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Re: Natural numbers and vases III

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
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	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
Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	WM
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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	FredJeffries
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
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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
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Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	WM
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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
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Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
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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	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	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	WM
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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	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
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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	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	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	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
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Re: Natural numbers and vases III	WM
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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
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Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	WM
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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

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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, 4 Aug 2022 17:55 UTC

On Thursday, August 4, 2022 at 7:28:14 PM UTC+2, Sergio wrote:
> On 8/4/2022 6:47 AM, WM wrote:
> >
> > Definition: An endsegment is called definable, if it can be omitted, together with all its predecessors, from the intersection of all endsegments without changing the result "empty set".
>
> QUacK!!! "defined" by "omission"

Sure, he does not know how to use the formal language of mathematics/set theory.

Now, wouldn't you consider the following a definition?

definable(E) :<-> En e IN: E = E(n) & ∩({E(k) : k ∈ ℕ} \ {E(1), ..., E(n)}) = { }

with E(n) = {m e IN : m >= n} (for all n e IN).

Alternatively (and slightly simpler), with e in {E(k) : k ∈ ℕ}:

definable(e) :<-> ∩({E(k) : k ∈ ℕ} \ {E(1), ..., E(min(e))}) = { }

This seems to be an appropreate formalization of WM's

| Definition: An endsegment is called definable, if it can be omitted, together with all its predecessors, from the intersection of all endsegments without changing the result "empty set".

You see: For any endsegment e: e = E(min(e)), and its "predecessors" are just E(1), E(2), ..., E(min(e)-1). We can "omit all these endsegments from {E(k) : k ∈ ℕ}" (or rather: just take the set difference {E(k) : k ∈ ℕ} \ {E(1), ..., E(min(e))} as operand for the (application of the) intersection operation.

Of course WM's formulation "from the intersection of all endsegments" is muddled, but I'm quite sure that he actually meant "from the set which would otherwise be the operand for the (application of the) intersection operation, i. e. the set of all endsegments".

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, 4 Aug 2022 18:03 UTC

On Thursday, August 4, 2022 at 7:35:49 PM UTC+2, Gus Gassmann wrote:
> On Thursday, 4 August 2022 at 12:27:20 UTC-3, Fritz Feldhase wrote:
> > On Thursday, August 4, 2022 at 5:01:03 PM UTC+2, FromTheRafters wrote:
> >
> > WM wrote the following nonsense:
> > > >
> > > > In order to remove a finite set, you have to give the last element.
> > > >
> > The last element of what? Of the finite set?
> >
> > What a blithering idiot!
> >
> > Let /a/ be a number from IN, and let /b/ be a number from IN \ {a}.
> >
> > Now I can consider the set difference IN \ {a, b} WITHOUT "giving" the last element.
> >
> > Of course each and every nonempty finite set of numbers HAS a maximal/last element, but in this case I/we do _not know_ if /a/ is the maximum or /b/.
> >
> > BUT we (except Mückenheim that is) DO know that EITHER a = b, OR a < b, OR b < a.
> >
> Again, without putting too fine a point to it, we (except Mückenheim that is) do know from your constraint b in ( IN \ {a} ) that a =/= b....

Right. I temporarily forgot about that precondition. (38° Grad Celsius!)

Makes things even simpler!

On the other hand, my claims are true anyway: We (except Mückenheim that is) DO know that EITHER a = b, OR a < b, OR b < a, even in this case, don't we? :-P

But -right- we also know that a =/= b. [...]

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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, 4 Aug 2022 18:05 UTC

On Thursday, August 4, 2022 at 7:40:16 PM UTC+2, Gus Gassmann wrote:
> On Thursday, 4 August 2022 at 13:42:27 UTC-3, WM wrote:

> > Your proofs are ninsense. Tho see it try to define enough endsegments to get an empty intersection.
> >
> "ninsense"?

38° Celsius!

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, 4 Aug 2022 18:06 UTC

Right. I temporarily forgot about that precondition. (38° Celsius!)

Makes things even simpler!

On the other hand, my claims are true anyway: We (except Mückenheim that is) DO know that EITHER a = b, OR a < b, OR b < a, even in this case, don't we? :-P

But -right- we also know that a =/= b. [...]

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
Date: Thu, 04 Aug 2022 14:20:50 -0400
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by: FromTheRafters - Thu, 4 Aug 2022 18:20 UTC

WM explained on 8/4/2022 :
> FromTheRafters schrieb am Donnerstag, 4. August 2022 um 16:52:11 UTC+2:
>> WM laid this down on his screen :
>>> FromTheRafters schrieb am Donnerstag, 4. August 2022 um 14:57:23 UTC+2:
>>>> WM presented the following explanation :
>>>>> zelos...@gmail.com schrieb am Donnerstag, 4. August 2022 um 13:41:58
>>>>> UTC+2:
>>>>>
>>>>>>> All definable endsegments can be removed without changing the result.
>>>>>>> Therefore the required endegments are undefinable.
>>>>>> Your "definable" is still UNDEFINED!
>>>>>
>>>>> Definition: An endsegment is called definable, if it can be omitted,
>>>>> together with all its predecessors,
>>>> Endsegments don't have predecessors.
>>>
>>> Wrong. E(1) is the predecessor of E(2).
>> In a *sequence* of endsegements. *An* endsegemnt is merely *an*
>> endsegment.
>
> Here we talk about the sequence. An endsegment is not of interest.

An endsegment is not of interest in your definition of definable
endsegment?

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by: FromTheRafters - Thu, 4 Aug 2022 18:32 UTC

WM explained :
> FromTheRafters schrieb am Donnerstag, 4. August 2022 um 17:01:03 UTC+2:
>> WM formulated on Thursday :
>
>>>> The set of all natural numbers with fewer than 444 digits in base ten
>>>> notation. I did not give you the last element, you need a theorem.
>
> It is the numer with 443 nines.

Which I did not give to you.

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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, 4 Aug 2022 18:51 UTC

On Thursday, 4 August 2022 at 14:55:11 UTC-3, Fritz Feldhase wrote:
> On Thursday, August 4, 2022 at 7:28:14 PM UTC+2, Sergio wrote:
> > On 8/4/2022 6:47 AM, WM wrote:
> > >
> > > Definition: An endsegment is called definable, if it can be omitted, together with all its predecessors, from the intersection of all endsegments without changing the result "empty set".
> >
> > QUacK!!! "defined" by "omission"
> Sure, he does not know how to use the formal language of mathematics/set theory.
>
> Now, wouldn't you consider the following a definition?
> definable(E) :<-> En e IN: E = E(n) & ∩({E(k) : k ∈ ℕ} \ {E(1), ..., E(n)}) = { }
> with E(n) = {m e IN : m >= n} (for all n e IN).
>
> Alternatively (and slightly simpler), with e in {E(k) : k ∈ ℕ}:
>
> definable(e) :<-> ∩({E(k) : k ∈ ℕ} \ {E(1), ..., E(min(e))}) = { }
>
> ?
>
> This seems to be an appropreate formalization of WM's

Sure. Problem still is, there is no way around the fact that *every* end segment is still /definable/. YOU know that, but Mucki steadfastly denies it.

> | Definition: An endsegment is called definable, if it can be omitted, together with all its predecessors, from the intersection of all endsegments without changing the result "empty set".
> You see: For any endsegment e: e = E(min(e)), and its "predecessors" are just E(1), E(2), ..., E(min(e)-1). We can "omit all these endsegments from {E(k) : k ∈ ℕ}" (or rather: just take the set difference {E(k) : k ∈ ℕ} \ {E(1), ..., E(min(e))} as operand for the (application of the) intersection operation.
>
> Of course WM's formulation "from the intersection of all endsegments" is muddled, but I'm quite sure that he actually meant "from the set which would otherwise be the operand for the (application of the) intersection operation, i. e. the set of all endsegments".

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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, 4 Aug 2022 18:53 UTC

On Thursday, 4 August 2022 at 15:05:23 UTC-3, Fritz Feldhase wrote:
> On Thursday, August 4, 2022 at 7:40:16 PM UTC+2, Gus Gassmann wrote:
> > On Thursday, 4 August 2022 at 13:42:27 UTC-3, WM wrote:
>
> > > Your proofs are ninsense. Tho see it try to define enough endsegments to get an empty intersection.
> > >
> > "ninsense"?
> 38° Celsius!

Just wanted to see if he could get himself to admit a simple typo. But at these temperatures, it's surely a keyboard malfunction...

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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, 4 Aug 2022 19:18 UTC

On Thursday, August 4, 2022 at 8:51:33 PM UTC+2, Gus Gassmann wrote:
> On Thursday, 4 August 2022 at 14:55:11 UTC-3, Fritz Feldhase wrote:
>
> > Now, wouldn't you consider the following a definition?
> >
> > definable(E) :<-> En e IN: E = E(n) & ∩({E(k) : k ∈ ℕ} \ {E(1), ..., E(n)}) = { }
> > with E(n) = {m e IN : m >= n} (for all n e IN).
> >
> > Alternatively (and slightly simpler), with e in {E(k) : k ∈ ℕ}:
> >
> > definable(e) :<-> ∩({E(k) : k ∈ ℕ} \ {E(1), ..., E(min(e))}) = { }
> >
> > This seems to be an appropreate formalization of WM's [...]
> >
> Sure. Problem still is, there is no way around the fact that *every* end segment is still /definable/. YOU know that, but Mucki steadfastly denies it.

Right:

FF> Then we get the result:
FF>
FF> AX e {E(k) : k ∈ ℕ}: definable(X)
FF>
FF> or
FF>
FF> Ak e IN: definable(E(k))
FF>
FF> "All endsegments are definable."

WM> Your claim is nonsense.

Well, you know (formal) definitions and (formal) proofs (based on these definitions) don't count in WM's world. His "math" is all (Dada) prose.

Re: Natural numbers and vases III

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From: inva...@invalid.com (Sergio)
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Subject: Re: Natural numbers and vases III
Date: Thu, 4 Aug 2022 14:22:42 -0500
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by: Sergio - Thu, 4 Aug 2022 19:22 UTC

On 8/4/2022 1:03 PM, Fritz Feldhase wrote:
> On Thursday, August 4, 2022 at 7:35:49 PM UTC+2, Gus Gassmann wrote:
>> On Thursday, 4 August 2022 at 12:27:20 UTC-3, Fritz Feldhase wrote:
>>> On Thursday, August 4, 2022 at 5:01:03 PM UTC+2, FromTheRafters wrote:
>>>
>>> WM wrote the following nonsense:
>>>>>
>>>>> In order to remove a finite set, you have to give the last element.
>>>>>
>>> The last element of what? Of the finite set?
>>>
>>> What a blithering idiot!
>>>
>>> Let /a/ be a number from IN, and let /b/ be a number from IN \ {a}.
>>>
>>> Now I can consider the set difference IN \ {a, b} WITHOUT "giving" the last element.
>>>
>>> Of course each and every nonempty finite set of numbers HAS a maximal/last element, but in this case I/we do _not know_ if /a/ is the maximum or /b/.
>>>
>>> BUT we (except Mückenheim that is) DO know that EITHER a = b, OR a < b, OR b < a.
>>>
>> Again, without putting too fine a point to it, we (except Mückenheim that is) do know from your constraint b in ( IN \ {a} ) that a =/= b...
>
> Right. I temporarily forgot about that precondition. (38° Grad Celsius!)
>
> Makes things even simpler!
>
> On the other hand, my claims are true anyway: We (except Mückenheim that is) DO know that EITHER a = b, OR a < b, OR b < a, even in this case, don't we? :-P
>
> But -right- we also know that a =/= b. [...]
>

well logically;

a ∨ b, a ∧ b, a NOR b, a NAND b, a ⊕ b, ¬a, ¬b , a ≡ b, a·b, a+b

and remember these oldies ?

https://en.wikipedia.org/wiki/List_of_logic_symbols

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
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by: Sergio - Thu, 4 Aug 2022 19:24 UTC

On 8/4/2022 12:39 PM, Gus Gassmann wrote:
> On Thursday, 4 August 2022 at 13:40:23 UTC-3, WM wrote:
>> FromTheRafters schrieb am Donnerstag, 4. August 2022 um 17:01:03 UTC+2:
>>> WM formulated on Thursday :
>>>>> The set of all natural numbers with fewer than 444 digits in base ten
>>>>> notation. I did not give you the last element, you need a theorem.
>> It is the numer with 443 nines.
>
> "numer"?

(the dark b version of number)

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From: FTR...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Thu, 04 Aug 2022 16:37:21 -0400
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by: FromTheRafters - Thu, 4 Aug 2022 20:37 UTC

It happens that Gus Gassmann formulated :
> On Thursday, 4 August 2022 at 14:55:11 UTC-3, Fritz Feldhase wrote:
>> On Thursday, August 4, 2022 at 7:28:14 PM UTC+2, Sergio wrote:
>>> On 8/4/2022 6:47 AM, WM wrote:
>>>>
>>>> Definition: An endsegment is called definable, if it can be omitted,
>>>> together with all its predecessors, from the intersection of all
>>>> endsegments without changing the result "empty set".
>>>
>>> QUacK!!! "defined" by "omission"
>> Sure, he does not know how to use the formal language of mathematics/set
>> theory.
>>
>> Now, wouldn't you consider the following a definition?
>> definable(E) :<-> En e IN: E = E(n) & ∩({E(k) : k ∈ ℕ} \ {E(1), ..., E(n)})
>> = { } with E(n) = {m e IN : m >= n} (for all n e IN).
>>
>> Alternatively (and slightly simpler), with e in {E(k) : k ∈ ℕ}:
>>
>> definable(e) :<-> ∩({E(k) : k ∈ ℕ} \ {E(1), ..., E(min(e))}) = { }
>>
>> ?
>>
>> This seems to be an appropreate formalization of WM's
>
> Sure. Problem still is, there is no way around the fact that *every* end
> segment is still /definable/. YOU know that, but Mucki steadfastly denies it.

I find it unacceptable. A set is a well defined collection of objects
called elements. He defines his objects as 'undefined' or even
'undefinable' and thinks he can use that collection as a set in ZFC
because 'a set is defined by its elements and nothing more' supported
by the 'Because I Said So' muckymath axiom and "Everything in ZFC is a
set" which is a misleading statement or at the very least, ambiguous.

Re: Natural numbers and vases III

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Thu, 4 Aug 2022 19:57:22 -0500
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by: Sergio - Fri, 5 Aug 2022 00:57 UTC

On 8/4/2022 2:18 PM, Fritz Feldhase wrote:
> On Thursday, August 4, 2022 at 8:51:33 PM UTC+2, Gus Gassmann wrote:
>> On Thursday, 4 August 2022 at 14:55:11 UTC-3, Fritz Feldhase wrote:
>>
>>> Now, wouldn't you consider the following a definition?
>>>
>>> definable(E) :<-> En e IN: E = E(n) & ∩({E(k) : k ∈ ℕ} \ {E(1), ..., E(n)}) = { }
>>> with E(n) = {m e IN : m >= n} (for all n e IN).
>>>
>>> Alternatively (and slightly simpler), with e in {E(k) : k ∈ ℕ}:
>>>
>>> definable(e) :<-> ∩({E(k) : k ∈ ℕ} \ {E(1), ..., E(min(e))}) = { }
>>>
>>> This seems to be an appropreate formalization of WM's [...]
>>>
>> Sure. Problem still is, there is no way around the fact that *every* end segment is still /definable/. YOU know that, but Mucki steadfastly denies it.
>
> Right:
>
> FF> Then we get the result:
> FF>
> FF> AX e {E(k) : k ∈ ℕ}: definable(X)
> FF>
> FF> or
> FF>
> FF> Ak e IN: definable(E(k))
> FF>
> FF> "All endsegments are definable."
>
> WM> Your claim is nonsense.
>
> Well, you know (formal) definitions and (formal) proofs (based on these definitions) don't count in WM's world. His "math" is all (Dada) prose.

from Tzara, "Dadaism" Dadaism
By Tristan Tzara

*There is a literature that does not reach the voracious mass. It is the work of
creators, issued from a real necessity in the author, produced for himself. It
expresses the knowledge of a supreme egoism, in which laws wither away. Every
page must explode, either by profound heavy seriousness, the whirlwind, poetic
frenzy, the new, the eternal, the crushing joke, enthusiasm for principles, or
by the way in which it is printed. On the one hand a tottering world in flight,
betrothed to the glockenspiel of hell, on the other hand: new men. Rough,
bouncing, riding on hiccups. Behind them a crippled world and literary quacks
with a mania for improvement.

....

I destroy the drawers of the brain and of social organization: spread
demoralization wherever I go and cast my hand from heaven to hell, my eyes from
hell to heaven, restore the fecund wheel of a universal circus to objective
forces and the imagination of every individual.

Dada; elegant and unprejudiced leap from a
harmony to the other sphere; trajectory of a word tossed like a screeching
phonograph record; to respect all individuals in their folly of the moment:
whether it be serious, fearful, timid, ardent, vigorous, determined,
enthusiastic; to divest one's church of every useless cumbersome accessory; to
spit out disagreeable or amorous ideas like a luminous waterfall, or coddle them
-with the extreme satisfaction that it doesn't matter in the least-with the same
intensity in the thicket of one's soul-pure of insects for blood well-born, and
gilded with bodies of archangels. Freedom: Dada Dada Dada, a roaring of tense
colors, and interlacing of opposites and of all contradictions, grotesques,
inconsistencies: LIFE

Like everything in life, Dada is useless.
Dada is without pretension, as life should be.
Perhaps you will understand me better when I tell you that Dada is a virgin
microbe that penetrates with the insistence of air into all the spaces that
reason has not been able to fill with words or conventions.

Yeppers! WMs DADA math

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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 - Fri, 5 Aug 2022 13:34 UTC

On Tuesday, 19 July 2022 at 08:27:34 UTC-4, 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.

That it has done!

>
> 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 - Fri, 5 Aug 2022 13:41 UTC

On Wednesday, 20 July 2022 at 08:58:49 UTC-4, PRIZE IDIOT sergi o wrote:
> On 7/20/2022 6:22 AM, WM wrote:
> > Fritz Feldhase schrieb am Dienstag, 19. Juli 2022 um 22:23:48 UTC+2:
> >
> >> Hint: Something might be in the DOMAIN of a bijection, or in its IMAGE or in its CODOMAIN.
> > Then it is in the bijection too.
> > 5 ∈ ℕ ⊂ ℝ ⊂ mathematical objects ==> 5 is in ℝ because it is a real number and 5 is in the mathematical objects with no doubt.
> IAW WM, how can 5 be a real number ? as WM will argue that 5 is not specified without all its digits, 5.0000000000000....

Those zeroes are not part of the representation of 5, you incorrigible imbecile.

Using a radix template, we don't even need zero, you fucking moron.

.... tens units RADIX tenths hundredths ....
5

.... fours units RADIX fourths sixteenths ...
1 1

Get it moron?

5 is a number because it is a name given to a complete measure.

Your constant drivel is annoying.

>
> AND preceeding digits, ...00000000000005.00000000000...
>
> Therefore, IAW WM, we will wait until you have written down all the digits first, before using the number.
>
> >
> > Regards, WM
>
>
>
> IAW => In Accordance With

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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 - Fri, 5 Aug 2022 13:43 UTC

On Friday, 5 August 2022 at 09:41:27 UTC-4, Eram semper recta wrote:
> On Wednesday, 20 July 2022 at 08:58:49 UTC-4, PRIZE IDIOT sergi o wrote:
> > On 7/20/2022 6:22 AM, WM wrote:
> > > Fritz Feldhase schrieb am Dienstag, 19. Juli 2022 um 22:23:48 UTC+2:
> > >
> > >> Hint: Something might be in the DOMAIN of a bijection, or in its IMAGE or in its CODOMAIN.
> > > Then it is in the bijection too.
> > > 5 ∈ ℕ ⊂ ℝ ⊂ mathematical objects ==> 5 is in ℝ because it is a real number and 5 is in the mathematical objects with no doubt.
> > IAW WM, how can 5 be a real number ? as WM will argue that 5 is not specified without all its digits, 5.0000000000000....
>
> Those zeroes are not part of the representation of 5, you incorrigible imbecile.
>
> Using a radix template, we don't even need zero, you fucking moron.
>
>
> ... tens units RADIX tenths hundredths ....
> 5
>
> ... fours units RADIX fourths sixteenths ...
> 1 1
>
> Get it moron?
>
> 5 is a number because it is a name given to a complete measure.
>
> Your constant drivel is annoying.

What I am teaching you, imbecile, is that you only need digits 1 thru base. Get it? Naaaaah.

>
> >
> > AND preceeding digits, ...00000000000005.00000000000...
> >
> > Therefore, IAW WM, we will wait until you have written down all the digits first, before using the number.
> >
> > >
> > > Regards, WM
> >
> >
> >
> > IAW => In Accordance With

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Fri, 5 Aug 2022 16:06 UTC

Fritz Feldhase schrieb am Donnerstag, 4. August 2022 um 19:13:02 UTC+2:
> On Thursday, August 4, 2022 at 6:28:11 PM UTC+2, WM wrote:
>
> > All endsegments together have an empty intersection
> > ∩{E(k) : k ∈ ℕ} = { } .
> Indeed. :-)
>
> > All individually definable
>
> READ: "Finitely many"
> > endsegments have an infinite intersection

Finitely many = individually definable.

> > Or can you individually define endsegments which have an empty intersection?
>
> No, we can't.
>
> > Can you remove from the set of endsegments {E(1), E(2), ...} so many endsegments that the intersection is empty
∩({E(1), E(2), E(3), ...} \ {E(1), E(2), ..., E(X)}) = { }
but removing another definable endsegment E(X+1) would change the result. Can you define X?

No, of course not.

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 - Fri, 5 Aug 2022 16:11 UTC

William schrieb am Donnerstag, 4. August 2022 um 19:35:47 UTC+2:
> On Thursday, August 4, 2022 at 1:28:11 PM UTC-3, WM wrote:
> > William schrieb am Donnerstag, 4. August 2022 um 16:08:39 UTC+2:

> > All individually definable endsegments have infinite intersection.
> Nope.

Then define individually endsegments which have an empty intersection.

> You are staring at a proof that each endsegment is "individually definable"

The better proof is mine: You are unable to define individually endsegments which have an empty intersection.

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 - Fri, 5 Aug 2022 16:15 UTC

Gus Gassmann schrieb am Donnerstag, 4. August 2022 um 20:51:33 UTC+2:

> Sure. Problem still is, there is no way around the fact that *every* end segment is still /definable/.

Define enough endsegments individually such that their intersection is empty. Fail.

Regards, WM

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by: Python - Fri, 5 Aug 2022 16:16 UTC

Crank Wolfgang Mückenheim, aka WM wrote:
> William schrieb am Donnerstag, 4. August 2022 um 19:35:47 UTC+2:
>> On Thursday, August 4, 2022 at 1:28:11 PM UTC-3, WM wrote:
>>> William schrieb am Donnerstag, 4. August 2022 um 16:08:39 UTC+2:
>
>>> All individually definable endsegments have infinite intersection.
>> Nope.
>
> Then define individually endsegments which have an empty intersection.

*sigh* *facepalm*

An "empty instersection" with what??

Crank Wolfgang Mückenheim, from Hochschule Augsburg (shame! shame!)
to "have an empty intersection" is not a attribute of a single set,
and cannot be. You are deeply mentally ill.

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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 - Fri, 5 Aug 2022 16:21 UTC

On Friday, 5 August 2022 at 13:15:49 UTC-3, WM wrote:
> Gus Gassmann schrieb am Donnerstag, 4. August 2022 um 20:51:33 UTC+2:
>
> > Sure. Problem still is, there is no way around the fact that *every* end segment is still /definable/.
> Define enough endsegments individually such that their intersection is empty. Fail.

Show me an undefinable end segment individually. Fail.

You are a fucking moron. Piss off.

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, 5 Aug 2022 16:24 UTC

Python schrieb am Freitag, 5. August 2022 um 18:16:58 UTC+2:
> Crank Wolfgang Mückenheim, aka WM wrote:
> > William schrieb am Donnerstag, 4. August 2022 um 19:35:47 UTC+2:
> >> On Thursday, August 4, 2022 at 1:28:11 PM UTC-3, WM wrote:
> >>> William schrieb am Donnerstag, 4. August 2022 um 16:08:39 UTC+2:
> >
> >>> All individually definable endsegments have infinite intersection.
> >> Nope.
> >
> > Then define individually endsegments which have an empty intersection.
>
> An "empty instersection" with what??

Together.
>
> Wolfgang Mückenheim, from Technische Hochschule Augsburg

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 - Fri, 5 Aug 2022 16:28 UTC

Gus Gassmann schrieb am Freitag, 5. August 2022 um 18:21:25 UTC+2:
> On Friday, 5 August 2022 at 13:15:49 UTC-3, WM wrote:
> > Gus Gassmann schrieb am Donnerstag, 4. August 2022 um 20:51:33 UTC+2:
> >
> > > Sure. Problem still is, there is no way around the fact that *every* end segment is still /definable/.
> > Define enough endsegments individually such that their intersection is empty. Fail.
> Show me an undefinable end segment individually. Fail.

Chuckle.

There is no white which is black. But I can prove the existence of dark endsegments. You can ony claim your wrong claim.

Proof: It is impossible to remove from the set of endsegments {E(1), E(2), ....} so many endsegments that the intersection is empty
∩({E(1), E(2), E(3), ...} \ {E(1), E(2), ..., E(X)}) = { }
but removing another definable endsegment E(X+1) would change the result.

Regards, WM

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by: Python - Fri, 5 Aug 2022 16:32 UTC

Crank Wolfgang Mückenheim, aka WM wrote:
> Python schrieb am Freitag, 5. August 2022 um 18:16:58 UTC+2:
>> Crank Wolfgang Mückenheim, aka WM wrote:
>>> William schrieb am Donnerstag, 4. August 2022 um 19:35:47 UTC+2:
>>>> On Thursday, August 4, 2022 at 1:28:11 PM UTC-3, WM wrote:
>>>>> William schrieb am Donnerstag, 4. August 2022 um 16:08:39 UTC+2:
>>>
>>>>> All individually definable endsegments have infinite intersection.
>>>> Nope.
>>>
>>> Then define individually endsegments which have an empty intersection.
>>
>> An "empty instersection" with what??
>
> Together.

Idiot, then all have this property.

>> Wolfgang Mückenheim, from Technische Hochschule Augsburg

You are a crank, it's an absolute disgrace you've ever been allowed to
teach.

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Subject: Re: Natural numbers and vases III
From: wpihug...@gmail.com (William)
Injection-Date: Fri, 05 Aug 2022 16:33:05 +0000
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by: William - Fri, 5 Aug 2022 16:33 UTC

On Friday, August 5, 2022 at 1:11:23 PM UTC-3, WM wrote:
> William schrieb am Donnerstag, 4. August 2022 um 19:35:47 UTC+2:
> > On Thursday, August 4, 2022 at 1:28:11 PM UTC-3, WM wrote:
> > > William schrieb am Donnerstag, 4. August 2022 um 16:08:39 UTC+2:
>
> > > All individually definable endsegments have infinite intersection.
> > Nope.
>
> Then define individually endsegments which have an empty intersection.

We need to deal with an infinite number of things. So we use a method, induction, that can deal with an infinite number of things. Use induction to show each endsegment in the set of endsegments is "individually definable". The set of endsegment is thus a set of "individually definable endsegments" and is the set you asked for.

--
William Hughes

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

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