On Friday, 1 October 2021 at 15:52:06 UTC-3, WM wrote:
> Gus Gassmann schrieb am Freitag, 1. Oktober 2021 um 20:32:34 UTC+2:
> > On Friday, 1 October 2021 at 15:18:05 UTC-3, WM wrote:
> > > Gus Gassmann schrieb am Donnerstag, 30. September 2021 um 21:04:33 UTC+2:
> > > > On Thursday, 30 September 2021 at 15:27:33 UTC-3, WM wrote:
> > > >
> > > > > ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo.
> > > > > ∀k ∈ ℕ_def: ∩{E(1), E(2), ..., E(k)} = E(k) /\ |E(k)| = ℵo
> > > > > See the universal quantifier?
> > > >
> > > > Yes. So?
> > > So the collection of all FISONs is a potentially infinite set because it does not reach the first actually infinite cardinal number.
> > A set is not infinite because it "reaches" anything
> The smallest actually infinite set reaches cardinality ℵo. A potentially infinite set will never reach it.

How many mistakes can you pack into a single line? Let's see:
1. There is no smallest infinite set.
2. Nothing "reaches" aleph_0.
3. "Potentially infinite set" is an oxy-moron.
Be careful with that last remaining marble -- if you still have it.

On 10/1/2021 1:32 PM, Gus Gassmann wrote:
> On Friday, 1 October 2021 at 15:18:05 UTC-3, WM wrote:
>> Gus Gassmann schrieb am Donnerstag, 30. September 2021 um 21:04:33 UTC+2:
>>> On Thursday, 30 September 2021 at 15:27:33 UTC-3, WM wrote:
>>>
>>>> ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo.
>>>> ∀k ∈ ℕ_def: ∩{E(1), E(2), ..., E(k)} = E(k) /\ |E(k)| = ℵo
>>>> See the universal quantifier?
>>>
>>> Yes. So?
>> So the collection of all FISONs is a potentially infinite set because it does not reach the first actually infinite cardinal number.
>
> A set is not infinite because it "reaches" anything, you moron. A set is infinite because its cardinality is aleph_0. You are terminally stupid. I'll let that one slide because you already lost a marble today and are now down to your last one.
>

Terminally Stupid Ants
Ants with no marbles left

Un-infinite Ants that cannot reach for infinity

first actually infinite cardinal Ants

universal quantifier Ants

On 10/1/2021 2:29 PM, Gus Gassmann wrote:
> On Friday, 1 October 2021 at 15:52:06 UTC-3, WM wrote:
>> Gus Gassmann schrieb am Freitag, 1. Oktober 2021 um 20:32:34 UTC+2:
>>> On Friday, 1 October 2021 at 15:18:05 UTC-3, WM wrote:
>>>> Gus Gassmann schrieb am Donnerstag, 30. September 2021 um 21:04:33 UTC+2:
>>>>> On Thursday, 30 September 2021 at 15:27:33 UTC-3, WM wrote:
>>>>>
>>>>>> ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo.
>>>>>> ∀k ∈ ℕ_def: ∩{E(1), E(2), ..., E(k)} = E(k) /\ |E(k)| = ℵo
>>>>>> See the universal quantifier?
>>>>>
>>>>> Yes. So?
>>>> So the collection of all FISONs is a potentially infinite set because it does not reach the first actually infinite cardinal number.
>>> A set is not infinite because it "reaches" anything
>> The smallest actually infinite set reaches cardinality ℵo. A potentially infinite set will never reach it.
>
> How many mistakes can you pack into a single line? Let's see:
> 1. There is no smallest infinite set.
> 2. Nothing "reaches" aleph_0.
> 3. "Potentially infinite set" is an oxy-moron.
> Be careful with that last remaining marble -- if you still have it.
>

it may be only a potential marble

On 10/1/2021 1:20 PM, WM wrote:
> FromTheRafters schrieb am Donnerstag, 30. September 2021 um 21:04:54 UTC+2:
>
>>>> You conveniently ignore the fact that even your ill fated stepwise
>>>> process essentially 'removes' each and every element from the
>>>> endsegments
>
> Why then is there no empty endsegment?
>
> Regards, WM
>

endsegments are written as E(k), so what is your empty one, E(empty) ??

On 10/1/2021 1:22 PM, WM wrote:
> zelos...@gmail.com schrieb am Freitag, 1. Oktober 2021 um 14:21:00 UTC+2:
>
>> All natural numbers have infinitely many natural numbers after,
>
> So they are not an actually infinite set.

read it again for the first time;

(in the set of ordered natural numbers) All natural numbers have infinitely many natural numbers after k (k is a natural number)

Note that two consecutive infinite sets of card aleph_0 are impossible in |N.

*when one chops an infinite sausage twice*,
*there are two finite pieces and one infinite piece*

WM, all your math is only about sausages.

>
> Regards, WM
>

On 9/27/2021 2:34 PM, WM wrote:
> zelos...@gmail.com schrieb am Montag, 27. September 2021 um 06:48:17 UTC+2:
>> fredag 24 september 2021 kl. 15:48:09 UTC+2 skrev WM:
>>> 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:
>>>
>>>>> My definition: Any natnumbers must have its UPF known in principle or knowable.
>>>>>
>>>> if I say n is a natural number, it is a natural number.
>>> It is not difficult to prove you wrong. You claim that every natural number has a decimal representation. Name the decimal representation of n. Fail.
>>>
>> n has a decimal representation, doesn't mean I have to give it.
>
> If you claim that n has a decimal representation and this is doubted, then you have to prove it by giving it.
>
> Regards, WM
>

if I say n is a natural number, it is a natural number.

On 9/30/2021 1:12 PM, WM wrote:
> zelos...@gmail.com schrieb am Dienstag, 28. September 2021 um 06:56:41 UTC+2:
>> måndag 27 september 2021 kl. 21:34:57 UTC+2 skrev WM:
>
>>> If you claim that n has a decimal representation and this is doubted, then you have to prove it by giving it.
>>>
>> Nope, I only have to prove all natural numbers have one and that is done already.
>
> Irrelevant since it is just doubted that n is a natural number. If a honest mathematician is asked to show n's decimal representation, then he will do so, if he can.
>
> Regards, WM
>

if I say n is a natural number, it is a natural number.

WM since you reject this statement above, You cannot do ANY math. Fail. Resign.

On 9/30/2021 1:32 PM, WM wrote:
> Greg Cunt schrieb am Donnerstag, 30. September 2021 um 20:19:56 UTC+2:
>> On Thursday, September 30, 2021 at 8:12:13 PM UTC+2, WM wrote:
>>
>> Let n be a natural number. [Or: Let n e IN.]
>>> it is just doubted that n is a natural number.
>> BY WHOM,
>
> Irrelevant.
> If n is a natural number, then its decimal representation can be given.
> Give it!

QuaCK!

>
>> Hint: BY DEFINITION (see above) n is an element in the set of all natural numbers.
>
> No, you misunderstand. "n ∈ ℕ" is simply an abbreviation for the sentence: "Consider any natural number".

WRONG. it says "n is an element of the set of Natural Numbers"

On 10/1/2021 12:51 PM, WM wrote:
> zelos...@gmail.com schrieb am Freitag, 1. Oktober 2021 um 07:06:23 UTC+2:
>> torsdag 30 september 2021 kl. 20:33:05 UTC+2 skrev WM:
>>> Greg Cunt schrieb am Donnerstag, 30. September 2021 um 20:19:56 UTC+2:
>>>> On Thursday, September 30, 2021 at 8:12:13 PM UTC+2, WM wrote:
>>>>
>>>> Let n be a natural number. [Or: Let n e IN.]
>>>>> it is just doubted that n is a natural number.
>>>> BY WHOM,
>>> Irrelevant.
>>> If n is a natural number, then its decimal representation can be given.
>>> Give it!
>>>> Hint: BY DEFINITION (see above) n is an element in the set of all natural numbers.
>>> No, you misunderstand. "n ∈ ℕ" is simply an abbreviation for the sentence: "Consider any natural number". By the way, you can also use k ∈ ℕ or m ∈ ℕ. Are they in trichotomy? k < m < n? Or m < k, n?
>>>> Does this set contain anything else except natural numbers?
>>> No, therefore it does not contain k, m, n.
>>>
>> are you insane or just mentally retarded?
>
> Do I claim that n is a number?
>
> Regards, WM
>

you have demonstrated you cannot, will not, follow a simple one line math statement.
I have promoted you to Clown Shoes.

On 10/1/2021 12:47 PM, WM wrote:
> Gus Gassmann schrieb am Donnerstag, 30. September 2021 um 21:10:40 UTC+2:
>> On Thursday, 30 September 2021 at 15:12:13 UTC-3, WM wrote:
>> [...]
>>> Irrelevant since it is just doubted that n is a natural number. If a honest mathematician is asked to show n's decimal representation, then he will do so, if he can.
>> I also presume that you can't give the decimal representation of Graham's number. Nonetheless, it is trivial to prove that by induction it has one.
>
> It could be givn in principle in ideal mathematics. That of n cannot be given because n is not a number.
>
> Regards, WM
>

wrong, n is simply a pattern of pixels on the computer screen.

On 10/1/2021 12:50 PM, WM wrote:
> zelos...@gmail.com schrieb am Freitag, 1. Oktober 2021 um 07:04:41 UTC+2:
>> torsdag 30 september 2021 kl. 20:12:13 UTC+2 skrev WM:
>>> zelos...@gmail.com schrieb am Dienstag, 28. September 2021 um 06:56:41 UTC+2:
>>>> måndag 27 september 2021 kl. 21:34:57 UTC+2 skrev WM:
>>>
>>>>> If you claim that n has a decimal representation and this is doubted, then you have to prove it by giving it.
>>>>>
>>>> Nope, I only have to prove all natural numbers have one and that is done already.
>>> Irrelevant since it is just doubted that n is a natural number. If a honest mathematician is asked to show n's decimal representation, then he will do so, if he can.
>
>> We do not need to know decimal expansions to know there is one and to do arguments about them and you do not doubt n is a natural number. If I say it is from the set of natural number it is by definition a natural number.
>
> It is not your competence to define what natural numbers are.
> Please mark the place of n on the following scale:
>
> ...1...10...100...1000...10000...
>
> Regards, WM
>

you failed to list the decimal representations, AND the prime co-factors of each, so they are not numbers

those are not numbers, they are simply degenerate pixel patterns on the screen

On Friday, October 1, 2021 at 7:51:03 PM UTC+2, WM wrote:

> Please mark the place of n on the following scale:
>
> ...1...10...100...1000...10000...

Please mark the place of Schnirelmann's constant on the follwoing scale, dumbo:

1, 2, 3, 4, 5, 6, 7, ...

See: https://mathworld.wolfram.com/SchnirelmannConstant.html

On 9/27/2021 3:12 PM, WM wrote:
> Gus Gassmann schrieb am Sonntag, 26. September 2021 um 03:16:34 UTC+2:
>> On Friday, 24 September 2021 at 16:57:04 UTC-3, 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?
>> I tell you what is not in it: Elements. The intersection over an infinite number of end segments is *EMPTY*.
>
> The intersection over infinite endsegments is infinite.

no. Name just one element in the intersection of all endsegments. Fail.

>
>> In particular no natural number n is an element of its successor's end segment E(n+1).
>
> What are the elements of the infinite endsegments? Are they also in |N?

by definition, and by dual citizenship of numbers to be in 2 places at the SAME TIME.

>
> Regards, WM
>

On 9/30/2021 1:50 PM, WM wrote:
> Gus Gassmann schrieb am Montag, 27. September 2021 um 22:45:39 UTC+2:
>> On Monday, 27 September 2021 at 17:12:55 UTC-3, WM wrote:
>
>>> The intersection over infinite endsegments is infinite.
>> Often stated, never proved
>
> Proved by inclusion monotony.

you can't talk the talk, nor walk the walk.

>>
>> Intersections over infinitely many end segments are empty:
>
> Why are the endsegments not empty?

they are defined that way. Each is a FIXED set of numbers.

> Why does their infinite contents differ from contents of their predecessors?

Defined that way. Google for it.

>
>>> What are the elements of the infinite endsegments? Are they also in |N?
>> You are repeating yourself, you are forgetting things, you are clearly dribbling at the mouth, and it seems you are losing control over your other bodily functions, too. Every end segments contains *ONLY* natural numbers. That is by definition
>
> Those are in all its predecessors. And infinitely many are in all infinite successors. It is useless to continue this simple argument. Unless you show an attempt to discuss these facts, EOD

you EOD Math long ago, if you ever had any.

>
> Regards, WM
>

On 9/30/2021 1:53 PM, WM wrote:
> Gus Gassmann schrieb am Montag, 27. September 2021 um 22:52:52 UTC+2:
>> On Monday, 27 September 2021 at 17:14:52 UTC-3, WM wrote:
>
>> Every end segment contains only natural numbers (infinitely many of them), so the intersection over end segments cannot contain anything else than natural numbers. No natural number n is an element of its successor's end segment E(n+1). So no natural number n can be a member of an intersection of end segments that contains E(n+1) or any other end segment E(m) with m > n.
>
> Nevertheless infinitely many natural numbers remain in every endsegment. Un less they are all excorcized the intersection will not become empty.

you fail to understand "intersection", there is no time required for it, it is not "excorcized"

there is no process, no step by step, there is no become empty.

>
>> Ergo, the infinite intersection is empty.
>
> Empty of definable natnumbers, filled of dark natnumbers.

you mind has filled in your non-definable natural numbers with dark numbers, yet there is no mathematical path to prove dark numbers are anywhere at all.

>
> Regards, WM
>

On 10/1/2021 1:00 PM, WM wrote:
> zelos...@gmail.com schrieb am Freitag, 1. Oktober 2021 um 07:02:54 UTC+2:
>> torsdag 30 september 2021 kl. 20:54:04 UTC+2 skrev WM:
>>> Gus Gassmann schrieb am Montag, 27. September 2021 um 22:52:52 UTC+2:
>>>> On Monday, 27 September 2021 at 17:14:52 UTC-3, WM wrote:
> ction because there is always at least 1 intersection not containing the element. So that is why it is empty. Why is this so fucking difficult for you?

that is not difficult for me

>
> Same holds for the endegments themselves. Every natural number is missing because there is at least one endsegment not containing it.

so there are no natural numbers in the intersection of all endsegments, glad you see that now.

> What are the infintely many remaining in all endegments?

wrong.

All endesegments are known fixed sets of numbers.

Numbers do not remain or get removed from an endesegment.

do you reject these facts ?

>
> Regards, WM
>

On 10/1/2021 12:58 PM, WM wrote:
> zelos...@gmail.com schrieb am Freitag, 1. Oktober 2021 um 07:03:30 UTC+2:
>> torsdag 30 september 2021 kl. 20:56:13 UTC+2 skrev WM:
>
>>> Just this is impossible for endsegments. Inclusion monotony!
>>>
>> Nope, that only shows that any FINITE intersection is non-empty, not that the intersection of ALL is emtpy
>
> Is one endsegment among all that is not the last of a finite intersection?
>
> Regards, WM
>

facts, do you deny them ?

The intersection of any two endesegments is infinite

The intersection of any finite number of endsegments is infinite

The intersection of all/or infinite number of endsegments is the null set, nada, {}, nothing, zero.

On 9/27/2021 3:20 PM, WM wrote:
> Jim Burns schrieb am Sonntag, 26. September 2021 um 19:14:45 UTC+2:
>> On 9/24/2021 12:42 PM, WM wrote:
>
>> "That" is a pronoun.
>> That is a natural number, when I refer to a natural number.
>
> Yes, if you refer to a certain number.

no.

>>
>> "n" is variable name, or a placeholder, or call it what you like.
>> n is a natural number, if I say it is.
>
> Yes, if you can say what is its prime decomposition.

red herring.

>
> Regards, WM
>

On 10/2/2021 10:15 AM, Serg io wrote:
> On 10/1/2021 1:00 PM, WM wrote:
>> zelos...@gmail.com schrieb am Freitag, 1. Oktober 2021 um 07:02:54 UTC+2:
>>> torsdag 30 september 2021 kl. 20:54:04 UTC+2 skrev WM:
>>>> Gus Gassmann schrieb am Montag, 27. September 2021 um 22:52:52 UTC+2:
>>>>> On Monday, 27 September 2021 at 17:14:52 UTC-3, WM wrote:
>> ction because there is always at least 1 intersection not containing the element. So that is why it is empty. Why is this so fucking difficult for you?
>
> that is not difficult for me
>
>>
>> Same holds for the endegments themselves. Every natural number is missing because there is at least one endsegment not containing it.
>
> so there are no natural numbers in the intersection of all endsegments, glad you see that now.
>
>
>> What are the infintely many remaining in all endegments?
>
> wrong.
>
> All endesegments are known fixed sets of numbers.
>
> Numbers do not remain or get removed from an endesegment.
>
> do you reject these facts ?
>
>
>>
>> Regards, WM
>>
>

Endsegment Facts;

Each Endsegment is a known, fixed set of natural numbers.

Numbers do not get added to, nor removed from, an specific Endsegment.

The intersection of any two endesegments is infinite.

The intersection of any finite number of endsegments is infinite.

The intersection of all/or infinite number of, endsegments is empty, the null set, nada, {}, nothing, zero.

On Friday, October 1, 2021 at 8:00:48 PM UTC+2, WM wrote:

> [Each and] Every natural number is missing [in the intersection of all endsegments] because there is at least one endsegment not containing it.

Exactly.

> What <bla>

Irrelevant.

On Friday, October 1, 2021 at 8:04:37 PM UTC+2, WM wrote:

> Why are the endsegments *not* empty?

Because they (i.e. all of them) are infinite sets BY DEFINITION (and hence not empty).

On Friday, October 1, 2021 at 8:04:37 PM UTC+2, WM wrote:

> In an infinite endsegment there are [bla bla bla] to yield an infinite intersection.

Yeah, whatever.

Actually, the intersection of all endsegments (each of which is infinite) is empty. A trivial fact.

On 10/2/2021 11:13 AM, Greg Cunt wrote:
> On Friday, October 1, 2021 at 8:04:37 PM UTC+2, WM wrote:
>
>> Why are the endsegments *not* empty?
>
> Because they (i.e. all of them) are infinite sets BY DEFINITION (and hence not empty).
>

It seems that WM doesn't think in terms of fixed objects now, they all seem to be movable or changing in his mind. Perhaps a limitation by only a few
marbles, only a few relations can exist at the same thinking moment in time.

An Endsegment, E(k), is only shorthand for this E(k) = {k,k+1,k+2,...} a fixed (by k) infinite set of natural numbers that does not change.

There are no empty endsegment.

Greg Cunt schrieb am Samstag, 2. Oktober 2021 um 02:32:38 UTC+2:
> On Friday, October 1, 2021 at 7:51:03 PM UTC+2, WM wrote:
>
> > Please mark the place of n on the following scale:
> >
> > ...1...10...100...1000...10000...
> Please mark the place of Schnirelmann's constant on the follwoing scale,

> 1, 2, 3, 4, 5, 6, 7, ...
>
If it is a constant number, then it has a place there which can be determined in principle. n has no place there.

Regards, WM

Gus Gassmann schrieb am Freitag, 1. Oktober 2021 um 20:27:08 UTC+2:
> On Friday, 1 October 2021 at 14:58:10 UTC-3, WM wrote:
> > zelos...@gmail.com schrieb am Freitag, 1. Oktober 2021 um 07:03:30 UTC+2:
> > > torsdag 30 september 2021 kl. 20:56:13 UTC+2 skrev WM:
> >
> > > > Just this is impossible for endsegments. Inclusion monotony!
> > > >
> > > Nope, that only shows that any FINITE intersection is non-empty, not that the intersection of ALL is emtpy
> > Is one endsegment among all that is not the last of a finite intersection?
> You are delusional if you think the talk here is about *finite* intersections.

Show an endsegment of all that is not in a finite intersection. Fail. So there is no infinite intersection for showable endsegments.

Regards, WM