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The good thing about standards is that there are so many to choose from. -- Andrew S. Tanenbaum


tech / sci.math / Re: Natural numbers and vases

SubjectAuthor
* Natural numbers and vasesWilliam
+- Re: Natural numbers and vasesRoss A. Finlayson
+* Re: Natural numbers and vasesWM
|+* Re: Natural numbers and vasesWilliam
||`* Re: Natural numbers and vasesWM
|| +- Re: Natural numbers and vasessergio
|| `* Re: Natural numbers and vasesWilliam
||  `* Re: Natural numbers and vasesWM
||   +- Re: Natural numbers and vasessergio
||   `* Re: Natural numbers and vasesWilliam
||    `* Re: Natural numbers and vasesWM
||     +- Re: Natural numbers and vasessergio
||     `* Re: Natural numbers and vasesWilliam
||      +- Re: Natural numbers and vasesFritz Feldhase
||      `* Re: Natural numbers and vasesWM
||       +* Re: Natural numbers and vasesWilliam
||       |+* Re: Natural numbers and vasesGus Gassmann
||       ||`* Re: Natural numbers and vasesFritz Feldhase
||       || `- Re: Natural numbers and vasesGus Gassmann
||       |`* Re: Natural numbers and vasesWM
||       | +- Re: Natural numbers and vasesGus Gassmann
||       | +* Re: Natural numbers and vasesWilliam
||       | |+* Re: Natural numbers and vasesWM
||       | ||+* Re: Natural numbers and vasesWilliam
||       | |||`* Re: Natural numbers and vasesWM
||       | ||| `* Re: Natural numbers and vasesWilliam
||       | |||  +* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |`- Re: Natural numbers and vasessergio
||       | |||  +* Re: Natural numbers and vasesGus Gassmann
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||+- Re: Natural numbers and vasesFromTheRafters
||       | |||  ||`- Re: Natural numbers and vasessergio
||       | |||  |+- Re: Natural numbers and vasesGus Gassmann
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||`- Re: Natural numbers and vasessergio
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesGus Gassmann
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||`- Re: Natural numbers and vasessergio
||       | |||  |+- Re: Natural numbers and vasesGus Gassmann
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||`- Re: Natural numbers and vasessergio
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesGus Gassmann
||       | |||  ||`- Re: Natural numbers and vasesChris M. Thomasson
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesGus Gassmann
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||+* Re: Natural numbers and vasesJim Burns
||       | |||  |||`* Re: Natural numbers and vasesWM
||       | |||  ||| +* Re: Natural numbers and vasesJim Burns
||       | |||  ||| |`* Re: Natural numbers and vasesWM
||       | |||  ||| | +* Re: Natural numbers and vasesJim Burns
||       | |||  ||| | |`* Re: Natural numbers and vasesWM
||       | |||  ||| | | +* Re: Natural numbers and vasesJim Burns
||       | |||  ||| | | |`* Re: Natural numbers and vasesWM
||       | |||  ||| | | | `- Re: Natural numbers and vasessergio
||       | |||  ||| | | `- Re: Natural numbers and vasessergio
||       | |||  ||| | `- Re: Natural numbers and vasessergio
||       | |||  ||| `- Re: Natural numbers and vasessergio
||       | |||  ||`* Re: Natural numbers and vasessergio
||       | |||  || `- Re: Natural numbers and vasesChet Hirasi
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||`- Re: Natural numbers and vasessergio
||       | |||  |+* Re: Natural numbers and vasesGus Gassmann
||       | |||  ||`- Re: Natural numbers and vasesChet Hirasi
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||`* Re: Natural numbers and vasessergio
||       | |||  || `* Re: Natural numbers and vasesWM
||       | |||  ||  `* Re: Natural numbers and vasessergio
||       | |||  ||   +* Re: Natural numbers and vasessergio
||       | |||  ||   |`* Re: Natural numbers and vasesFredJeffries
||       | |||  ||   | `- Re: Natural numbers and vasessergio
||       | |||  ||   `* Re: Natural numbers and vasesChris M. Thomasson
||       | |||  ||    `* Re: Natural numbers and vasessergio
||       | |||  ||     +* Re: Natural numbers and vasesChris M. Thomasson
||       | |||  ||     |`- Re: Natural numbers and vasessergio
||       | |||  ||     `* Re: Natural numbers and vasesChris M. Thomasson
||       | |||  ||      `* Re: Natural numbers and vasessergio
||       | |||  ||       `* Re: Natural numbers and vasesChris M. Thomasson
||       | |||  ||        +* Re: Natural numbers and vasesChris M. Thomasson
||       | |||  ||        |`- Re: Natural numbers and vasessergio
||       | |||  ||        `- Re: Natural numbers and vasessergio
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||`- Re: Natural numbers and vasessergio
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||`- Re: Natural numbers and vasessergio
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||+- Re: Natural numbers and vasessergio
||       | |||  ||`* Re: Natural numbers and vasesChris M. Thomasson
||       | |||  || +* Re: Natural numbers and vasesFromTheRafters
||       | |||  || `* Re: Natural numbers and vasessergio
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesGus Gassmann
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesGus Gassmann
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesGus Gassmann
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |`* Re: Natural numbers and vasesWM
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vaseszelos...@gmail.com
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vaseszelos...@gmail.com
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vaseszelos...@gmail.com
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vaseszelos...@gmail.com
||       | |||  +- Re: Natural numbers and vaseszelos...@gmail.com
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vaseszelos...@gmail.com
||       | |||  `- Re: Natural numbers and vaseszelos...@gmail.com
||       | ||`- Re: Natural numbers and vasessergio
||       | |`* Re: Natural numbers and vasesWM
||       | +- Re: Natural numbers and vasessergio
||       | `* Re: Natural numbers and vasesJim Burns
||       `- Re: Natural numbers and vasessergio
|+- Re: Natural numbers and vasesRoss A. Finlayson
|`- Re: Natural numbers and vasesFritz Feldhase
+* Re: Natural numbers and vasesChris M. Thomasson
+* Re: Natural numbers and vasesMostowski Collapse
`- Re: Natural numbers and vasesSocratis T.n.p.

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Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: askaske...@gmail.com (WM)
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 by: WM - Mon, 16 May 2022 16:59 UTC

Jim Burns schrieb am Montag, 16. Mai 2022 um 18:12:23 UTC+2:
> On 5/16/2022 10:52 AM, WM wrote:

> We know that,
> for each index k,

Please talk to the topic. Later on we may discuss other aspects.

We check the number of indexes by bijecting them with the fractions of the first column (we could use every other column or line as well). When applying the indexes for indexing fractions according to m/n gets the index k from
k = (m + n - 1)(m + n - 2)/2 + m
with the result
1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ...
then the integer fractions have to supply these indexes. They are stripped off these indexes.

Can you understand this argument or can't you?

Regards, WM

Re: Natural numbers and vases

<t5u22a$2op$1@gioia.aioe.org>

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From: inva...@invalid.com (sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Mon, 16 May 2022 12:36:09 -0500
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 by: sergio - Mon, 16 May 2022 17:36 UTC

On 5/16/2022 11:59 AM, WM wrote:
> Jim Burns schrieb am Montag, 16. Mai 2022 um 18:12:23 UTC+2:
>> On 5/16/2022 10:52 AM, WM wrote:
>
>> We know that,
>> for each index k,
>
> Please talk to the topic. Later on we may discuss other aspects.
>
> We check the number of indexes by bijecting them with the fractions of the first column

that does not make any sense at all.

> (we could use every other column or line as well).

> When applying the indexes for indexing fractions according to m/n gets the index k from
> k = (m + n - 1)(m + n - 2)/2 + m
> with the result
> 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ...
> then the integer fractions have to supply these indexes.

So you agree that Cantor's enumeration is correct!

> They are stripped off these indexes.

wrong. and intentionally misleading. do you fck with your students this way ?

>
> Can you understand this argument or can't you?

your "argument" is 100% bullshit.

>
> Regards, WM
>
>

yes, the cheese has slid off your cracker.

Re: Natural numbers and vases

<t5u55e$ae$1@dont-email.me>

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From: nom...@afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Mon, 16 May 2022 11:28:59 -0700
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 by: FromTheRafters - Mon, 16 May 2022 18:28 UTC

WM formulated the question :
> sergio schrieb am Montag, 16. Mai 2022 um 04:33:52 UTC+2:
>> On 5/15/2022 3:16 PM, WM wrote:
>>> sergio schrieb am Sonntag, 15. Mai 2022 um 17:32:27 UTC+2:
>>>> On 5/15/2022 9:00 AM, WM wrote:
>>>>> I wrote: "For each place with a swap into it, there is a swap out of it.
>>>>> Never all swaps are completed."This means potential infinity.
>>>> wrong, you stopped at k again.
>>>
>>> At which k?
>
>> FISON(k)
>
> At which k? k is not a number and therefore not finite.

Liar, k is an element of N.

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: askaske...@gmail.com (WM)
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 by: WM - Mon, 16 May 2022 19:14 UTC

FromTheRafters schrieb am Montag, 16. Mai 2022 um 20:29:12 UTC+2:
> WM formulated the question :
> > sergio schrieb am Montag, 16. Mai 2022 um 04:33:52 UTC+2:
> >> On 5/15/2022 3:16 PM, WM wrote:
> >>> sergio schrieb am Sonntag, 15. Mai 2022 um 17:32:27 UTC+2:
> >>>> On 5/15/2022 9:00 AM, WM wrote:
> >>>>> I wrote: "For each place with a swap into it, there is a swap out of it.
> >>>>> Never all swaps are completed."This means potential infinity.
> >>>> wrong, you stopped at k again.
> >>>
> >>> At which k?
> >
> >> FISON(k)
> >
> > At which k? k is not a number and therefore not finite.
> k is an element of N.

Which one is it?

Regards, WM

Re: Natural numbers and vases

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From: james.g....@att.net (Jim Burns)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Mon, 16 May 2022 16:06:38 -0400
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 by: Jim Burns - Mon, 16 May 2022 20:06 UTC

On 5/16/2022 12:59 PM, WM wrote:
> Jim Burns schrieb
> am Montag, 16. Mai 2022 um 18:12:23 UTC+2:

>> We know that,
>> for each index k,
>
> Please talk to the topic.

We know various claims about a fraction.

Among what we know are some claims which describe
a fraction, statements true of a fraction
no matter which fraction is referred to.

These claims we know are _complete_ in the sense that
the are true of _each thing we are talking about_
when it's fractions we are talking about.
Completely true.

Starting from these initial claims true of
each fraction, which is to say: _completely true_
we can prove _other_ claims true of
each fraction, which is to say: _completely true_

We do not step through fractions.
We do not step through indices.
We step through _claims_
We step through _completely true_ claims.

This is how we know what we know
_for each index k_ and so on.

I think that I have mentioned that once or twice.
But it doesn't become less true by repetition.

----
>>> We know that every index used to index a non-integer
>>> fraction or an integer fraction has to be taken from
>>> an integer fraction.

For some collections,
each element can be matched to a proper subset.

For example,
start Bob at 1
OXXXX...

Match 1 and 2. Swap.
XOXXX...

Match 2 and 3. Swap.
XXOXX...

Match 3 and 4. Swap.
XXXOX...

....

For each place with a swap into it,
there is a swap out of it.

After all swaps,
Bob is not at a place with a swap out of it,
and
Bob is not at a place without a swap into it.

There are no other places.

Thus,
after all swaps,
Bob is not at a place, any place.

The places in {1,2,3,...} match
the places in {2,3,4,...}.

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: wpihug...@gmail.com (William)
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 by: William - Mon, 16 May 2022 21:36 UTC

The set of indexes is N_p. No *element* of N_p can leave no 0. The *set* N_p can leave no 0. A set of elements can do something that no element of the set can. No element can be infinite. The set, N_p, like any Peano set. is infinite.

--
William Hughes

Re: Natural numbers and vases

<t5um70$pfa$1@dont-email.me>

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From: chris.m....@gmail.com (Chris M. Thomasson)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Mon, 16 May 2022 16:19:58 -0700
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 by: Chris M. Thomasson - Mon, 16 May 2022 23:19 UTC

On 5/16/2022 7:52 AM, WM wrote:
> Jim Burns schrieb am Sonntag, 15. Mai 2022 um 23:01:49 UTC+2:
>> On 5/15/2022 4:24 PM, WM wrote:
>>> Jim Burns schrieb
>>> am Sonntag, 15. Mai 2022 um 18:13:56 UTC+2:
>>>> And what does "potential infinity" mean when
>>>> you use it?
>>>
>>> Cantor thought: By
>>> k = (m + n - 1)(m + n - 2)/2 + m
>>> all the fractions of the sequence
>>> 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ...
>>> are enumerated.
>>> In fact we cannot find an exception.
>> We know that no exceptions exist.
>
> Wrong. We know that every index used to index a non-integer fraction or an integer fraction has to be taken from an integer fraction.
>
>> There is no requirement keeping numerators and
>> denominators from also being indexes.
>
> That is not claimed by me. Try to understand that every index used to index a non-integer fraction or an integer fraction has to be taken from an integer fraction.
[...]

I am curious... Have you ever implemented Cantor's paring function in a
programming language?

Re: Natural numbers and vases

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From: james.g....@att.net (Jim Burns)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Mon, 16 May 2022 20:00:05 -0400
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 by: Jim Burns - Tue, 17 May 2022 00:00 UTC

On 5/16/2022 7:19 PM, Chris M. Thomasson wrote:
> On 5/16/2022 7:52 AM, WM wrote:
>> Jim Burns schrieb
>> am Sonntag, 15. Mai 2022 um 23:01:49 UTC+2:

> [...]
>
> I am curious... Have you ever implemented Cantor's
> paring function in a programming language?

It would need to be pseudo-code, since any real-world
language would face some sort of maximum condition.

Apart from that, it's almost too simple.

from fraction to index

j = (p+q-1)*(p+q-2)/2 + p

from index to fraction

s = ceiling((sqrt(8*i+1)+1)/2)
p = i - (s-1)*(s-2)/2
q = s = p

I haven't given any thought to which language. Many.

I suppose one could define a Turing machine
to do the job, if one wanted to, for some reason.

Re: Natural numbers and vases

<t5v4s0$ff7$1@gioia.aioe.org>

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From: inva...@invalid.com (sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Mon, 16 May 2022 22:30:07 -0500
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 by: sergio - Tue, 17 May 2022 03:30 UTC

On 5/16/2022 7:00 PM, Jim Burns wrote:
> On 5/16/2022 7:19 PM, Chris M. Thomasson wrote:
>> On 5/16/2022 7:52 AM, WM wrote:
>>> Jim Burns schrieb
>>> am Sonntag, 15. Mai 2022 um 23:01:49 UTC+2:
>
>> [...]
>>
>> I am curious... Have you ever implemented Cantor's
>> paring function in a  programming language?
>
> It would need to be pseudo-code, since any real-world
> language would face some sort of maximum condition.
>
> Apart from that, it's almost too simple.
>
> from fraction to index
>
> j = (p+q-1)*(p+q-2)/2 + p
>
> from index to fraction
>
> s = ceiling((sqrt(8*i+1)+1)/2)
> p = i - (s-1)*(s-2)/2
> q = s = p
>
> I haven't given any thought to which language. Many.
>
> I suppose one could define a Turing machine
> to do the job, if one wanted to, for some reason.
>
>
>

you can find on line calculators that will do it for you,
and several different mappings too, p,q can be mapped several different ways to a single index k

Re: Natural numbers and vases

<t5v8g4$p2o$1@dont-email.me>

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From: chris.m....@gmail.com (Chris M. Thomasson)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Mon, 16 May 2022 21:32:04 -0700
Organization: A noiseless patient Spider
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 by: Chris M. Thomasson - Tue, 17 May 2022 04:32 UTC

On 5/16/2022 8:30 PM, sergio wrote:
> On 5/16/2022 7:00 PM, Jim Burns wrote:
>> On 5/16/2022 7:19 PM, Chris M. Thomasson wrote:
>>> On 5/16/2022 7:52 AM, WM wrote:
>>>> Jim Burns schrieb
>>>> am Sonntag, 15. Mai 2022 um 23:01:49 UTC+2:
>>
>>> [...]
>>>
>>> I am curious... Have you ever implemented Cantor's
>>> paring function in a  programming language?
>>
>> It would need to be pseudo-code, since any real-world
>> language would face some sort of maximum condition.
>>
>> Apart from that, it's almost too simple.
>>
>> from fraction to index
>>
>> j = (p+q-1)*(p+q-2)/2 + p
>>
>> from index to fraction
>>
>> s = ceiling((sqrt(8*i+1)+1)/2)
>> p = i - (s-1)*(s-2)/2
>> q = s = p
>>
>> I haven't given any thought to which language. Many.
>>
>> I suppose one could define a Turing machine
>> to do the job, if one wanted to, for some reason.
>>
>>
>>
>
> you can find on line calculators that will do it for you,
> and several different mappings too, p,q can be mapped several different
> ways to a single index k

I have implemented it several times in different languages. For whats it
worth, I am thinking about creating a new test on my fractal247 site
using WebAudio along with my fractals... Might be interesting.

http://fractallife247.com/test/hmac_cipher/ver_0_0_0_1?ct_hmac_cipher=b85a6d3e801b88cb94f84159f77f2c2918e4592d6bf5e077b3291124dc47806d1171591275327d2ee9375f848568ad5ac8798f9cb0536d3eb655b59f5e49cecac0f4830da20a87e619

Re: Natural numbers and vases

<t5v8ka$p2o$2@dont-email.me>

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From: chris.m....@gmail.com (Chris M. Thomasson)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Mon, 16 May 2022 21:34:18 -0700
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 by: Chris M. Thomasson - Tue, 17 May 2022 04:34 UTC

On 5/16/2022 8:30 PM, sergio wrote:
> On 5/16/2022 7:00 PM, Jim Burns wrote:
>> On 5/16/2022 7:19 PM, Chris M. Thomasson wrote:
>>> On 5/16/2022 7:52 AM, WM wrote:
>>>> Jim Burns schrieb
>>>> am Sonntag, 15. Mai 2022 um 23:01:49 UTC+2:
>>
>>> [...]
>>>
>>> I am curious... Have you ever implemented Cantor's
>>> paring function in a  programming language?
>>
>> It would need to be pseudo-code, since any real-world
>> language would face some sort of maximum condition.
>>
>> Apart from that, it's almost too simple.
>>
>> from fraction to index
>>
>> j = (p+q-1)*(p+q-2)/2 + p
>>
>> from index to fraction
>>
>> s = ceiling((sqrt(8*i+1)+1)/2)
>> p = i - (s-1)*(s-2)/2
>> q = s = p
>>
>> I haven't given any thought to which language. Many.
>>
>> I suppose one could define a Turing machine
>> to do the job, if one wanted to, for some reason.
>>
>>
>>
>
> you can find on line calculators that will do it for you,
> and several different mappings too, p,q can be mapped several different
> ways to a single index k

Oops! I used a different password than the default:

http://fractallife247.com/test/hmac_cipher/ver_0_0_0_1?ct_hmac_cipher=d6dd8ccccaa77535de0512404b43995624317db103ede8b0f5c7bce7261a2f871f79682f933075b82df5970a590e78f74d7230971a3e02a1fdffc389baf07583566d364f5aa967318fff9f3f44855e7f5015

Can you read the ciphertext above?

Re: Natural numbers and vases

<t5vhn6$cle$1@dont-email.me>

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From: nom...@afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Tue, 17 May 2022 00:09:23 -0700
Organization: Peripheral Visions
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 by: FromTheRafters - Tue, 17 May 2022 07:09 UTC

WM used his keyboard to write :
> FromTheRafters schrieb am Montag, 16. Mai 2022 um 20:29:12 UTC+2:
>> WM formulated the question :
>>> sergio schrieb am Montag, 16. Mai 2022 um 04:33:52 UTC+2:
>>>> On 5/15/2022 3:16 PM, WM wrote:
>>>>> sergio schrieb am Sonntag, 15. Mai 2022 um 17:32:27 UTC+2:
>>>>>> On 5/15/2022 9:00 AM, WM wrote:
>>>>>>> I wrote: "For each place with a swap into it, there is a swap out of
>>>>>>> it. Never all swaps are completed."This means potential infinity.
>>>>>> wrong, you stopped at k again.
>>>>>
>>>>> At which k?
>>>
>>>> FISON(k)
>>>
>>> At which k? k is not a number and therefore not finite.
>> k is an element of N.
>
> Which one is it?

No matter, every element of N is finite.

Re: Natural numbers and vases

<710d5745-1624-4735-84ed-e6b31c8df42en@googlegroups.com>

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Subject: Re: Natural numbers and vases
From: askaske...@gmail.com (WM)
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 by: WM - Tue, 17 May 2022 13:21 UTC

Jim Burns schrieb am Montag, 16. Mai 2022 um 22:06:48 UTC+2:
> On 5/16/2022 12:59 PM, WM wrote:

> We do not step through fractions.
> We do not step through indices.

Wrong. Abzählen is basic to set theory. It means going through the natural numbers.

> For example,
> start Bob at 1
> OXXXX...
>
....
> Thus,
> after all swaps,
> Bob is not at a place, any place.

He is at a dark place with blurred border. Otherwise, in a set with only well-defined lit elements, there would have been a last place where he was.
>
> The places in {1,2,3,...} match
> the places in {2,3,4,...}.

That is wrong because the upper set has one more element.

Please talk to the topic. Later on we may discuss other aspects.

We check the number of indexes by bijecting them with the fractions of the first column (we could use every other column or line as well). When applying the indexes for indexing fractions according to m/n gets the index k from
k = (m + n - 1)(m + n - 2)/2 + m
with the result
1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ...
then the integer fractions have to supply these indexes. They are stripped off these indexes.

Can you understand this argument or can't you?

Regards, WM

Re: Natural numbers and vases

<bd266bcf-6197-4ec3-9784-098ec2605d6fn@googlegroups.com>

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Subject: Re: Natural numbers and vases
From: askaske...@gmail.com (WM)
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 by: WM - Tue, 17 May 2022 13:24 UTC

William schrieb am Montag, 16. Mai 2022 um 23:36:52 UTC+2:
> The set of indexes is N_p. No *element* of N_p can leave no 0. The *set* N_p can leave no 0. A set of elements can do something that no element of the set can. No element can be infinite. The set, N_p, like any Peano set. is infinite.
>
Please talk to the topic. Later on we may discuss other aspects.

We check the number of indexes by bijecting them with the fractions of the first column (we could use every other column or line as well). When applying the indexes for indexing fractions according to m/n gets the index k from
k = (m + n - 1)(m + n - 2)/2 + m
with the result
1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ...
then the integer fractions have to supply these indexes. They are stripped off these indexes.

Can you understand this argument or can't you?

Regards, WM

Re: Natural numbers and vases

<48bf5f89-250d-458c-96e4-556e8706a476n@googlegroups.com>

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Subject: Re: Natural numbers and vases
From: askaske...@gmail.com (WM)
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 by: WM - Tue, 17 May 2022 13:26 UTC

FromTheRafters schrieb am Dienstag, 17. Mai 2022 um 09:09:37 UTC+2:
> WM used his keyboard to write :

> >>> At which k? k is not a number and therefore not finite.
> >> k is an element of N.
> >
> > Which one is it?
> No matter, every element of N is finite.

You said k is an elements of |N. Which is it?

Regards, WM

Re: Natural numbers and vases

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From: inva...@invalid.com (sergi o)
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Subject: Re: Natural numbers and vases
Date: Tue, 17 May 2022 08:51:25 -0500
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 by: sergi o - Tue, 17 May 2022 13:51 UTC

On 5/17/2022 8:21 AM, WM wrote:
> Jim Burns schrieb am Montag, 16. Mai 2022 um 22:06:48 UTC+2:
>> On 5/16/2022 12:59 PM, WM wrote:
>
>> We do not step through fractions.
>> We do not step through indices.
>
> Wrong. Abzählen is basic to set theory. It means going through the natural numbers.

that is seldom required in set theory.
Counting is used for sheeps and rocks.

>
>> For example,
>> start Bob at 1
>> OXXXX...
>>
> ...
>> Thus,
>> after all swaps,
>> Bob is not at a place, any place.
>
>>
>> The places in {1,2,3,...} match
>> the places in {2,3,4,...}.
>
>
> We check the number of indexes by bijecting them with

the natural numbers

When applying the indexes for indexing fractions according to m/n gets the index k from
> k = (m + n - 1)(m + n - 2)/2 + m
> with the result
> 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ...

Cantors Enumeration, good for you.

> then the integer fractions have to supply these indexes. They are stripped off these indexes.

100% wrong

>
> Can you understand this argument or can't you?

It is pure diversion and you are nuts.

>
> Regards, WM
>

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: wpihug...@gmail.com (William)
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 by: William - Tue, 17 May 2022 13:57 UTC

> the integer fractions have to supply these indexes.

The set of integer fractions, like the set N_p, like any Peano set, has cadinality aleph_0. There is no problem with this set supplying a set of indexes with cardinality aleph_0 You do not like the idea of a bijection between a set of cardinality aleph_0 and a proper subset, but this is not a contradiction it is something you do not like. There is a bijection between the set S={1/1.1/2. 2/1.1/3., ..} and a proper subset of S, the integer fractions

--
William Hughes

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
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 by: sergi o - Tue, 17 May 2022 14:00 UTC

On 5/16/2022 11:34 PM, Chris M. Thomasson wrote:
> On 5/16/2022 8:30 PM, sergio wrote:
>> On 5/16/2022 7:00 PM, Jim Burns wrote:
>>> On 5/16/2022 7:19 PM, Chris M. Thomasson wrote:
>>>> On 5/16/2022 7:52 AM, WM wrote:
>>>>> Jim Burns schrieb
>>>>> am Sonntag, 15. Mai 2022 um 23:01:49 UTC+2:
>>>
>>>> [...]
>>>>
>>>> I am curious... Have you ever implemented Cantor's
>>>> paring function in a  programming language?
>>>
>>> It would need to be pseudo-code, since any real-world
>>> language would face some sort of maximum condition.
>>>
>>> Apart from that, it's almost too simple.
>>>
>>> from fraction to index
>>>
>>> j = (p+q-1)*(p+q-2)/2 + p
>>>
>>> from index to fraction
>>>
>>> s = ceiling((sqrt(8*i+1)+1)/2)
>>> p = i - (s-1)*(s-2)/2
>>> q = s = p
>>>
>>> I haven't given any thought to which language. Many.
>>>
>>> I suppose one could define a Turing machine
>>> to do the job, if one wanted to, for some reason.
>>>
>>>
>>>
>>
>> you can find on line calculators that will do it for you,
>> and several different mappings too, p,q can be mapped several different ways to a single index k
>
> Oops! I used a different password than the default:
>
> http://fractallife247.com/test/hmac_cipher/ver_0_0_0_1?ct_hmac_cipher=d6dd8ccccaa77535de0512404b43995624317db103ede8b0f5c7bce7261a2f871f79682f933075b82df5970a590e78f74d7230971a3e02a1fdffc389baf07583566d364f5aa967318fff9f3f44855e7f5015
>
>
> Can you read the ciphertext above?

yep,

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
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 by: sergi o - Tue, 17 May 2022 14:10 UTC

On 5/17/2022 8:26 AM, WM wrote:
> FromTheRafters schrieb am Dienstag, 17. Mai 2022 um 09:09:37 UTC+2:
>> WM used his keyboard to write :
>
>>>>> At which k? k is not a number and therefore not finite.
>>>> k is an element of N.
>>>
>>> Which one is it?
>> No matter, every element of N is finite.
>
> You said k is an elements of |N. Which is it?
>
> Regards, WM

yes, k is an element of the set of natural numbers, k∈ N
it is the one between k-1 and k+1

it is the one you stop at, to end an infinite series, so you can proclaim the rest are Darkies,

Re: Natural numbers and vases

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 by: sergi o - Tue, 17 May 2022 14:14 UTC

On 5/17/2022 8:24 AM, WM wrote:
> William schrieb am Montag, 16. Mai 2022 um 23:36:52 UTC+2:
>> The set of indexes is N_p. No *element* of N_p can leave no 0. The *set* N_p can leave no 0. A set of elements can do something that no element of the set can. No element can be infinite. The set, N_p, like any Peano set. is infinite.
>>
>
> We check the number of indexes by bijecting them with the fractions of the first column (we could use every other column or line as well). When applying the indexes for indexing fractions according to m/n gets the index k from
> k = (m + n - 1)(m + n - 2)/2 + m
> with the result
> 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ...

<snip misleading and wrong crap>

>
> Regards, WM

Re: Natural numbers and vases

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From: nom...@afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Tue, 17 May 2022 07:15:32 -0700
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 by: FromTheRafters - Tue, 17 May 2022 14:15 UTC

WM formulated the question :
> FromTheRafters schrieb am Dienstag, 17. Mai 2022 um 09:09:37 UTC+2:
>> WM used his keyboard to write :
>
>>>>> At which k? k is not a number and therefore not finite.
>>>> k is an element of N.
>>>
>>> Which one is it?
>> No matter, every element of N is finite.
>
> You said k is an elements of |N. Which is it?

It doesn't matter! It is a feature of each and every element.

Re: Natural numbers and vases

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From: nom...@afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Tue, 17 May 2022 07:18:26 -0700
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 by: FromTheRafters - Tue, 17 May 2022 14:18 UTC

WM expressed precisely :
> Jim Burns schrieb am Montag, 16. Mai 2022 um 22:06:48 UTC+2:
>> On 5/16/2022 12:59 PM, WM wrote:
>
>> We do not step through fractions.
>> We do not step through indices.
>
> Wrong. Abzählen is basic to set theory. It means going through the natural
> numbers.
>
>> For example,
>> start Bob at 1
>> OXXXX...
>>
> ...
>> Thus,
>> after all swaps,
>> Bob is not at a place, any place.
>
> He is at a dark place with blurred border. Otherwise, in a set with only
> well-defined lit elements, there would have been a last place where he was.
>>
>> The places in {1,2,3,...} match
>> the places in {2,3,4,...}.
>
> That is wrong because the upper set has one more element.

The second set is a proper subset of the first, and is the same size.

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: franz.fr...@gmail.com (Fritz Feldhase)
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 by: Fritz Feldhase - Tue, 17 May 2022 14:19 UTC

On Tuesday, May 17, 2022 at 3:22:01 PM UTC+2, WM wrote:
> Jim Burns schrieb am Montag, 16. Mai 2022 um 22:06:48 UTC+2:
> > On 5/16/2022 12:59 PM, WM wrote:
> >
> > We do not step through fractions.
> > We do not step through indices.
> >
> Wrong. Abzählen [counting] is basic to set theory. It means going through the natural numbers.

Indeed! Note that Chuck Norris counted to infinity - twice.

Re: Natural numbers and vases

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From: nom...@afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Tue, 17 May 2022 07:25:26 -0700
Organization: Peripheral Visions
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 by: FromTheRafters - Tue, 17 May 2022 14:25 UTC

Fritz Feldhase submitted this idea :
> On Tuesday, May 17, 2022 at 3:22:01 PM UTC+2, WM wrote:
>> Jim Burns schrieb am Montag, 16. Mai 2022 um 22:06:48 UTC+2:
>>> On 5/16/2022 12:59 PM, WM wrote:
>>>
>>> We do not step through fractions.
>>> We do not step through indices.
>>>
>> Wrong. Abzählen [counting] is basic to set theory. It means going through
>> the natural numbers.
>
> Indeed! Note that Chuck Norris counted to infinity - twice.

Once with each hand, or in succession? :)

Re: Natural numbers and vases

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Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Tue, 17 May 2022 09:42:43 -0500
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 by: sergi o - Tue, 17 May 2022 14:42 UTC

On 5/17/2022 9:19 AM, Fritz Feldhase wrote:
> On Tuesday, May 17, 2022 at 3:22:01 PM UTC+2, WM wrote:
>> Jim Burns schrieb am Montag, 16. Mai 2022 um 22:06:48 UTC+2:
>>> On 5/16/2022 12:59 PM, WM wrote:
>>>
>>> We do not step through fractions.
>>> We do not step through indices.
>>>
>> Wrong. Abzählen [counting] is basic to set theory. It means going through the natural numbers.
>
> Indeed! Note that Chuck Norris counted to infinity - twice.

I heard he may have also counted by 3's to infinity, but it took the same amount of time

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