   |    |     | +- Re: Dark unit fractionsWilliam
|   |    |     | +- Re: Dark unit fractionsWM
|   |    |     | +- Re: Dark unit fractionsWilliam
|   |    |     | +- Re: Dark unit fractionsWM
|   |    |     | +- Re: Dark unit fractionsWilliam
|   |    |     | +- Re: Dark unit fractionsWM
|   |    |     | +- Re: Dark unit fractionsWilliam
|   |    |     | +- Re: Dark unit fractionsWM
|   |    |     | +- Re: Dark unit fractionsWilliam
|   |    |     | +* Re: Dark unit fractionsWM
|   |    |     | |`- Re: Dark unit fractionsSergio
|   |    |     | +- Re: Dark unit fractionsWilliam
|   |    |     | +* Re: Dark unit fractionsWM
|   |    |     | |`- Re: Dark unit fractionsSergio
|   |    |     | +- Re: Dark unit fractionsWilliam
|   |    |     | `* Re: Dark unit fractionsWM
|   |    |     |  `* Re: Dark unit fractionsSergio
|   |    |     |   `* Re: Dark unit fractionsWM
|   |    |     |    `- Re: Dark unit fractionsSergio
|   |    |     +* Re: Dark unit fractionsFromTheRafters
|   |    |     |`* Re: Dark unit fractionsWM
|   |    |     | `- Re: Dark unit fractionsFromTheRafters
|   |    |     `- Re: Dark unit fractionsSergio
|   |    `* Re: Dark unit fractionsWM
|   |     `* Re: Dark unit fractionsGus Gassmann
|   |      `* Re: Dark unit fractionsWM
|   |       +* Re: Dark unit fractionsGus Gassmann
|   |       |`* Re: Dark unit fractionsWM
|   |       | +- Re: Dark unit fractionsSergio
|   |       | +* Re: Dark unit fractionsDan Christensen
|   |       | |`* Re: Dark unit fractionsWM
|   |       | | `* Re: Dark unit fractionsDan Christensen
|   |       | |  `* Re: Dark unit fractionsWM
|   |       | |   `* Re: Dark unit fractionsSergio
|   |       | |    `* Re: Dark unit fractionsWM
|   |       | |     +- Re: Dark unit fractionsWilliam
|   |       | |     +- Re: Dark unit fractionsEram semper recta
|   |       | |     `- Re: Dark unit fractionsWM
|   |       | `* Re: Dark unit fractionsGus Gassmann
|   |       `* Re: Dark unit fractionsGreg Cunt
|   `* Re: Dark unit fractionsGus Gassmann
+* Re: Dark unit fractionsSergio
+* Re: Dark unit fractionsWilliam
+* Re: Dark unit fractionsEram semper recta
+- Re: Dark unit fractionsmitchr...@gmail.com
+* Re: Dark unit fractionsGus Gassmann
+* Re: Dark unit fractionsJim Burns
+* Re: Dark unit fractionsEram semper recta
`- Re: Dark unit fractionsChris M. Thomasson

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Re: Dark unit fractions

<96ec44ec-2bf3-4910-95d3-67d2203e5840n@googlegroups.com>

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Subject: Re: Dark unit fractions
From: wolfgang...@hs-augsburg.de (WM)
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 by: WM - Sat, 7 Aug 2021 14:30 UTC

Greg Cunt schrieb am Freitag, 6. August 2021 um 22:46:17 UTC+2:
> On Friday, August 6, 2021 at 10:19:47 PM UTC+2, WM wrote:
>
> > E(1) can have all natural numbers, but not all aleph_0 endsegments can have aleph_0 natural numbers.
> Nope, each and every endsegment contains aleph_0 natural numbers (as elements). :-)
>
> That's because there is no last/biggest natural number. (!!!)

If not all natural numbers could be applied or removed, then you could not apply or remove all natural numbers(for instance in the intersection). But you claim to be able. You even claim that all are definable and all have aleph_0 successors, such that all are not all.

Regards, WM

Re: Dark unit fractions

<e465d484-6a61-4008-b0c4-c83a4776331an@googlegroups.com>

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Subject: Re: Dark unit fractions
From: franz.fr...@gmail.com (Greg Cunt)
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 by: Greg Cunt - Sat, 7 Aug 2021 14:40 UTC

On Saturday, August 7, 2021 at 4:30:32 PM UTC+2, WM wrote:

> then you could not [...] remove all natural numbers [...] in the intersection.

No one claimed that we can.

Hint: There's no need to "remove" anything from the intersection of all endsegments - after all it's empty.

> But you claim to be able.

Nope. It clearly is YOUR claim, crank.

> You [...] claim that [...] all [natural numbers] have aleph_0 successors

Right: Each and every natural number n has INFINITELY MANY successor, namely n+1, n+2, n+3, ...

Re: Dark unit fractions

<8f464b5d-eb32-4eec-a54b-74fcb3964bd1n@googlegroups.com>

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Subject: Re: Dark unit fractions
From: wolfgang...@hs-augsburg.de (WM)
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 by: WM - Sat, 7 Aug 2021 14:41 UTC

Greg Cunt schrieb am Samstag, 7. August 2021 um 16:18:16 UTC+2:
> On Saturday, August 7, 2021 at 3:36:04 PM UTC+2, WM wrote:
>
> > For every [...] natnumber n, the [infinitely many successors] n, n+1, n+2, ... [are] available.
>
> Indeed!
> > But if all natnumbers have been used to enumerate all endsegments, then nothing remains.
> Remains FOR WHAT?

If all natnumbers have been used to enumerate all endsegments, then nothing remains which is larger than all natnumbers.
> Yeah, if the set of ALL natural numbers is the domain of f, then there is NO natural number which is NOT in the domain of f.
>
> An incredible insight,

Obviously never taken into account by matheologians.

Regards, WM

Re: Dark unit fractions

<f74e9944-75d3-4b53-b18e-981eeed152f3n@googlegroups.com>

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Subject: Re: Dark unit fractions
From: horand.g...@gmail.com (Gus Gassmann)
Injection-Date: Sat, 07 Aug 2021 14:55:39 +0000
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 by: Gus Gassmann - Sat, 7 Aug 2021 14:55 UTC

On Saturday, 7 August 2021 at 10:39:31 UTC-3, WM wrote:
> Gus Gassmann schrieb am Freitag, 6. August 2021 um 18:11:13 UTC+2:
> > On Friday, 6 August 2021 at 11:16:10 UTC-3, WM wrote:
>
> > > There is no switch but the statement of set theory: The bijection exhausts all natural numbers.
> > [...]
> > You say "the bijection", but you never specify what the bijection /is/. Just for your information: There is a bijection of |N onto the set {2, 4, 6, ...}. The image of this bijection is a strict subset of |N. The bijection of |N onto E(n) is a bijection for every natural number n. It is not clear in what sense either of these examples "exhausts all natural numbers".
>
> A bijection is surjective. No natnumber remains outside of a bijection |N with an infinite set like the endsegments.

I can't decipher what that means. Are you acknowledging that both examples of are bijections, or is this supposed to be a criticism of my previous statement, which you conveniently snipped, so the context has gotten lost. I'll be charitable and attribute that to dementia, rather than malicious intent.

Re: Dark unit fractions

<c05d722d-a962-467d-9c2d-012b35289e8fn@googlegroups.com>

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https://www.novabbs.com/tech/article-flat.php?id=69908&group=sci.math#69908

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Subject: Re: Dark unit fractions
From: horand.g...@gmail.com (Gus Gassmann)
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 by: Gus Gassmann - Sat, 7 Aug 2021 14:58 UTC

On Saturday, 7 August 2021 at 10:56:42 UTC-3, WM wrote:
> William schrieb am Freitag, 6. August 2021 um 17:44:37 UTC+2:
> > On Friday, August 6, 2021 at 11:05:44 AM UTC-4, WM wrote:
>
> > > If A is an actually infinite set, then all available natnumbers are used up.
> > Indeed, A is an actually infinite sequence and for every element k of |N_F there is an element i(k) of |N_F such that k is "deleteted" at the element i(k) (note this element may change). However, there is no index i by which all the elements of |N_F are deleted.
>
> No definable index. But if not all indexes are used then there is no surjection.
>
> > At every element i there remain an infinite number of elements of |N_F for the set B(i). So we have
>
> At every definable index, yes. But not after all indexes have been exhausted.
> >
> > -An infinite sequence of sets B(i)
> > -each B(i) contains only elements greater than its index i
> > -each B(i) contains an infinite number of elements
>
> Each i is not decisive because it has aleph_0 successors. Only if you consider the totality of all aleph_0 natnumbers, then you cover all.
> >
> > B is a counterexample.
>
> No. It is only an example of switching between actual infinity (in oder to prove equinumerosity) and potential infinity (in order to defend set theory).
>
> Regards, WM

Are you truly too dense to understand that 1, 2, 3, ... represents potential infinity and {1, 2, 3, ...} represents actual infinity?

Re: Dark unit fractions

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Subject: Re: Dark unit fractions
From: horand.g...@gmail.com (Gus Gassmann)
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 by: Gus Gassmann - Sat, 7 Aug 2021 15:01 UTC

On Saturday, 7 August 2021 at 11:41:29 UTC-3, WM wrote:
> Greg Cunt schrieb am Samstag, 7. August 2021 um 16:18:16 UTC+2:
> > On Saturday, August 7, 2021 at 3:36:04 PM UTC+2, WM wrote:
> >
> > > For every [...] natnumber n, the [infinitely many successors] n, n+1, n+2, ... [are] available.
> >
> > Indeed!
> > > But if all natnumbers have been used to enumerate all endsegments, then nothing remains.
> > Remains FOR WHAT?
> If all natnumbers have been used to enumerate all endsegments, then nothing remains which is larger than all natnumbers.
> > Yeah, if the set of ALL natural numbers is the domain of f, then there is NO natural number which is NOT in the domain of f.
> >
> > An incredible insight,
> Obviously never taken into account by matheologians.

I diagnose an appalling lack of reading comprehension in your first statement and a sorely missing sarcasm detector in the second. Both could be related to Alzheimer's.

Re: Dark unit fractions

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Dark unit fractions
Date: Sat, 7 Aug 2021 10:32:06 -0500
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 by: Sergio - Sat, 7 Aug 2021 15:32 UTC

On 8/7/2021 9:30 AM, WM wrote:
> Greg Cunt schrieb am Freitag, 6. August 2021 um 22:46:17 UTC+2:
>> On Friday, August 6, 2021 at 10:19:47 PM UTC+2, WM wrote:
>>
>>> E(1) can have all natural numbers, but not all aleph_0 endsegments can have aleph_0 natural numbers.
>> Nope, each and every endsegment contains aleph_0 natural numbers (as elements). :-)
>>
>> That's because there is no last/biggest natural number. (!!!)
>

> If not all natural numbers could be applied or removed, then you could not apply or remove all natural numbers

amazing logic!

Re: Dark unit fractions

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Subject: Re: Dark unit fractions
From: franz.fr...@gmail.com (Greg Cunt)
Injection-Date: Sat, 07 Aug 2021 15:45:29 +0000
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 by: Greg Cunt - Sat, 7 Aug 2021 15:45 UTC

On Saturday, August 7, 2021 at 5:32:17 PM UTC+2, Sergio wrote:
> On 8/7/2021 9:30 AM, WM wrote:
> >
> > If not all natural numbers could be applied or removed, then you could not apply or remove all natural numbers
> >
> amazing logic!

Oh, missed that one.

Irrefutable!

Re: Dark unit fractions

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Dark unit fractions
Date: Sat, 7 Aug 2021 13:03:17 -0500
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 by: Sergio - Sat, 7 Aug 2021 18:03 UTC

On 8/7/2021 10:45 AM, Greg Cunt wrote:
> On Saturday, August 7, 2021 at 5:32:17 PM UTC+2, Sergio wrote:
>> On 8/7/2021 9:30 AM, WM wrote:
>>>
>>> If not all natural numbers could be applied or removed, then you could not apply or remove all natural numbers
>>>
>> amazing logic!
>
> Oh, missed that one.
>
> Irrefutable!
>

reminds me of that quote from Buckaroo Bonzi, "No matter where you go,
there you are."

Re: Dark unit fractions

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Subject: Re: Dark unit fractions
From: franz.fr...@gmail.com (Greg Cunt)
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 by: Greg Cunt - Sat, 7 Aug 2021 18:08 UTC

On Saturday, August 7, 2021 at 8:03:28 PM UTC+2, Sergio wrote:
> On 8/7/2021 10:45 AM, Greg Cunt wrote:
> > On Saturday, August 7, 2021 at 5:32:17 PM UTC+2, Sergio wrote:
> >> On 8/7/2021 9:30 AM, WM wrote:
> >>>
> >>> If not all natural numbers could be applied or removed, then you could not apply or remove all natural numbers
> >>>
> >> amazing logic!
> >
> > Oh, missed that one.
> >
> > Irrefutable!
> >
> reminds me of that quote from Buckaroo Bonzi, "No matter where you go,
> there you are."

No one can do what can't be done - except Chuck Norris, of course.

Re: Dark unit fractions

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Subject: Re: Dark unit fractions
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From: pyt...@python.invalid (Python)
Date: Sat, 7 Aug 2021 23:26:14 +0200
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 by: Python - Sat, 7 Aug 2021 21:26 UTC

Gus Gassmann wrote:
> On Saturday, 7 August 2021 at 10:39:31 UTC-3, WM wrote:
>> Gus Gassmann schrieb am Freitag, 6. August 2021 um 18:11:13 UTC+2:
>>> On Friday, 6 August 2021 at 11:16:10 UTC-3, WM wrote:
>>
>>>> There is no switch but the statement of set theory: The bijection exhausts all natural numbers.
>>> [...]
>>> You say "the bijection", but you never specify what the bijection /is/. Just for your information: There is a bijection of |N onto the set {2, 4, 6, ...}. The image of this bijection is a strict subset of |N. The bijection of |N onto E(n) is a bijection for every natural number n. It is not clear in what sense either of these examples "exhausts all natural numbers".
>>
>> A bijection is surjective. No natnumber remains outside of a bijection |N with an infinite set like the endsegments.
>
> I can't decipher what that means. Are you acknowledging that both examples of are bijections, or is this supposed to be a criticism of my previous statement, which you conveniently snipped, so the context has gotten lost. I'll be charitable and attribute that to dementia, rather than malicious intent.

Likely, it's both.

Re: Dark unit fractions

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Subject: Re: Dark unit fractions
From: horand.g...@gmail.com (Gus Gassmann)
Injection-Date: Sat, 07 Aug 2021 23:04:38 +0000
Content-Type: text/plain; charset="UTF-8"
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 by: Gus Gassmann - Sat, 7 Aug 2021 23:04 UTC

On Saturday, 7 August 2021 at 11:55:44 UTC-3, Gus Gassmann wrote:
> On Saturday, 7 August 2021 at 10:39:31 UTC-3, WM wrote:
> > Gus Gassmann schrieb am Freitag, 6. August 2021 um 18:11:13 UTC+2:
> > > On Friday, 6 August 2021 at 11:16:10 UTC-3, WM wrote:
> >
> > > > There is no switch but the statement of set theory: The bijection exhausts all natural numbers.
> > > [...]
> > > You say "the bijection", but you never specify what the bijection /is/. Just for your information: There is a bijection of |N onto the set {2, 4, 6, ...}. The image of this bijection is a strict subset of |N. The bijection of |N onto E(n) is a bijection for every natural number n. It is not clear in what sense either of these examples "exhausts all natural numbers".
> >
> > A bijection is surjective. No natnumber remains outside of a bijection |N with an infinite set like the endsegments.
> I can't decipher what that means. Are you acknowledging that both examples of are bijections, or is this supposed to be a criticism of my previous statement, which you conveniently snipped, so the context has gotten lost. I'll be charitable and attribute that to dementia, rather than malicious intent.

That should of course have said "... both are examples of bijections ...". My bad.

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