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Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: wpihug...@gmail.com (William)
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by: William - Wed, 20 Jul 2022 14:26 UTC

On Wednesday, July 20, 2022 at 8:29:44 AM UTC-3, WM wrote:
> William schrieb am Dienstag, 19. Juli 2022 um 21:30:04 UTC+2:

> > "All elements of |N" ( i.e. the set |N) is not followed by an element of |N.
> If removing all elements differs from removing the set, then something is rotten to the core in Cantor-land. By what should it differ?

It does not. "all elements of |N" is the set |N. So removing "all elements of |N" means removing |N. |N\|N = {} so "all elements of |N" is not followed by an element of |N.

--
William Hughes

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
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by: sergi o - Wed, 20 Jul 2022 15:51 UTC

On 7/19/2022 8:10 AM, sergi o wrote:
> On 7/19/2022 7:19 AM, WM wrote:
>> FromTheRafters schrieb am Dienstag, 19. Juli 2022 um 02:05:32 UTC+2:
>>> sergi o pretended :
>>>> On 7/18/2022 4:29 PM, WM wrote:
>>>>> William schrieb am Montag, 18. Juli 2022 um 20:17:17 UTC+2:
>>>>>> On Monday, July 18, 2022 at 2:47:34 PM UTC-3, WM wrote:
>>>>>
>>>>>> Let |N_b be the subset of |N of elements that are in the bijection,
>>>>>> Let |N_s be the subset of |N of elements that have a successor
>>>>>>>> Simple induction shows that 1. each element (without exception) is in
>>>>>>>> the bijection
>>>>>
>>>>> By the way, this is wrong. Simple induction shows that every element in the
>>>>> bijection has infinitely many successors.
>>>>
>>>> can you put that in terms of MATH ?
>>>>
>>>>>
>>>>>> So 1. is |N_b = |N
>>>>>>
>>>>>>> Removing them leaves nothing.
>>>>>>
>>>>>> |N\|N_b = {}
>>>>>>>> and 2. each element (without exception) has a successor.
>>>>>> So 2. is |N_s = |N
>>>>>>> Removing them leaves infinitely many succesors
>>>>>> Nope |N\|N_s={}. Correct is to say "removing any element of |N_s leaves
>>>>>> infinitely many successors". However "them", |N_s, is not an element of
>>>>>> |N_s ,
>>>>>
>>>>> All elements of |N_s are elements of |N_s.
>>>>
>>>> converse: All elements of |N_s are elements of |N_s.
>>>> Inverse : all elements not of |N_s are elements not of |N_s.
>>>> Contrapositive : all elements not of |N_s are elements not of |N_s.
>>>>
>>>> golly REAL LOGIC here, Folks!
>>> Each (and every) element of |N_s is an element of |N_s.
>>
>> Yes. If all elements were definable,
>
> you put on your CLOWN SHOES when you drag out your "definable", with its "colors of the rainbow", "raps", taps, beeps, flashes of light, and shows you
> have an unsound mind.
>
>
>> then removing all elements was possible element by element and would yield the same result as removing the set.
>
> your words have failed you for YEARS and YEARS. Try equations. Oh, equations would show your math is BS.
>
>
>> But that is wrong according to WH. He claims that instead of all elements automaticalle the set must be used. He does not explain why this is so. I
>> explain it.
>
> Fail. you have failed every time over years to explain, you may want it so. But it is not. Accept that fact. You're even discussing your hordes of
> shuffling darkies.
>
>>
>> Regards, WM
>
>

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
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by: Fritz Feldhase - Wed, 20 Jul 2022 17:37 UTC

On Wednesday, July 20, 2022 at 4:26:17 PM UTC+2, William wrote:

> "all elements of IN" is the set IN.

Actually, no!

___ THE SET OF all elements of IN is the set IN. ___

{n : n e IN} = IN.

Holy shit!

You guys are going nuts. Too much Mückenheim, it seems.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Wed, 20 Jul 2022 18:19 UTC

William schrieb am Mittwoch, 20. Juli 2022 um 16:26:17 UTC+2:
> On Wednesday, July 20, 2022 at 8:29:44 AM UTC-3, WM wrote:
> > William schrieb am Dienstag, 19. Juli 2022 um 21:30:04 UTC+2:
>
> > > "All elements of |N" ( i.e. the set |N) is not followed by an element of |N.
> > If removing all elements differs from removing the set, then something is rotten to the core in Cantor-land. By what should it differ?
> It does not. "all elements of |N" is the set |N.

True.

> So removing "all elements of |N" means removing |N.

True. But removing all individually definable elements leaves ℵ₀ elements.

|N\|N = {} so "all elements of |N" is not followed by an element of |N.
>
Remove element by element individually. Yu will not remove all. The reason is: You cannot remove all. Any idea why?

Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Wed, 20 Jul 2022 18:21 UTC

Fritz Feldhase schrieb am Mittwoch, 20. Juli 2022 um 19:37:46 UTC+2:
> On Wednesday, July 20, 2022 at 4:26:17 PM UTC+2, William wrote:
>
> > "all elements of IN" is the set IN.
>
> Actually, no!

Every set is defined by its elements and by nothing else. Therefore the set is nothing else.

Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: wpihug...@gmail.com (William)
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by: William - Wed, 20 Jul 2022 18:30 UTC

On Wednesday, July 20, 2022 at 3:19:23 PM UTC-3, WM wrote:
> William schrieb am Mittwoch, 20. Juli 2022 um 16:26:17 UTC+2:
> > On Wednesday, July 20, 2022 at 8:29:44 AM UTC-3, WM wrote:
> > > William schrieb am Dienstag, 19. Juli 2022 um 21:30:04 UTC+2:
> >
> > > > "All elements of |N" ( i.e. the set |N) is not followed by an element of |N.
> > > If removing all elements differs from removing the set, then something is rotten to the core in Cantor-land. By what should it differ?
> > It does not. "all elements of |N" is the set |N.
> True.
> > So removing "all elements of |N" means removing |N.
> True.
So "all elements of |N" is not followed by an element of N.

<skip>

> Remove element by element individually. Yu will not remove all.

Indeed, a stepwise , element by element, process will not work. There are plenty of ways that do work.

--
William Hughes

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Wed, 20 Jul 2022 18:35 UTC

William schrieb am Mittwoch, 20. Juli 2022 um 20:30:29 UTC+2:
> On Wednesday, July 20, 2022 at 3:19:23 PM UTC-3, WM wrote:
> > William schrieb am Mittwoch, 20. Juli 2022 um 16:26:17 UTC+2:
> > > On Wednesday, July 20, 2022 at 8:29:44 AM UTC-3, WM wrote:
> > > > William schrieb am Dienstag, 19. Juli 2022 um 21:30:04 UTC+2:
> > >
> > > > > "All elements of |N" ( i.e. the set |N) is not followed by an element of |N.
> > > > If removing all elements differs from removing the set, then something is rotten to the core in Cantor-land. By what should it differ?
> > > It does not. "all elements of |N" is the set |N.
> > True.
> > > So removing "all elements of |N" means removing |N.
> > True.
> So "all elements of |N" is not followed by an element of N.
>
> <skip>
> > Remove element by element individually. You will not remove all.
> Indeed, a stepwise , element by element, process will not work.

It would however, if every element could be defined individually.

Regards, WM

Re: Natural numbers and vases III

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From: nom...@afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Wed, 20 Jul 2022 14:38:16 -0400
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by: FromTheRafters - Wed, 20 Jul 2022 18:38 UTC

After serious thinking WM wrote :
> Fritz Feldhase schrieb am Mittwoch, 20. Juli 2022 um 19:37:46 UTC+2:
>> On Wednesday, July 20, 2022 at 4:26:17 PM UTC+2, William wrote:
>>
>>> "all elements of IN" is the set IN.
>>
>> Actually, no!
>
> Every set is defined by its elements and by nothing else. Therefore the set
> is nothing else.

No, a set is a 'collection of elements' which *also* conform to the
axioms of set theory and thus forms a set under that theory.

Re: Natural numbers and vases III

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From: nom...@afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Wed, 20 Jul 2022 14:44:03 -0400
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by: FromTheRafters - Wed, 20 Jul 2022 18:44 UTC

WM pretended :
> William schrieb am Mittwoch, 20. Juli 2022 um 16:26:17 UTC+2:
>> On Wednesday, July 20, 2022 at 8:29:44 AM UTC-3, WM wrote:
>>> William schrieb am Dienstag, 19. Juli 2022 um 21:30:04 UTC+2:
>>>> "All elements of |N" ( i.e. the set |N) is not followed by an element of
>>>> |N.
>>> If removing all elements differs from removing the set, then something is
>>> rotten to the core in Cantor-land. By what should it differ?
>> It does not. "all elements of |N" is the set |N.
>
> True.

Wrong, but all elements of |N are contained in |N -- it can be thought
of like shoes in a shoebox, the shoes are not the box.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: wpihug...@gmail.com (William)
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by: William - Wed, 20 Jul 2022 18:45 UTC

On Wednesday, July 20, 2022 at 3:35:12 PM UTC-3, WM wrote:
> William schrieb am Mittwoch, 20. Juli 2022 um 20:30:29 UTC+2:
> > On Wednesday, July 20, 2022 at 3:19:23 PM UTC-3, WM wrote:
> > > William schrieb am Mittwoch, 20. Juli 2022 um 16:26:17 UTC+2:
> > > > On Wednesday, July 20, 2022 at 8:29:44 AM UTC-3, WM wrote:
> > > > > William schrieb am Dienstag, 19. Juli 2022 um 21:30:04 UTC+2:
> > > >
> > > > > > "All elements of |N" ( i.e. the set |N) is not followed by an element of |N.
> > > > > If removing all elements differs from removing the set, then something is rotten to the core in Cantor-land. By what should it differ?
> > > > It does not. "all elements of |N" is the set |N.
> > > True.
> > > > So removing "all elements of |N" means removing |N.
> > > True.
> > So "all elements of |N" is not followed by an element of N.
> >
> > <skip>
> > > Remove element by element individually. You will not remove all.
> > Indeed, a stepwise , element by element, process will not work
..
> It would however if every element could be defined individually.

Since it is not true that "every element can be written down" this is vacuously true. So what? The ways that do work still work.

--
William Hughes

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
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by: Fritz Feldhase - Wed, 20 Jul 2022 21:32 UTC

On Wednesday, July 20, 2022 at 8:21:42 PM UTC+2, WM wrote:
> Fritz Feldhase schrieb am Mittwoch, 20. Juli 2022 um 19:37:46 UTC+2:
> > On Wednesday, July 20, 2022 at 4:26:17 PM UTC+2, William wrote:
> > >
> > > "all elements of IN" is the set IN.
> > >
> > Actually, no!
> >
> Every set is defined by its elements and by nothing else.

Right.

> Therefore the set is nothing else.

Nope.

Hints:

1. {a} =/= a for any a (in ZFC).

2. The empty set is not nothing, it exists (though it does NOT contain any elements).

3. William is an idiot. Maybe suffering from dementia, just like you.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Thu, 21 Jul 2022 08:19 UTC

Fritz Feldhase schrieb am Mittwoch, 20. Juli 2022 um 23:32:41 UTC+2:
> On Wednesday, July 20, 2022 at 8:21:42 PM UTC+2, WM wrote:
> > Fritz Feldhase schrieb am Mittwoch, 20. Juli 2022 um 19:37:46 UTC+2:
> > > On Wednesday, July 20, 2022 at 4:26:17 PM UTC+2, William wrote:
> > > >
> > > > "all elements of IN" is the set IN.
> > > >
> > > Actually, no!
> > >
> > Every set is defined by its elements and by nothing else.
> Right.
> > Therefore the set is nothing else.
> Nope.
>
> Hints:
>
> 1. {a} =/= a for any a (in ZFC).

Therefore ZFC is rubbish.

In mathematics there are also sets. Does the knowledge of the elements determine the set? Or is there more required? No, not in mathematics.
>
> 2. The empty set is not nothing, it exists (though it does NOT contain any elements).

No, it has only been blown up by mediocre adherents of set theory.

Not even Zermelo was convinced of this. "It is not a genuine set and was introduced by me only for formal reasons." [E. Zermelo, letter to A. Fraenkel (1 Mar 1921)] "I increasingly doubt the justifiability of the 'null set'. Perhaps one can dispense with it by restricting the axiom of separation in a suitable way. Indeed, it serves only the purpose of formal simplification." [E. Zermelo, letter to A. Fraenkel (9 May 1921)]

Also Richard Dedekind discarded the empty set.

So it is, strictly speaking, not existing as such." [Cantor, p. 146]

Gottlob Frege shared his opinion: "If, according to our previous use of the word, a class consists of things, is a collection, a collective union of them, then it must disappear when these things disappear. If we burn down all the trees of a forest, then we burn down the forest. Thus an empty class cannot exist." [G. Frege: "Kleine Schriften", I. Agelelli (ed.), 2nd ed., Olms, Hildesheim (1990) p. 195]

Conclusion: A set is determined by its elements and nothing else. A set does not conatin more than its elements. Therefore a set is nothing more than its elements.

Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Thu, 21 Jul 2022 08:22 UTC

William schrieb am Mittwoch, 20. Juli 2022 um 20:45:44 UTC+2:
> On Wednesday, July 20, 2022 at 3:35:12 PM UTC-3, WM wrote:

> > > > Remove element by element individually. You will not remove all.
> > > Indeed, a stepwise , element by element, process will not work
> .
> > It would however if every element could be defined individually.
>
> Since it is not true that "every element can be written down" this is vacuously true.

It is a truth to be taught to the disciples of ZFC. They counterfactually claim the contrary.

> So what? The ways that do work still work.

Yes, we can remove the whole set, i.e., more than we can define individually.

Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Thu, 21 Jul 2022 08:24 UTC

FromTheRafters schrieb am Mittwoch, 20. Juli 2022 um 20:44:17 UTC+2:
> WM pretended :
> > William schrieb am Mittwoch, 20. Juli 2022 um 16:26:17 UTC+2:
> >> On Wednesday, July 20, 2022 at 8:29:44 AM UTC-3, WM wrote:
> >>> William schrieb am Dienstag, 19. Juli 2022 um 21:30:04 UTC+2:
> >>>> "All elements of |N" ( i.e. the set |N) is not followed by an element of
> >>>> |N.
> >>> If removing all elements differs from removing the set, then something is
> >>> rotten to the core in Cantor-land. By what should it differ?
> >> It does not. "all elements of |N" is the set |N.
> >
> > True.
> Wrong, but all elements of |N are contained in |N -- it can be thought
> of like shoes in a shoebox, the shoes are not the box.

What remains from the set after all elements have been subtracted?

Regards, WM

Re: Natural numbers and vases III

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From: nom...@afraid.org (FromTheRafters)
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Subject: Re: Natural numbers and vases III
Date: Thu, 21 Jul 2022 05:40:26 -0400
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by: FromTheRafters - Thu, 21 Jul 2022 09:40 UTC

WM formulated the question :
> Fritz Feldhase schrieb am Mittwoch, 20. Juli 2022 um 23:32:41 UTC+2:
>> On Wednesday, July 20, 2022 at 8:21:42 PM UTC+2, WM wrote:
>>> Fritz Feldhase schrieb am Mittwoch, 20. Juli 2022 um 19:37:46 UTC+2:
>>>> On Wednesday, July 20, 2022 at 4:26:17 PM UTC+2, William wrote:
>>>>>
>>>>> "all elements of IN" is the set IN.
>>>>>
>>>> Actually, no!
>>>>
>>> Every set is defined by its elements and by nothing else. Right.
>>> Therefore the set is nothing else.
>> Nope.
>>
>> Hints:
>>
>> 1. {a} =/= a for any a (in ZFC).
>
> Therefore ZFC is rubbish.
>
> In mathematics there are also sets. Does the knowledge of the elements
> determine the set? Or is there more required? No, not in mathematics.
>>
>> 2. The empty set is not nothing, it exists (though it does NOT contain any
>> elements).
>
> No, it has only been blown up by mediocre adherents of set theory.
>
> Not even Zermelo was convinced of this. "It is not a genuine set and was
> introduced by me only for formal reasons." [E. Zermelo, letter to A. Fraenkel
> (1 Mar 1921)] "I increasingly doubt the justifiability of the 'null set'.
> Perhaps one can dispense with it by restricting the axiom of separation in a
> suitable way. Indeed, it serves only the purpose of formal simplification."
> [E. Zermelo, letter to A. Fraenkel (9 May 1921)]
>
> Also Richard Dedekind discarded the empty set.
>
> So it is, strictly speaking, not existing as such." [Cantor, p. 146]
>
> Gottlob Frege shared his opinion: "If, according to our previous use of the
> word, a class consists of things, is a collection, a collective union of
> them, then it must disappear when these things disappear. If we burn down all
> the trees of a forest, then we burn down the forest. Thus an empty class
> cannot exist." [G. Frege: "Kleine Schriften", I. Agelelli (ed.), 2nd ed.,
> Olms, Hildesheim (1990) p. 195]
>
> Conclusion: A set is determined by its elements and nothing else. A set does
> not conatin more than its elements. Therefore a set is nothing more than its
> elements.

That appears to be only *your* conclusion.

Re: Natural numbers and vases III

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From: nom...@afraid.org (FromTheRafters)
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Subject: Re: Natural numbers and vases III
Date: Thu, 21 Jul 2022 05:46:01 -0400
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by: FromTheRafters - Thu, 21 Jul 2022 09:46 UTC

WM wrote on 7/21/2022 :
> FromTheRafters schrieb am Mittwoch, 20. Juli 2022 um 20:44:17 UTC+2:
>> WM pretended :
>>> William schrieb am Mittwoch, 20. Juli 2022 um 16:26:17 UTC+2:
>>>> On Wednesday, July 20, 2022 at 8:29:44 AM UTC-3, WM wrote:
>>>>> William schrieb am Dienstag, 19. Juli 2022 um 21:30:04 UTC+2:
>>>>>> "All elements of |N" ( i.e. the set |N) is not followed by an element of
>>>>>>> N.
>>>>> If removing all elements differs from removing the set, then something is
>>>>> rotten to the core in Cantor-land. By what should it differ?
>>>> It does not. "all elements of |N" is the set |N.
>>>
>>> True.
>> Wrong, but all elements of |N are contained in |N -- it can be thought
>> of like shoes in a shoebox, the shoes are not the box.
>
> What remains from the set after all elements have been subtracted?

Nothing happens to the set, they still don't change, you just create a
new set with only the elements you want in it. If you don't want any
elements in it, you have the emptyset, that is, just the box.

Also, it is not about the box and it is not about the shoes, it is
about the relation, epsilon, or set membership.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: wpihug...@gmail.com (William)
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by: William - Thu, 21 Jul 2022 14:41 UTC

On Thursday, July 21, 2022 at 5:22:31 AM UTC-3, WM wrote:
> William schrieb am Mittwoch, 20. Juli 2022 um 20:45:44 UTC+2:
> > On Wednesday, July 20, 2022 at 3:35:12 PM UTC-3, WM wrote:
>
> > > > > Remove element by element individually. You will not remove all.
> > > > Indeed, a stepwise , element by element, process will not work
> > .
> > > It would however if every element could be defined individually.
> >
> > Since it is not true that "every element can be written down" this is vacuously true.
> It is a truth to be taught to the disciples of ZFC. They counterfactually claim the contrary.

Piffle. Everyone claims that "every element of |N can be written down" is false, So the statement "if every element of |N can be written down them WM is the pope" is true

--
William Hughes

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: jrennenk...@googlemail.com (JVR)
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by: JVR - Thu, 21 Jul 2022 14:54 UTC

On Thursday, July 21, 2022 at 10:24:10 AM UTC+2, WM wrote:
> FromTheRafters schrieb am Mittwoch, 20. Juli 2022 um 20:44:17 UTC+2:
> > WM pretended :
> > > William schrieb am Mittwoch, 20. Juli 2022 um 16:26:17 UTC+2:
> > >> On Wednesday, July 20, 2022 at 8:29:44 AM UTC-3, WM wrote:
> > >>> William schrieb am Dienstag, 19. Juli 2022 um 21:30:04 UTC+2:
> > >>>> "All elements of |N" ( i.e. the set |N) is not followed by an element of
> > >>>> |N.
> > >>> If removing all elements differs from removing the set, then something is
> > >>> rotten to the core in Cantor-land. By what should it differ?
> > >> It does not. "all elements of |N" is the set |N.
> > >
> > > True.
> > Wrong, but all elements of |N are contained in |N -- it can be thought
> > of like shoes in a shoebox, the shoes are not the box.
> What remains from the set after all elements have been subtracted?
>
> Regards, WM

That's easy: An empty-headed prefosser remains.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
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by: Fritz Feldhase - Thu, 21 Jul 2022 16:37 UTC

On Thursday, July 21, 2022 at 10:19:41 AM UTC+2, WM wrote:
> Fritz Feldhase schrieb am Mittwoch, 20. Juli 2022 um 23:32:41 UTC+2:
> > On Wednesday, July 20, 2022 at 8:21:42 PM UTC+2, WM wrote:
> > > Fritz Feldhase schrieb am Mittwoch, 20. Juli 2022 um 19:37:46 UTC+2:
> > > > On Wednesday, July 20, 2022 at 4:26:17 PM UTC+2, William wrote:
> > > > >
> > > > > "all elements of IN" is the set IN.
> > > > >
> > > > Actually, no!
> > > >
> > > Every set is defined by its elements and by nothing else.
> > >
> > Right.
> > >
> > > Therefore the set is nothing else.
> > >
> > Nope.
> >
> > Hints:
> >
> > 1. {a} =/= a for any a (in ZFC).
> >
> Therefore ZFC is rubbish.

If you say so.

> > 2. The empty set is not nothing, it exists (though it does NOT contain any elements).
> >
> No

Yes. At least in any contemporary/axiomatic system of set theory.

> Not even Zermelo

Zermelo:

| "II. Axiom of elementary sets:
|
| There is a set, the null set 0, which contains no elements at all. [...]"

[Zermelo, Ernst: Untersuchungen über die Grundlagen der Mengenlehre, 1907, in: Mathematische Annalen 65 (1908), S. 261–281]

> Also Richard Dedekind

| "[...] On the other hand, we want to completely exclude here the empty set, which contains no element at all, for certain reasons,
although it may be convenient for other investigations to invent one."

[Dedekind, Was sind und was sollen die Zahlen, 1888]

Hint: 1888 => preaxiomatic!

> So it is, strictly speaking, not existing as such." [Cantor, p. 146]

Hint: Cantor => preaxiomatic!

> Gottlob Frege [...]: "If, according to our previous use of the word, a class consists of things, is a collection, a collective union of them, then it must disappear when these things disappear. If we burn down all the trees of a forest, then we burn down the forest. Thus an empty class cannot exist." [G. Frege: "Kleine Schriften", I. Agelelli (ed.), 2nd ed., Olms, Hildesheim (1990) p. 195]

This was a critical remark concerning Schröder's system of "classes", you silly idiot. Of course, Frege had an empty "Begriffsumfang" in his system.

> Conclusion: <nonsense>

Lit.: Kanamori, A. (2003): The Empty Set, the Singleton, and the Ordered Pair

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: horand.g...@gmail.com (Gus Gassmann)
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by: Gus Gassmann - Thu, 21 Jul 2022 18:20 UTC

On Thursday, 21 July 2022 at 13:37:23 UTC-3, Fritz Feldhase wrote:
[...]
> > > 2. The empty set is not nothing, it exists (though it does NOT contain any elements).
> > >
> > No
> Yes. At least in any contemporary/axiomatic system of set theory.

Well, it is not clear what he objects to, the existence or the emptiness. Maybe the empty set contains dark numbers according to his empty head? That's another way to remove the apparent contradiction involving IN \ E(n) and IN \ [union{n in IN} E(n)]... Since the numbers are dark, nobody can see them, which clearly proves that they must exist! (Oh dear!)
[...]

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Thu, 21 Jul 2022 20:11 UTC

William schrieb am Donnerstag, 21. Juli 2022 um 16:41:48 UTC+2:
> On Thursday, July 21, 2022 at 5:22:31 AM UTC-3, WM wrote:
> > William schrieb am Mittwoch, 20. Juli 2022 um 20:45:44 UTC+2:
> > > On Wednesday, July 20, 2022 at 3:35:12 PM UTC-3, WM wrote:
> >
> > > > > > Remove element by element individually. You will not remove all.
> > > > > Indeed, a stepwise , element by element, process will not work
> > > .
> > > > It would however if every element could be defined individually.
> > >
> > > Since it is not true that "every element can be written down" this is vacuously true.
> > It is a truth to be taught to the disciples of ZFC. They counterfactually claim the contrary.
> Piffle. Everyone claims that "every element of |N can be written down" is false,

I have counter evidence but I am too lazy to present it here.

> So the statement "if every element of |N can be written down them WM is the pope" is true

The set of natnumbers which can be written down is not the set |N but it is not empty either.

Regrds, WM

Re: Natural numbers and vases III

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by: FromTheRafters - Thu, 21 Jul 2022 20:26 UTC

WM wrote :
> William schrieb am Donnerstag, 21. Juli 2022 um 16:41:48 UTC+2:
>> On Thursday, July 21, 2022 at 5:22:31 AM UTC-3, WM wrote:
>>> William schrieb am Mittwoch, 20. Juli 2022 um 20:45:44 UTC+2:
>>>> On Wednesday, July 20, 2022 at 3:35:12 PM UTC-3, WM wrote:
>>>>>>> Remove element by element individually. You will not remove all.
>>>>>> Indeed, a stepwise , element by element, process will not work .
>>>>> It would however if every element could be defined individually.
>>>>
>>>> Since it is not true that "every element can be written down" this is
>>>> vacuously true.
>>> It is a truth to be taught to the disciples of ZFC. They counterfactually
>>> claim the contrary.
>> Piffle. Everyone claims that "every element of |N can be written down" is
>> false,
>
> I have counter evidence but I am too lazy to present it here.

Margins are too small eh?

>> So the statement "if every element of |N can be written down them WM is the
>> pope" is true
>
> The set of natnumbers which can be written down is not the set |N but it is
> not empty either.

They each seem to be arbitrary finite proper subsets of |N if one can
define the ability to 'write them down' to be a resource restriction
like not enough time or not enough lead in your pencil.

How long does it take in muckymath to find the intersection of any two
such arbitrary sets? Say each has a cardinality of arond 1000?

I bet ZFC is quicker.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: wpihug...@gmail.com (William)
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by: William - Thu, 21 Jul 2022 20:29 UTC

On Thursday, July 21, 2022 at 5:11:11 PM UTC-3, WM wrote:
>> The set of natnumbers which can be written down is not the set |N but it is not empty either.

Trivial. So What? We still have

1. Each element of |N (not every one of which can be written down) is in the bijection,. i.e. |N\N_b={}.
2. Each element of |N (not every one of which can be written down) has infinitely many successors. i.e. |N\N_s={}

The fact that you cannot "remove" |N_s using a stepwise, element by element, process does not mean 2. is false.
--
William Hughes

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Fri, 22 Jul 2022 12:55 UTC

William schrieb am Donnerstag, 21. Juli 2022 um 22:29:33 UTC+2:
> On Thursday, July 21, 2022 at 5:11:11 PM UTC-3, WM wrote:
> >> The set of natnumbers which can be written down is not the set |N but it is not empty either.
> Trivial. So What?

You have just accepted the existence of a potentially infinite collection: The set of natnumbers which can be written down is less than the actually infinite set |N, but not bounded by a finite number.

> We still have
>
> 1. Each element of |N (not every one of which can be written down) is in the bijection,. i.e. |N\N_b={}.

How could that be checked for elements which cannot be written down?

> 2. Each element of |N (not every one of which can be written down) has infinitely many successors. i.e. |N\N_s={}

If all elements of |N could be removed element by element, then no successors would remain. But that is not possible. And that is not a matter of time or ressources. It is a matter of the difference between actual infinity and potential infinity.

Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: wpihug...@gmail.com (William)
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by: William - Fri, 22 Jul 2022 15:36 UTC

On Friday, July 22, 2022 at 9:55:21 AM UTC-3, WM wrote:

<snop>

> > We still have
> >
> > 1. Each element of |N (not every one of which can be written down) is in the bijection,. i.e. |N\N_b={}.
> How could that be checked for elements which cannot be written down?

One does not "check" element by element but uses a method (e.g. induction) that "checks" all the elements (whether or not they can be written down) at once.

> > 2. Each element of |N (not every one of which can be written down) has infinitely many successors. i.e. |N\N_s={}

> If all elements of |N could be removed element by element, then no successors would remain.

Correct.
>But that is not possible.

So what? A stepwise process cannot show |N\|N_s={}. There are methods (e.g. induction) that do show |N\N_s={}

--
William Hughes

Subject	Author
Natural numbers and vases III	WM
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	sergi o
Re: Natural numbers and vases III	sergi o
Re: Natural numbers and vases III	FromTheRafters
Re: Natural numbers and vases III	sergi o
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	sergi o
Re: Natural numbers and vases III	sergi o
Re: Natural numbers and vases III	William
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Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	sergi o
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	sergi o
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	FromTheRafters
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	FromTheRafters
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	FromTheRafters
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	FromTheRafters
Re: Natural numbers and vases III	Surgio
Re: Natural numbers and vases III	Jim Burns
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	Jim Burns
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Surgio
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Surgio
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	Jim Africani
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	William
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Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	FredJeffries
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	FredJeffries
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	FromTheRafters
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	Eduardo Faqtardo
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	Archimedes Plutonium
Re: Natural numbers and vases III	Archimedes Plutonium