Greg Cunt schrieb am Freitag, 24. September 2021 um 18:55:47 UTC+2:
> On Friday, September 24, 2021 at 6:43:02 PM UTC+2, WM wrote:
> > zelos...@gmail.com schrieb am Freitag, 24. September 2021 um 07:08:11 UTC+2:
> > > torsdag 23 september 2021 kl. 15:23:55 UTC+2 skrev WM:
> > >
> > > If
>
> Zelos defines /n/ to be
>
> > > a[n arbitrary] natural number, it is a natural number
>
> in that [i.e. his] context.

Nonsense. n is neither a number nor a circle or a cube. It can denote a number or something else if this is uniquely defined.

Regards, WM

Gus Gassmann schrieb am Freitag, 24. September 2021 um 20:55:39 UTC+2:
> On Friday, 24 September 2021 at 13:45:07 UTC-3, WM wrote:

> > > > There are definable natural numbers each of which is followed by infinitely many natural numbers. All natural numbers together are not followed by any natural number. Can you see a difference between "definable natural numbers" and "all natural numbers"? What causes this difference?
> > Of course no answer.
> Cute! You snip what I write, and then you complain about not getting an answer.

That was not an answer. You are obviously not able to follow this discussion.

Regards, WM

Jim Burns schrieb am Freitag, 24. September 2021 um 20:20:30 UTC+2:
> On 9/24/2021 12:54 PM, WM wrote:
> >
> Each FISON is followed by infinitely-many FISONs.

It is followed by natural numbers.

> > All natural numbers
> > including the successors of all definable numbers
> > have no successors (because these are included).
> No, that's not the reason.

That is precisely the reason. If all natnumbers have successors, then all natnumbers are not all natnumbers. Simple as that.

All definable natnumbers have successors.
All natnumbers have no successors.

∀n ∈ ℕ: ℕ \ F(n) =/= { }

When subtracting them from ℕ infinitely many numbers will remain.

Obviously collectively more can be subtracted, namely all:

ℕ \ ℕ = { }

Regards, WM

Gus Gassmann schrieb am Freitag, 24. September 2021 um 21:05:15 UTC+2:

> The intersection over infinitely many end segments is empty.

Infinitely many endsegments are more than every finite set of endsegments? What is in the infinite set that is not in at least one of all finite sets making the intersection infinite?

Regards, WM

On 9/24/2021 2:38 PM, Transfinity wrote:
> Gus Gassmann schrieb am Freitag, 24. September 2021 um 20:55:39 UTC+2:
>> On Friday, 24 September 2021 at 13:45:07 UTC-3, WM wrote:
>
>>>>> There are definable natural numbers each of which is followed by infinitely many natural numbers. All natural numbers together are not followed by any natural number. Can you see a difference between "definable natural numbers" and "all natural numbers"? What causes this difference?
>>> Of course no answer.
>> Cute! You snip what I write, and then you complain about not getting an answer.
>
> That was not an answer. You are obviously not able to follow this discussion.
>
> Regards, WM
>

I dont think anyone can follow your discussion;

"There are definable natural numbers each of which is followed by infinitely many natural numbers. All natural numbers together are not followed by any
natural number. Can you see a difference between "definable natural numbers" and "all natural numbers"? What causes this difference?"

try expressing it in Mathematics, you know, "EQUATIONS"

On 9/24/2021 11:46 AM, WM wrote:
> FromTheRafters schrieb am Freitag, 24. September 2021 um 00:08:40 UTC+2:
>> WM has brought this to us :
>>> Gus Gassmann schrieb am Donnerstag, 23. September 2021 um 15:36:27 UTC+2:
>>>> "Infinite" means that there is *no end* to the successor operation.
>>>
>>> Nevertheless there is an end to the natural numbers, namely omega. Like the
>>> zero ends the sequence of unit fractions.
>> Stop lying.
>
> Start thinking.

start Learning Math!

WHY CANT YOU USE EQUATIONS ?

>
>> Each natural number is both definable and is "followed" by infinitely
>> more definable natural nunbers.
>>> All natural numbers together are not followed by any
>>> natural number. Can you see a difference between "definable natural numbers"
>>> and "all natural numbers"?
>
> Consider all natural numbers which can be last of a FISON F(n). They are by definition the definable natnumbers.
>
> ∀n ∈ ℕ: ℕ \ F(n) =/= { }
>
> When subtracting them from ℕ infinitely many numbers will remain.
>
> Obviously collectively more can be subtracted, namely all:
>
> ℕ \ ℕ = { }
>
> What causes this difference?
>
>> Your unfounded implication that the 'defined' ara a proper subset of
>> the 'just plain old' naturals. they are not, you just have a half-baked
>> notion that you want them to be.
>
> I have the proof. What else causes the difference?

yet another FIB, you have no proof at all, you have SPOOF.

the above are unrelated statements.

>
> Regards, WM
>

On 9/24/2021 3:17 PM, Transfinity wrote:
> Greg Cunt schrieb
> am Freitag, 24. September 2021 um 18:55:47 UTC+2:
>> On Friday, September 24, 2021 at 6:43:02 PM UTC+2,
>> WM wrote:
>>> zelos...@gmail.com schrieb
>>> am Freitag, 24. September 2021 um 07:08:11 UTC+2:

>>>> If
>>
>> Zelos defines /n/ to be
>>
>>>> a[n arbitrary] natural number, it is a natural number
>>
>> in that [i.e. his] context.
>
> Nonsense.
> n is neither a number nor a circle or a cube.

It's possible that n is either, neither, or both.

Which case holds might be discoverable later.
Or it might not be.

> It can denote a number or something else
> if this is uniquely defined.

Your requirement that n transform from placeholder to number
when certain information about n is revealed
is incoherent.

Consider three mathematicians, Ingrid, Janice, and Kathleen.
Each one has different information about i,j,k.
Ingrid knows that i + 2j + 3k = 14.
Janice knows that 2i + 3j + k = 11.
Kathleen knows that 3i + j + 2k = 11.

To Ingrid, i,j,k are not numbers?
To Janice, i,j,k are not numbers?
To Kathleen, i,j,k are not numbers?

*UNLESS* the mathematicians compare notes.
Then, i,j,k are uniquely identified,
and, *POOF*, they turn into numbers.

This raises a host of questions.
What are the implications of special relativity to
the POOF? Suppose Ingrid, Janice and Kathleen are
in motion relative to one another and the placeholders
being POOFed into numbers are in the Andromeda Galaxy?

Whose reference frame here determines, way out there,
at what local time the placeholders are POOFed?
Don't you (WM) claim placeholders and numbers must
have a physical reality? Then there must be an answer.
What could it be?

----
Your placeholders are a pointless complication.
Unless the point is to complicate, in order to hide
your ignorance. I think that is the point.

On 9/24/2021 2:53 PM, Transfinity wrote:
> That is precisely the reason. If all natnumbers have successors, then all natnumbers are not all natnumbers. Simple as that.
>
> All definable natnumbers have successors.
> All natnumbers have no successors.
>
> ∀n ∈ ℕ: ℕ \ F(n) =/= { }
>
> When subtracting them from ℕ infinitely many numbers will remain.
>
> Obviously collectively more can be subtracted, namely all:
>
> ℕ \ ℕ = { }
>
> Regards, WM

above post compacted for the trash man;

ThatispreciselythereasonIfallnatnumbers
havesuccessorsthenallnatnumbersarenoal
lnatnumbersSimple as thatAll definable
natnumbershavesuccessorsAllnatnumbersh
avenosuccessors∀n∈ℕ:ℕ\F(n)=/={}Whens
ubtractingthemfromℕinfinitelymanynum
berswillremainObviouslycollectivelymo
recanbesubtractednamelyallℕ\ℕ={}Retar
dsWM

On 9/24/2021 2:56 PM, Transfinity wrote:
> Gus Gassmann schrieb am Freitag, 24. September 2021 um 21:05:15 UTC+2:
>
>> The intersection over infinitely many end segments is empty.
>
> Infinitely many endsegments are more than every finite set of endsegments? What is in the infinite set that is not in at least one of all finite sets making the intersection infinite?
>
> Regards, WM
>

True or false ?

Infinitely many endsegments sets are more than every finite set of endsegments, and in the infinite set that is at least one of all finite sets making
the intersection infinite, every finitely many endsegments are less than every infinitely set of endsegments, then the infinite set that is not in at
least one of all infinite sets making the intersection infinite intersection.

On 9/24/2021 11:58 AM, Transfinity wrote:
> Serg io schrieb am Freitag, 24. September 2021 um 01:48:30 UTC+2:
>>
>> There is no element common to all endsegments.
>
> But all have infinitely many elements in common with E(1). So they must be disjoint. Do you claim that?
>
> Regards, WM
>

There is no element common to all endsegments. Therefore the intersection of all endsegments is empty. do you disagree ?

Serg io presented the following explanation :
> On 9/24/2021 2:56 PM, Transfinity wrote:
>> Gus Gassmann schrieb am Freitag, 24. September 2021 um 21:05:15 UTC+2:
>>
>>> The intersection over infinitely many end segments is empty.
>>
>> Infinitely many endsegments are more than every finite set of endsegments?
>> What is in the infinite set that is not in at least one of all finite sets
>> making the intersection infinite?
>>
>> Regards, WM
>>
>
> True or false ?
>
> Infinitely many endsegments sets are more than every finite set of
> endsegments, and in the infinite set that is at least one of all finite sets
> making the intersection infinite, every finitely many endsegments are less
> than every infinitely set of endsegments, then the infinite set that is not
> in at least one of all infinite sets making the intersection infinite
> intersection.

I think you have a case of matheologititus, WM should have worn a mask.

On 9/24/2021 5:05 PM, FromTheRafters wrote:
> Serg io presented the following explanation :
>> On 9/24/2021 2:56 PM, Transfinity wrote:
>>> Gus Gassmann schrieb am Freitag, 24. September 2021 um 21:05:15 UTC+2:
>>>
>>>> The intersection over infinitely many end segments is empty.
>>>
>>> Infinitely many endsegments are more than every finite set of endsegments? What is in the infinite set that is not in at least one of all finite sets
>>> making the intersection infinite?
>>>
>>> Regards, WM
>>>
>>
>> True or false ?
>>
>> Infinitely many endsegments sets are more than every finite set of endsegments, and in the infinite set that is at least one of all finite sets making
>> the intersection infinite, every finitely many endsegments are less than every infinitely set of endsegments, then the infinite set that is not in at
>> least one of all infinite sets making the intersection infinite intersection.
>
> I think you have a case of matheologititus, WM should have worn a mask.

AHHHhh....! it spreads through the internet, and I was not wearing my mask! (...finite, indexer, infinity, endsegment, set,... ahh... )

On 9/24/2021 2:15 PM, Transfinity wrote:
> Greg Cunt schrieb am Freitag, 24. September 2021 um 18:53:27 UTC+2:
>> On Friday, September 24, 2021 at 6:39:51 PM UTC+2, WM wrote:
>>> Greg Cunt schrieb am Freitag, 24. September 2021 um 05:27:09 UTC+2:
>>>> On Thursday, September 23, 2021 at 10:08:15 PM UTC+2, WM wrote:
>>>>
>>>> Let n e IN \ {1}.
>>>>
>>>>> These things 1,2,3,4,5,... are just those which have [a] unique prime [factorization].
>>>>
>>>> Certainly 1 is not one of "these things". Btw. these things are the natural numbers > 1. n is one of them.
>>>>
>>> They have prime factorizations that can be known. n has not.
>> n does not need to have a KNOWN prime factorization.
>>
>> Hint: The Schnirelmann constant, which certainly is a natural number,
>
> Contrary to n which is no number with certainty.
>
> Regards, WM
>

no, in math we say "let n be a natural number" that means that n is a natural number.

then in math we say "n = 1 + 1", therefore n is 2

n is called a "variable",

and since we said "let n be a natural number", we know throughout the problem that n is a natural number.

factorization is diversion.

On 9/24/2021 3:36 PM, Jim Burns wrote:
> On 9/24/2021 3:17 PM, Transfinity wrote:
>> Greg Cunt schrieb
>> am Freitag, 24. September 2021 um 18:55:47 UTC+2:
>>> On Friday, September 24, 2021 at 6:43:02 PM UTC+2,
>>> WM wrote:
>>>> zelos...@gmail.com schrieb
>>>> am Freitag, 24. September 2021 um 07:08:11 UTC+2:
>
>>>>> If
>>>
>>> Zelos defines /n/ to be
>>>
>>>>> a[n arbitrary] natural number, it is a natural number
>>>
>>> in that [i.e. his] context.
>>
>> Nonsense.
>> n is neither a number nor a circle or a cube.
>
> It's possible that n is either, neither, or both.
>
> Which case holds might be discoverable later.
> Or it might not be.
>
>> It can denote a number or something else
>> if this is uniquely defined.
>
> Your requirement that n transform from placeholder to number
> when certain information about n is revealed
> is incoherent.
>
> Consider three mathematicians, Ingrid, Janice, and Kathleen.
> Each one has different information about i,j,k.
> Ingrid knows that  i + 2j + 3k = 14.
> Janice knows that  2i + 3j + k = 11.
> Kathleen knows that 3i + j + 2k = 11.
>
> To Ingrid, i,j,k are not numbers?
> To Janice, i,j,k are not numbers?
> To Kathleen, i,j,k are not numbers?
>
> *UNLESS* the mathematicians compare notes.
> Then, i,j,k are uniquely identified,
> and, *POOF*, they turn into numbers.
>
> This raises a host of questions.
> What are the implications of special relativity to
> the POOF? Suppose Ingrid, Janice and Kathleen are
> in motion relative to one another and the placeholders
> being POOFed into numbers are in the Andromeda Galaxy?
>
> Whose reference frame here determines, way out there,
> at what local time the placeholders are POOFed?
> Don't you (WM) claim placeholders and numbers must
> have a physical reality? Then there must be an answer.
> What could it be?
>
> ----
> Your placeholders are a pointless complication.
> Unless the point is to complicate, in order to hide
> your ignorance. I think that is the point.
>
>

you POOFed WM's SPOOF

On 9/24/2021 11:37 AM, WM wrote:
> Jim Burns schrieb am Donnerstag, 23. September 2021 um 23:04:42 UTC+2:
>
>> *What we do not want to do* is to _re-define_ our topic
>
> My definition is the valid one.
>
>> It is a _theorem_ not a _definition_ that
>> a natural number >= 2 has a unique prime factorization.
>
> That is what we use for the definition of natural numbers if some fools claim that the expression "natural number" is a natural number.

wrong, you have it backwards again.

The definition of a natural number is not in any way dependent upon prime factorization.

your factorization is your intentional diversion, like Framed Achilles and that poor turtle, you keep tossing out red herrings to obscure your very poor
math, but that does not work at all. ZOD says that JG has better math skills than WM.

>
> Regards, WM
>

On 9/24/2021 11:03 PM, Serg io wrote:
> On 9/24/2021 3:36 PM, Jim Burns wrote:

>> Your requirement that n transform from placeholder to number
>> when certain information about n is revealed
>> is incoherent.
>>
>> Consider three mathematicians, Ingrid, Janice, and Kathleen.
>> Each one has different information about i,j,k.
>> Ingrid knows that  i + 2j + 3k = 14.
>> Janice knows that  2i + 3j + k = 11.
>> Kathleen knows that 3i + j + 2k = 11.
>>
>> To Ingrid, i,j,k are not numbers?
>> To Janice, i,j,k are not numbers?
>> To Kathleen, i,j,k are not numbers?
>>
>> *UNLESS* the mathematicians compare notes.
>> Then, i,j,k are uniquely identified,
>> and, *POOF*, they turn into numbers.
>>
>> This raises a host of questions.
>> What are the implications of special relativity to
>> the POOF? Suppose Ingrid, Janice and Kathleen are
>> in motion relative to one another and the placeholders
>> being POOFed into numbers are in the Andromeda Galaxy?
>>
>> Whose reference frame here determines, way out there,
>> at what local time the placeholders are POOFed?
>> Don't you (WM) claim placeholders and numbers must
>> have a physical reality? Then there must be an answer.
>> What could it be?

> you POOFed WM's SPOOF

relativistically poofed placeholder ants

On 9/24/2021 10:55 PM, Jim Burns wrote:
> On 9/24/2021 11:03 PM, Serg io wrote:
>> On 9/24/2021 3:36 PM, Jim Burns wrote:
>
>>> Your requirement that n transform from placeholder to number
>>> when certain information about n is revealed
>>> is incoherent.
>>>
>>> Consider three mathematicians, Ingrid, Janice, and Kathleen.
>>> Each one has different information about i,j,k.
>>> Ingrid knows that  i + 2j + 3k = 14.
>>> Janice knows that  2i + 3j + k = 11.
>>> Kathleen knows that 3i + j + 2k = 11.
>>>
>>> To Ingrid, i,j,k are not numbers?
>>> To Janice, i,j,k are not numbers?
>>> To Kathleen, i,j,k are not numbers?
>>>
>>> *UNLESS* the mathematicians compare notes.
>>> Then, i,j,k are uniquely identified,
>>> and, *POOF*, they turn into numbers.
>>>
>>> This raises a host of questions.
>>> What are the implications of special relativity to
>>> the POOF? Suppose Ingrid, Janice and Kathleen are
>>> in motion relative to one another and the placeholders
>>> being POOFed into numbers are in the Andromeda Galaxy?
>>>
>>> Whose reference frame here determines, way out there,
>>> at what local time the placeholders are POOFed?
>>> Don't you (WM) claim placeholders and numbers must
>>> have a physical reality? Then there must be an answer.
>>> What could it be?
>
>> you POOFed  WM's SPOOF
>
> relativistically poofed placeholder ants

Good one! :^D

FromTheRafters schrieb am Freitag, 24. September 2021 um 21:12:12 UTC+2:
> WM used his keyboard to write :

> > Consider all natural numbers which can be last of a FISON F(n). They are by
> > definition the definable natnumbers.
> Since each and every natural number has that property,

Wrong. Provably wrong:
∀n ∈ ℕ: |ℕ \ {1, 2, 3, ..., n}| = ℵo.
But it is possible that you can't understand what follows.

Regards, WM

Jim Burns schrieb am Freitag, 24. September 2021 um 22:36:54 UTC+2:
> On 9/24/2021 3:17 PM, Transfinity wrote:

> > n is neither a number nor a circle or a cube.
> It's possible that n is either, neither, or both.

Of course. If n is defined to denote 3, then n is a number.
>
> > It can denote a number or something else
> > if this is uniquely defined.
> Your requirement that n transform from placeholder to number
> when certain information about n is revealed
> is incoherent.

It is fact.
>
> Consider three mathematicians, Ingrid, Janice, and Kathleen.
> Each one has different information about i,j,k.
> Ingrid knows that i + 2j + 3k = 14.
> Janice knows that 2i + 3j + k = 11.
> Kathleen knows that 3i + j + 2k = 11.
>
> To Ingrid, i,j,k are not numbers?
> To Janice, i,j,k are not numbers?
> To Kathleen, i,j,k are not numbers?

Yes.
>
> *UNLESS* the mathematicians compare notes.
> Then, i,j,k are uniquely identified,
> and, *POOF*, they turn into numbers.

Yes.
>
> This raises a host of questions.
> What are the implications of special relativity to
> the POOF? Suppose Ingrid, Janice and Kathleen are
> in motion relative to one another and the placeholders
> being POOFed into numbers are in the Andromeda Galaxy?
>
> Whose reference frame here determines, way out there,
> at what local time the placeholders are POOFed?

Interesting questions. They do not change the fact that n with no further specifications than n ∈ ℕ is not a number.

> Don't you (WM) claim placeholders and numbers must
> have a physical reality? Then there must be an answer.
> What could it be?

The possible numbers represented by n can be all or some or only one. In this case n represents a number.

Regards, WM

On 9/25/2021 3:39 PM, WM wrote:
> Jim Burns schrieb am Freitag, 24. September 2021 um 22:36:54 UTC+2:
>> On 9/24/2021 3:17 PM, Transfinity wrote:
>
>>> n is neither a number nor a circle or a cube.
>> It's possible that n is either, neither, or both.
>
> Of course. If n is defined to denote 3, then n is a number.
>>
>>> It can denote a number or something else
>>> if this is uniquely defined.
>> Your requirement that n transform from placeholder to number
>> when certain information about n is revealed
>> is incoherent.
>
> It is fact.
>>
>> Consider three mathematicians, Ingrid, Janice, and Kathleen.
>> Each one has different information about i,j,k.
>> Ingrid knows that i + 2j + 3k = 14.
>> Janice knows that 2i + 3j + k = 11.
>> Kathleen knows that 3i + j + 2k = 11.
>>
>> To Ingrid, i,j,k are not numbers?
>> To Janice, i,j,k are not numbers?
>> To Kathleen, i,j,k are not numbers?
>
> Yes.
>>
>> *UNLESS* the mathematicians compare notes.
>> Then, i,j,k are uniquely identified,
>> and, *POOF*, they turn into numbers.
>
> Yes.
>>
>> This raises a host of questions.
>> What are the implications of special relativity to
>> the POOF? Suppose Ingrid, Janice and Kathleen are
>> in motion relative to one another and the placeholders
>> being POOFed into numbers are in the Andromeda Galaxy?
>>
>> Whose reference frame here determines, way out there,
>> at what local time the placeholders are POOFed?
>
> Interesting questions. They do not change the fact that n with no further specifications than n ∈ ℕ is not a number.

wrong-O,

did you know that "n ∈ ℕ" says "n is a element of the set of natural numbers" ?

WM brought next idea :
> FromTheRafters schrieb am Freitag, 24. September 2021 um 21:12:12 UTC+2:
>> WM used his keyboard to write :
>
>>> Consider all natural numbers which can be last of a FISON F(n). They are by
>>> definition the definable natnumbers.
>> Since each and every natural number has that property,
>
> Wrong. Provably wrong:
> ∀n ∈ ℕ: |ℕ \ {1, 2, 3, ..., n}| = ℵo.
> But it is possible that you can't understand what follows.

You don't understand what you just wrote. Each FISON is finite by
definition and has a least and a greatest element. Subtracting finite
proper subsets from the naturals does not change the superset's
cardinality.

WM formulated on Saturday :
> Jim Burns schrieb am Freitag, 24. September 2021 um 22:36:54 UTC+2:
>> On 9/24/2021 3:17 PM, Transfinity wrote:
>
>>> n is neither a number nor a circle or a cube.
>> It's possible that n is either, neither, or both.
>
> Of course. If n is defined to denote 3, then n is a number.
>>
>>> It can denote a number or something else
>>> if this is uniquely defined.
>> Your requirement that n transform from placeholder to number
>> when certain information about n is revealed
>> is incoherent.
>
> It is fact.
>>
>> Consider three mathematicians, Ingrid, Janice, and Kathleen.
>> Each one has different information about i,j,k.
>> Ingrid knows that i + 2j + 3k = 14.
>> Janice knows that 2i + 3j + k = 11.
>> Kathleen knows that 3i + j + 2k = 11.
>>
>> To Ingrid, i,j,k are not numbers?
>> To Janice, i,j,k are not numbers?
>> To Kathleen, i,j,k are not numbers?
>
> Yes.
>>
>> *UNLESS* the mathematicians compare notes.
>> Then, i,j,k are uniquely identified,
>> and, *POOF*, they turn into numbers.
>
> Yes.
>>
>> This raises a host of questions.
>> What are the implications of special relativity to
>> the POOF? Suppose Ingrid, Janice and Kathleen are
>> in motion relative to one another and the placeholders
>> being POOFed into numbers are in the Andromeda Galaxy?
>>
>> Whose reference frame here determines, way out there,
>> at what local time the placeholders are POOFed?
>
> Interesting questions. They do not change the fact that n with no further
> specifications than n ∈ ℕ is not a number.

Elements of the set of natural numbers are not numbers? No wonder your
matheology fails.

On 9/25/2021 4:39 PM, WM wrote:
> Jim Burns schrieb
> am Freitag, 24. September 2021 um 22:36:54 UTC+2:
>> On 9/24/2021 3:17 PM, Transfinity wrote:

>>> n is neither a number nor a circle or a cube.
>> It's possible that n is either, neither, or both.
>
> Of course.
> If n is defined to denote 3, then n is a number.

If n can be counted to in principle,
then n is a natural number.

If n cannot be counted to in principle,
then n is not a natural number.

n can be counted to in principle iff
the FISON {0,...,n} from 0 to n exists.

{0,...,n} is the FISON from 0 to n iff
{0,...,n} is a collection
with a transitive and connected order '<' such that
{0,...,n} begins at 0, ends at n, and
for each _split_ BEFORE,AFTER of {0,...,k},
a _crossing-pair_ j,j+1 exists.

j+1 is the successor of j
Each successor has a unique successor
0 has a unique successor.
0 is not a successor.
(j+1 = k+1) iff (j = k)

>>> It can denote a number or something else
>>> if this is uniquely defined.

In the example below, i,j,k did not change.
To suggest that they changed is bizarre and incoherent.
They are not physical.

Ingrid, Janice, and Kathleen changed.
Their knowledge of i,j,k changed from
(individually) not enough to determine i,j,k to
(jointly) enough to determine i,j,k.

>> Consider three mathematicians, Ingrid, Janice, and Kathleen.
>> Each one has different information about i,j,k.
>> Ingrid knows that i + 2j + 3k = 14.
>> Janice knows that 2i + 3j + k = 11.
>> Kathleen knows that 3i + j + 2k = 11.
>>
>> To Ingrid, i,j,k are not numbers?
>> To Janice, i,j,k are not numbers?
>> To Kathleen, i,j,k are not numbers?
>
> Yes.
>
>> *UNLESS* the mathematicians compare notes.
>> Then, i,j,k are uniquely identified,
>> and, *POOF*, they turn into numbers.
>
> Yes.
>
>> This raises a host of questions.
>> What are the implications of special relativity to
>> the POOF? Suppose Ingrid, Janice and Kathleen are
>> in motion relative to one another and the placeholders
>> being POOFed into numbers are in the Andromeda Galaxy?
>>
>> Whose reference frame here determines, way out there,
>> at what local time the placeholders are POOFed?
>
> Interesting questions.
> They do not change the fact that
> n with no further specifications than n ∈ ℕ is not a number.

We reason about n starting from the fact that
n can be counted to in principle.
Imagine, for the sake of argument that, instead of
a natural number, n was a hyper-intelligent shade of blue
or n was a flying rainbow sparkle pony *AND*
n could be counted to in principle.

Then nothing of significance has changed.
No argument from n being able to be counted to in principle
needs to change one iota.

On Friday, September 24, 2021 at 7:01:18 PM UTC+2, Transfinity wrote:

> Proof: <bla>

Nonsense.

On 9/25/2021 5:03 PM, FromTheRafters wrote:
> WM brought next idea :
>> FromTheRafters schrieb am Freitag, 24. September 2021 um 21:12:12 UTC+2:
>>> WM used his keyboard to write :
>>
>>>> Consider all natural numbers which can be last of a FISON F(n). They are by definition the definable natnumbers.
>>> Since each and every natural number has that property,
>>
>> Wrong. Provably wrong:
>> ∀n ∈ ℕ: |ℕ \ {1, 2, 3, ..., n}| = ℵo.
>> But it is possible that you can't understand what follows.
>
> You don't understand what you just wrote. Each FISON is finite by definition and has a least and a greatest element. Subtracting finite proper subsets
> from the naturals does not change the superset's cardinality.

WM does not understand, this is re-beating a dead stale horse, "partitioning the real numbers", what I cant figure out is how he stays stuck on his
fisons and endsegments, this is very simple stuff, covered in depth in 15 min in a real class.