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Natural numbers and vases III

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Subject: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Mon, 18 Jul 2022 21:29 UTC

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.

> 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.

> so the fact that "removing them" leave nothing is not a contradiction.

We don't remove the set but all its elements. If this is not the same, then something is wrong in Cantor-land.
>
> From "removing any element of |N_s leaves infinitely many successors" we can conclude that "removing any finite subset of |N_s leaves infinitely many successors". However, "them", |N_s, is not a finite subset of |N_s , so the fact that "removing them" leave nothing is not a contradiction.

It is a contradiction that the elements cannot be handled as elements. The reason is of course that set theory fails otherwise.

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 - Mon, 18 Jul 2022 21:43 UTC

On Monday, July 18, 2022 at 11:29:37 PM UTC+2, WM wrote:

> All elements of |N_s are elements of |N_s.

WHAT AN INCREDIBLE INSIGHT, MÜCKENHEIM!

This one is absolutely true!

Actually, it follows from the more general law:

All X are X.

Keep up the good work, Mückenheim!

Re: Natural numbers and vases III

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by: sergi o - Mon, 18 Jul 2022 22:13 UTC

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 ?

golly REAL LOGIC here, Folks!

>
>> so the fact that "removing them" leave nothing is not a contradiction.
>
> We don't remove the set but all its elements.

you did not remove the car, you remove a car battery.

>>
>> From "removing any element of |N_s leaves infinitely many successors" we can conclude that "removing any finite subset of |N_s leaves infinitely many successors". However, "them", |N_s, is not a finite subset of |N_s , so the fact that "removing them" leave nothing is not a contradiction.
>
> It is a contradiction that the elements cannot be handled as elements.

What do you mean by "handled" ? Man-handled? That is not a Math term.

OH, do you mean an "operator" term ?

> The reason is of course that set theory fails otherwise.

Agree, your reasoning and understanding of set theory fails.

>
> 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 - Mon, 18 Jul 2022 23:31 UTC

On Monday, July 18, 2022 at 6:29:37 PM UTC-3, 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.

Nope. Induction can show many things two thing it can show are 1. Each element is in the bijection. 2. Each element in the bijection has an infinite number of successors. There is a contradiction iff there is a last element.

--
William Hughes

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
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by: Gus Gassmann - Mon, 18 Jul 2022 23:54 UTC

On Monday, 18 July 2022 at 18:43:46 UTC-3, Fritz Feldhase wrote:
> On Monday, July 18, 2022 at 11:29:37 PM UTC+2, WM wrote:
>
> > All elements of |N_s are elements of |N_s.
> WHAT AN INCREDIBLE INSIGHT, MÜCKENHEIM!

Holy moly! Another Fields-medal moment!

Re: Natural numbers and vases III

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by: FromTheRafters - Tue, 19 Jul 2022 00:05 UTC

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.

Re: Natural numbers and vases III

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by: sergi o - Tue, 19 Jul 2022 02:30 UTC

On 7/18/2022 7:05 PM, FromTheRafters wrote:
> 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.

totally agree, each and every is more precise, "all" is a fuzzy word.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
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by: zelos...@gmail.com - Tue, 19 Jul 2022 02:46 UTC

måndag 18 juli 2022 kl. 23:29:37 UTC+2 skrev WM:
> 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.

They do, but they are still equal to N

>
> > 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.
>
> > so the fact that "removing them" leave nothing is not a contradiction.
>
> We don't remove the set but all its elements. If this is not the same, then something is wrong in Cantor-land.
> >
> > From "removing any element of |N_s leaves infinitely many successors" we can conclude that "removing any finite subset of |N_s leaves infinitely many successors". However, "them", |N_s, is not a finite subset of |N_s , so the fact that "removing them" leave nothing is not a contradiction.
>
> It is a contradiction that the elements cannot be handled as elements. The reason is of course that set theory fails otherwise.

There is no contradiction, the issue is your puny brain

>
> Regards, WM

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Subject: Re: Natural numbers and vases III
From: thenewca...@gmail.com (Eram semper recta)
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by: Eram semper recta - Tue, 19 Jul 2022 03:06 UTC

On Tuesday, 19 July 2022 at 00:29:37 UTC+3, 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
>

But wtf is an "element" and a "set"? They are both the same thing and they are not the same thing. They are both everything and nothing. LMAO.

@5:02 "Now don't think that sets are so simple. But inside a set could be other sets and inside them could be other sets. So you see how tricky sets could be .... You have a rather sophisticated and uh, uh, ... rich concept. The set theoretic foundation of mathematics is the set and everything that we talk about in there, is a set. Great simplifier. Everything is a set" - Professor Harvey Friedman

This is Harvey's lecture on the Foundations of Bullshit: https://youtu.be/mogMr45UTj4

This is my 164 second rebuttal: https://youtu.be/KvxjOMW6Q9w

> By the way, this is wrong.

Not even wrong, so to speak.

> Simple induction shows that every element in the bijection has infinitely many successors.
>
> > 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.

All sets of |N_s are sets of |N_s. Chuckle.

>
> > so the fact that "removing them" leave nothing is not a contradiction.
>
> We don't remove the set but all its elements.

But the elements are sets? Chuckle.

> If this is not the same, then something is wrong in Cantor-land.

You think?! ROFLMAO

Sometimes you are a funny man Wolfgang. EVERYTHING is wrong in Cantor-land.

> >
> > From "removing any element of |N_s leaves infinitely many successors" we can conclude that "removing any finite subset of |N_s leaves infinitely many successors". However, "them", |N_s, is not a finite subset of |N_s , so the fact that "removing them" leave nothing is not a contradiction.
>
> It is a contradiction that the elements cannot be handled as elements.

But why? As Harvey says, "A set is everything and a set is nothing. Very rich concept". 🤣🤣🤣🤣🤣🤣

> The reason is of course that set theory fails otherwise.

Set theory never actually succeeded.

>
> Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
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by: Eram semper recta - Tue, 19 Jul 2022 03:17 UTC

On Tuesday, 19 July 2022 at 06:06:47 UTC+3, Eram semper recta wrote:
> On Tuesday, 19 July 2022 at 00:29:37 UTC+3, 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
> >
> But wtf is an "element" and a "set"? They are both the same thing and they are not the same thing. They are both everything and nothing. LMAO.
>
> @5:02 "Now don't think that sets are so simple. But inside a set could be other sets and inside them could be other sets. So you see how tricky sets could be .... You have a rather sophisticated and uh, uh, ... rich concept.. The set theoretic foundation of mathematics is the set and everything that we talk about in there, is a set. Great simplifier. Everything is a set" - Professor Harvey Friedman
>
> This is Harvey's lecture on the Foundations of Bullshit: https://youtu.be/mogMr45UTj4
>
> This is my 164 second rebuttal: https://youtu.be/KvxjOMW6Q9w
> > By the way, this is wrong.
> Not even wrong, so to speak.
> > Simple induction shows that every element in the bijection has infinitely many successors.
> >
> > > 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.
> All sets of |N_s are sets of |N_s. Chuckle.
> >
> > > so the fact that "removing them" leave nothing is not a contradiction..
> >
> > We don't remove the set but all its elements.
> But the elements are sets? Chuckle.
> > If this is not the same, then something is wrong in Cantor-land.
> You think?! ROFLMAO
>
> Sometimes you are a funny man Wolfgang. EVERYTHING is wrong in Cantor-land.
> > >
> > > From "removing any element of |N_s leaves infinitely many successors" we can conclude that "removing any finite subset of |N_s leaves infinitely many successors". However, "them", |N_s, is not a finite subset of |N_s , so the fact that "removing them" leave nothing is not a contradiction.
> >
> > It is a contradiction that the elements cannot be handled as elements.
> But why? As Harvey says, "A set is everything and a set is nothing. Very rich concept". 🤣🤣🤣🤣🤣🤣
> > The reason is of course that set theory fails otherwise.
> Set theory never actually succeeded.
>
> >
> > Regards, WM

Bullshit Baffles (peanut) Brains.

But what can you expect when the author of all these ideas was an insane moron? If Cantor had defecated, his followers would smell the feces and go "Hm. Nice!"

Short Anecdote: A long time ago in a country (UK) not so far away, I worked in Londinium for 18 months. My colleagues, told me about a very disgusting place where women relieve themselves on a transparent floor overhead and (defective) males stared upwards in wonder. But hey, mainstream math academics have a brain consisting of 95% scat. It should not come as a surprise.

Kronecker (also a Jew), rejected Cantor's drivel, but the stench of Cantor's scat was irresistible to Hilbert and followers. They took a deep sniff and couldn't get enough.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
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by: Eram semper recta - Tue, 19 Jul 2022 03:34 UTC

On Tuesday, 19 July 2022 at 06:18:05 UTC+3, Eram semper recta wrote:
> On Tuesday, 19 July 2022 at 06:06:47 UTC+3, Eram semper recta wrote:
> > On Tuesday, 19 July 2022 at 00:29:37 UTC+3, 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
> > >
> > But wtf is an "element" and a "set"? They are both the same thing and they are not the same thing. They are both everything and nothing. LMAO.
> >
> > @5:02 "Now don't think that sets are so simple. But inside a set could be other sets and inside them could be other sets. So you see how tricky sets could be .... You have a rather sophisticated and uh, uh, ... rich concept. The set theoretic foundation of mathematics is the set and everything that we talk about in there, is a set. Great simplifier. Everything is a set" - Professor Harvey Friedman
> >
> > This is Harvey's lecture on the Foundations of Bullshit: https://youtu.be/mogMr45UTj4
> >
> > This is my 164 second rebuttal: https://youtu.be/KvxjOMW6Q9w
> > > By the way, this is wrong.
> > Not even wrong, so to speak.
> > > Simple induction shows that every element in the bijection has infinitely many successors.
> > >
> > > > 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.
> > All sets of |N_s are sets of |N_s. Chuckle.
> > >
> > > > so the fact that "removing them" leave nothing is not a contradiction.
> > >
> > > We don't remove the set but all its elements.
> > But the elements are sets? Chuckle.
> > > If this is not the same, then something is wrong in Cantor-land.
> > You think?! ROFLMAO
> >
> > Sometimes you are a funny man Wolfgang. EVERYTHING is wrong in Cantor-land.
> > > >
> > > > From "removing any element of |N_s leaves infinitely many successors" we can conclude that "removing any finite subset of |N_s leaves infinitely many successors". However, "them", |N_s, is not a finite subset of |N_s , so the fact that "removing them" leave nothing is not a contradiction.
> > >
> > > It is a contradiction that the elements cannot be handled as elements..
> > But why? As Harvey says, "A set is everything and a set is nothing. Very rich concept". 🤣🤣🤣🤣🤣🤣
> > > The reason is of course that set theory fails otherwise.
> > Set theory never actually succeeded.
> >
> > >
> > > Regards, WM
> Bullshit Baffles (peanut) Brains.
>
> But what can you expect when the author of all these ideas was an insane moron? If Cantor had defecated, his followers would smell the feces and go "Hm. Nice!"
>
> Kronecker rejected Cantor's drivel, but the stench of Cantor's scat was irresistible to Hilbert and followers. They took a deep sniff and couldn't get enough.

Re: Natural numbers and vases III

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by: Eduardo Faqtardo - Tue, 19 Jul 2022 04:32 UTC

On 7/18/2022 2:29 PM, WM wrote:
> nothing <

Post it 156,457 more times you impotent blithering wankmaggot.

Re: Natural numbers and vases III

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by: zelos...@gmail.com - Tue, 19 Jul 2022 05:24 UTC

tisdag 19 juli 2022 kl. 05:06:47 UTC+2 skrev Eram semper recta:
> On Tuesday, 19 July 2022 at 00:29:37 UTC+3, 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
> >
> But wtf is an "element" and a "set"? They are both the same thing and they are not the same thing. They are both everything and nothing. LMAO.

in set theory all objects are sets, an element is a description of a relationship between two objects where one object is in the other.
>
> @5:02 "Now don't think that sets are so simple. But inside a set could be other sets and inside them could be other sets. So you see how tricky sets could be .... You have a rather sophisticated and uh, uh, ... rich concept.. The set theoretic foundation of mathematics is the set and everything that we talk about in there, is a set. Great simplifier. Everything is a set" - Professor Harvey Friedman
>
> This is Harvey's lecture on the Foundations of Bullshit: https://youtu.be/mogMr45UTj4
>
> This is my 164 second rebuttal: https://youtu.be/KvxjOMW6Q9w
> > By the way, this is wrong.
> Not even wrong, so to speak.
> > Simple induction shows that every element in the bijection has infinitely many successors.
> >
> > > 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.
> All sets of |N_s are sets of |N_s. Chuckle.
> >
> > > so the fact that "removing them" leave nothing is not a contradiction..
> >
> > We don't remove the set but all its elements.
> But the elements are sets? Chuckle.
> > If this is not the same, then something is wrong in Cantor-land.
> You think?! ROFLMAO

You never think.

>
> Sometimes you are a funny man Wolfgang. EVERYTHING is wrong in Cantor-land.
> > >
> > > From "removing any element of |N_s leaves infinitely many successors" we can conclude that "removing any finite subset of |N_s leaves infinitely many successors". However, "them", |N_s, is not a finite subset of |N_s , so the fact that "removing them" leave nothing is not a contradiction.
> >
> > It is a contradiction that the elements cannot be handled as elements.
> But why? As Harvey says, "A set is everything and a set is nothing. Very rich concept". 🤣🤣🤣🤣🤣🤣
> > The reason is of course that set theory fails otherwise.
> Set theory never actually succeeded.

Yet it does

>
> >
> > Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: thenewca...@gmail.com (Eram semper recta)
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by: Eram semper recta - Tue, 19 Jul 2022 06:35 UTC

Note to stupid reprobate Harvey Friedman:

Now don't think that ratios of magnitudes are so simple. The measure of a ratio is called a NUMBER. In algebra, there are numbers and in equations there are numbers. You have a very sophisticated and rich concept of measure derived from NOTHING starting with geometry and transferring all the properties to algebra through the abstract unit. Unlike set theory, there are no sets within sets and thousands of rules to remember, or any of that garbage.. In the true foundations of mathematics (Euclid's Elements) that were never actually replaced, every concept is well formed. You won't find drivel like "is element of" or a matryoshka doll scheme of set theory. Everything is about ratio and number. Mathematics is the science of MEASURE and NUMBER.

>
> This is Harvey's lecture on the Foundations of Bullshit: https://youtu.be/mogMr45UTj4
>
> This is my 164 second rebuttal: https://youtu.be/KvxjOMW6Q9w
> > By the way, this is wrong.
> Not even wrong, so to speak.
> > Simple induction shows that every element in the bijection has infinitely many successors.
> >
> > > 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.
> All sets of |N_s are sets of |N_s. Chuckle.
> >
> > > so the fact that "removing them" leave nothing is not a contradiction..
> >
> > We don't remove the set but all its elements.
> But the elements are sets? Chuckle.
> > If this is not the same, then something is wrong in Cantor-land.
> You think?! ROFLMAO
>
> Sometimes you are a funny man Wolfgang. EVERYTHING is wrong in Cantor-land.
> > >
> > > From "removing any element of |N_s leaves infinitely many successors" we can conclude that "removing any finite subset of |N_s leaves infinitely many successors". However, "them", |N_s, is not a finite subset of |N_s , so the fact that "removing them" leave nothing is not a contradiction.
> >
> > It is a contradiction that the elements cannot be handled as elements.
> But why? As Harvey says, "A set is everything and a set is nothing. Very rich concept". 🤣🤣🤣🤣🤣🤣
> > The reason is of course that set theory fails otherwise.
> Set theory never actually succeeded.
>
> >
> > Regards, WM

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Tue, 19 Jul 2022 11:02 UTC

Fritz Feldhase schrieb am Montag, 18. Juli 2022 um 23:43:46 UTC+2:
> On Monday, July 18, 2022 at 11:29:37 PM UTC+2, WM wrote:
>
> > All elements of |N_s are elements of |N_s.
>
> This one is absolutely true!

Not according to WH.
If you remove all elements, then infinitely many successors remain.
If you remove the set of all elements, then nothing remains. Therefore the set contains more than all elements. (It contains mainly dark elements.)

Regards, WM

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Tue, 19 Jul 2022 12:16 UTC

William schrieb am Dienstag, 19. Juli 2022 um 01:31:47 UTC+2:
> On Monday, July 18, 2022 at 6:29:37 PM UTC-3, 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.
> Nope. Induction can show many things two thing it can show are 1. Each element is in the bijection.

That excludes 2.

> 2. Each element in the bijection has an infinite number of successors. There is a contradiction iff there is a last element.

No, there is a contradiction if there are all elements (definable).
> >
> > All elements of |N_s are element[s of |N_s.
>
> Nope "All elements of |N_s" is the set |N_s.

Therefore it is a contradiction if you claim that instead of all elements the set must be used. Of course a property of elements may differ from the properties of the set: Every element is a number, the set is not a number. But some properties are valid for both: The elements and the set are objects of mathematics. And one property in particular must not cahnge: If you remove all elemets then it is tantamount with removing the set. As this is wrong for definable elements (each one has infinitely many successors, almost all of which are dark) we see a proof of dark elements in all infinite sets..

> Thus "all elements of |N_s" is not an element of |N_s as the set |N_s is not an element of |N_s.

All elements of the set are elements of the set and can be removed. This is same as removing the set. Your denial shows your being afraid of dark numbers.

Note that "three elements of the set" is not an element of the set. Nevertheless three elements can be removed.

Regards, WM

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Tue, 19 Jul 2022 12:19 UTC

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, then removing all elements was possible element by element and would yield the same result as removing the set. 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.

Regards, WM

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by: WM - Tue, 19 Jul 2022 12:21 UTC

zelos...@gmail.com schrieb am Dienstag, 19. Juli 2022 um 04:47:04 UTC+2:
> måndag 18 juli 2022 kl. 23:29:37 UTC+2 skrev WM:
> > 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.
> They do, but they are still equal to N

Of course. Dark successors and definable elements are the element of |N.

> > We don't remove the set but all its elements. If this is not the same, then something is wrong in Cantor-land.

Regards, WM

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by: WM - Tue, 19 Jul 2022 12:27 UTC

Eram semper recta schrieb am Dienstag, 19. Juli 2022 um 05:06:47 UTC+2:

> Set theory never actually succeeded.

Unfortunately set theory has actually succeeded to fill millions with enthusiasm (including myself) and to distract them from serious work.

Regards, WM

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by: sergi o - Tue, 19 Jul 2022 13:03 UTC

On 7/19/2022 6:02 AM, WM wrote:
> Fritz Feldhase schrieb am Montag, 18. Juli 2022 um 23:43:46 UTC+2:
>> On Monday, July 18, 2022 at 11:29:37 PM UTC+2, WM wrote:
>>
>>> All elements of |N_s are elements of |N_s.
>>
>> This one is absolutely true!
>
> Not according to WH.
> If you remove all elements, then infinitely many successors remain.
> If you remove the set of all elements, then nothing remains. Therefore the set contains more than all elements. (It contains mainly dark elements.)
>
> Regards, WM
>

delusional, or your "sets" are infected.

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by: sergi o - Tue, 19 Jul 2022 13:10 UTC

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
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by: sergi o - Tue, 19 Jul 2022 13:13 UTC

On 7/19/2022 7:21 AM, WM wrote:
> zelos...@gmail.com schrieb am Dienstag, 19. Juli 2022 um 04:47:04 UTC+2:
>> måndag 18 juli 2022 kl. 23:29:37 UTC+2 skrev WM:
>>> 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.
>> They do, but they are still equal to N
>
> Of course. Dark successors and definable elements are the element of |N.

Wrong. dark numbers cannot be elements of any set, as that requires identification.

>
>>> We don't remove the set but all its elements. If this is not the same, then something is wrong in Cantor-land.
>
> Regards, WM

Re: Natural numbers and vases III

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by: sergi o - Tue, 19 Jul 2022 13:14 UTC

On 7/19/2022 7:27 AM, WM wrote:
> Eram semper recta schrieb am Dienstag, 19. Juli 2022 um 05:06:47 UTC+2:
>
>> Set theory never actually succeeded.
>
> Unfortunately set theory has actually succeeded to fill millions with enthusiasm (including myself) and to distract them from serious work.
>
> Regards, WM

glad to see you teaming up with Mr Rectum, where you both can continue your "*serious work*" !

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by: William - Tue, 19 Jul 2022 14:37 UTC

On Tuesday, July 19, 2022 at 9:16:10 AM UTC-3, WM wrote:

> Note that "three elements of the set" is not an element of the set. Nevertheless three elements can be removed.

Correct. If X is not an element of the set it may or may not be able to be removed , e.g. if X is a subset of |N it can be removed if X is finite.
"three element of the set" is a finite subset of |N and can be removed Note that "all elements of the set" is not a finite subset set.

--
William Hughes

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
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by: WM - Tue, 19 Jul 2022 15:08 UTC

William schrieb am Dienstag, 19. Juli 2022 um 16:37:41 UTC+2:
> On Tuesday, July 19, 2022 at 9:16:10 AM UTC-3, WM wrote:
>
>
> > Note that "three elements of the set" is not an element of the set. Nevertheless three elements can be removed.
> Correct. If X is not an element of the set it may or may not be able to be removed , e.g. if X is a subset of |N it can be removed if X is finite.

Who made up this restriction? Did you feel forced to put it up? Why only finite subsets?

> "three element of the set" is a finite subset of |N and can be removed Note that "all elements of the set" is not a finite subset set.

Why do you think infinite subsets cannot be removed without all their successors? Here is the answer: Because infinite subsets contain dark elements. They cannot be removed as individuals. Therefore you have to remove the whole set. Defined = finite, having a last defined element. Definable: defined during the lifetime of the universe.

Regards, WM

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
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Re: Natural numbers and vases III	FromTheRafters
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Re: Natural numbers and vases III	Fritz Feldhase
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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
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Re: Natural numbers and vases III	sergi o
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	Fritz Feldhase
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Re: Natural numbers and vases III	FromTheRafters
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	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
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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
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Re: Natural numbers and vases III	FredJeffries
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
Re: Natural numbers and vases III	FredJeffries
Re: Natural numbers and vases III	WM
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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
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Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
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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