Greg Cunt schrieb am Freitag, 10. September 2021 um 19:00:59 UTC+2:
> On Friday, September 10, 2021 at 6:52:16 PM UTC+2, WM wrote:
> > Greg Cunt schrieb am Freitag, 10. September 2021 um 18:49:34 UTC+2:
> > > On Friday, September 10, 2021 at 6:26:12 PM UTC+2, WM wrote:
> > > >
> > > > As long as the endsegments are infinite, the intersection is infinite too.
> > > >
> > > Actually, the intersection of (the set of) all endsegments is empty.
> > >
> > Actually it is the minimum endsegment.
> The MINIMAL ENDSEGMENT??? Huh???!!!
>
> There IS NO MINIMAL ENDSEGMENT,

If all endsegments have card aleph_0, then all are minimal.

> Hint: For all n e IN: E(n+1) c E(n) & E(n+1) =/= E(n).

Hint cardinality is same.

Regards, WM

On Friday, September 10, 2021 at 10:29:35 PM UTC+2, WM wrote:
> Greg Cunt schrieb am Freitag, 10. September 2021 um 18:44:29 UTC+2:
> > On Friday, September 10, 2021 at 6:17:54 PM UTC+2, WM wrote:
> > > Greg Cunt schrieb am Freitag, 10. September 2021 um 15:32:37 UTC+2:
> > > > On Friday, September 10, 2021 at 3:18:07 PM UTC+2, WM wrote:
> > > > >
> > > > > The sequence is inclusion monotonic. Therefore its intersection cannot be empty if no endsegment is empty.
> > > >
> > > > Please prove this argument.
> > > >
> > > If the intersection is not infinite, then there must be a first infinite endsegment with finite intersection because of
> > > stepwise loss ∀k ∈ ℕ: E(k+1) = E(k) \ {k}.
> > >
> > Please prove this argument.
> >
> No proof requird because

Of course, it is, you silly crank!

In the context of mathematicas we have to PROVE our claims.

Why don't you go and just fuck yourself, dumbo?

> it is the definition of the endsegments.

"it"? What? The proof is a definition, or what?

So you won't provide a proof for your claim

| If the intersection is not infinite, then there must be a first infinite endsegment with finite intersection because
| of stepwise loss ∀k ∈ ℕ: E(k+1) = E(k) \ {k}

?

Well, little wonder. Since the claim is false.

You are just a silly crank full of shit, Mückenheim.

On Friday, September 10, 2021 at 10:30:46 PM UTC+2, WM wrote:
> Greg Cunt schrieb am Freitag, 10. September 2021 um 18:46:54 UTC+2:
> >
> > Let n be an element in IN_F and let m be an element in IN_F\{n}. Then m =/= n.
> >
> Wrong.

Well, you REALLY are ready for the psychiatric ward, man.

On Friday, September 10, 2021 at 10:37:04 PM UTC+2, WM wrote:
> Greg Cunt schrieb am Freitag, 10. September 2021 um 19:00:59 UTC+2:
> > On Friday, September 10, 2021 at 6:52:16 PM UTC+2, WM wrote:
> > > Greg Cunt schrieb am Freitag, 10. September 2021 um 18:49:34 UTC+2:
> > > > On Friday, September 10, 2021 at 6:26:12 PM UTC+2, WM wrote:
> > > > >
> > > > > As long as the endsegments are infinite, the intersection is infinite too.
> > > > >
> > > > Actually, the intersection of (the set of) all endsegments is empty..
> > > >
> > > Actually it is the minimum endsegment.
> > >
> > The MINIMAL ENDSEGMENT??? Huh???!!!
> >
> > There IS NO MINIMAL ENDSEGMENT,
> >
> If [bl abla] then all are minimal.

Time to consult a psychiatrist, Mückenheim.

On Friday, September 10, 2021 at 11:45:16 AM UTC-7, Serg io wrote:
> On 9/10/2021 9:45 AM, Ross A. Finlayson wrote:
> > On Friday, September 10, 2021 at 3:15:23 AM UTC-7, FromTheRafters wrote:
> >> Ross A. Finlayson was thinking very hard :
> >>> On Thursday, September 9, 2021 at 7:25:37 PM UTC-7, FromTheRafters wrote:
> >>>> Gus Gassmann pretended :
> >>>>> On Thursday, 9 September 2021 at 18:07:28 UTC-3, FromTheRafters wrote:
> >>>>>> Serg io was thinking very hard :
> >>>>>>> On 9/9/2021 8:01 AM, WM wrote:
> >>>>>>>> zelos...@gmail.com schrieb am Donnerstag, 9. September 2021 um 07:03:00
> >>>>>>>> UTC+2:
> >>>>>>>>> onsdag 8 september 2021 kl. 21:38:49 UTC+2 skrev WM:
> >>>>>>>>>> Jim Burns schrieb am Mittwoch, 8. September 2021 um 00:33:30 UTC+2:
> >>>>>>>>>>
> >>>>>>>>>>> If there is no last end segment of all end segments,
> >>>>>>>>>>> then the intersection of all end segments is
> >>>>>>>>>> Then there is no "all endsegments". "All" can only be proved by
> >>>>>>>>>> showing the last.
> >>>>>>>>>>
> >>>>>>>>> Where does it say that "all" must mean a last?
> >>>>>>>>
> >>>>>>>> In linear order nobody should believe the claim of all without being
> >>>>>>>> shown the last element.
> >>>>>>>
> >>>>>>>
> >>>>>>> all natural numbers => 1,2,3,...
> >>>>>>>
> >>>>>>> so according to WM do not believe in Natural Numbers unless WM can show
> >>>>>>> you the Last one.
> >>>>>> Sure, there's the last one, this current one, and the next one.
> >>>>>
> >>>>> Cool. So, in an inductive set it should indeed be sufficient to be shown
> >>>>> the last one, because you then have this current one, as well as the next
> >>>>> one! Is that what the great perfessor is taking about?
> >>>> Who knows what he's talking about, he hasn't made any sense for
> >>>> decades.
> >>>
> >>>
> >>> It's always "infinite induction exhausts" never satisfying related rates
> >>> problems or the countable and uncountable in functional analysis and
> >>> infinite domains.
> >>>
> >>> (WM is _plainly_ mostly Hodges' hopeless and sometimes "infinite integers
> >>> as discredited as possible".)
> >>>
> >>> Is it a paradox that the differential via countable additivity both
> >>> integrates under any continuous functions but there are uncountably many
> >>> points on it?
> >>>
> >>> Is it not because there aren't uncountably partitions of the unit interval
> >>> because each would contain a rational?
> >>>
> >>> Doesn't well-ordering the reals have a subset that is well-ordering
> >>> uncountably many, in their order?
> >>>
> >>>
> >>> Counterexamples....
> >>>
> >>>
> >>> I know what's he's talking about, just doing it wrong, not enough, and the
> >>> wrong way.
> >> Yeah, I guess it is easy to know what he is talking about when you
> >> consider his goal is to use his misunderstandings about "series" to
> >> show Cantor's diagonal method of 'listing; the rationals is flawed
> >> because Cantor ignores WM's 'Dark Numbers' which he says cannot be
> >> mapped because they can't be exactly expressed as a finite sequence.
> >>
> >> He tries to shoehorn in some 'Dark Numbers' into ZFC and when it
> >> doesn't work he exclaims "ZFC is inconsistent" because it ignores his
> >> "Dark Numbers".
> >
> > Yeah that's wrong, given usual formalisms and facts like "irrational numbers
> > exist and are dense in the reals", the antidiagonal argument, nested intervals
> > and other results in topology of numbers about uncountability. That said, the
> > rationals are HUGE in a sense, i.e. in a usual sense much larger a "set" than
> > the integers, a set in th etopology of the numbers, in all the supersets of the
> > rationals and the integers as a subset, of the rationals, by their values.
> what ?
> >
> > Many people have a number model of values with attributes of being integer,
> > rational, real, ..., for each value, and that R > Q > N means subset and also size.
> > (In those labels of those sets under that extensionality.) For many people R-values
> > is enough numbers for the purposes of scalars in vector spaces.
> What ?
> >
> > Then, for something like "ZF is inconsistent for example according to Russell
> > a model of it as a set contains itself so it's not consistent its axioms those
> > that restrict comprehension i.e. well-foundedness and 'ordinary' omega".
> > is a way to re-frame usual paradoxes as what arrived at those axioms already.
> Buzz word BOT spew.
> >
> > What theorists would have not exist....
> >

"Rationals HUGE" is a reference to Harvey Friedman ideas that include
that "though countable, the rationals are HUGE".

You might find more of his posts on FOM, where, of course, FOM is
an initialism for "Foundations of Mathematics".

https://cs.nyu.edu/pipermail/fom/

Most people's model of numbers is integer part and non-integer part,
being totally ordered in the integer and non-integer part and about
that in the theory of vector spaces, there is the scalar, and, real
numbers as values are the scalar values, and rationals have thier
integer part and non-integer part as real numbers, and of course integers
have their integer parts, making for the simplest model of numbers
most understood by everybody in the world.

If you've never studied well-orderings of the reals, it's an interesting
thing about that any set in ZFC has a well-ordering, but, nobody can come
up with an example for the reals, without, more than less having their
integer parts well-ordered and non-integer parts well-ordered.

When it comes to bots, it's pretty simple that anybody with a usual
working knowledge and some time spent in writing chat-bots, could
make quite a few, basically populating the chat with spew. (I am not one.)

Of course, it's not expected they're particularly sophisticated or flexible,
and, when given inputs what make them thrash because they don't have
much the apparatus of holistic opinion, they are farmed out massive wide
in parallel then the ones that start thinking get culled and the ones that
amuse the bot-swarm sock-puppeteer get re-inflicted on sci.amth.
(Bot's a bot, other bots are bots, some bots are bots, all bots are bots.)

(The "bot fly" is a particularly gruesome insect.)

If you don't know the history of Gottlob Frege and his Grundgesetze,
it was an effort in fundamental logic about the end of the 19'th century.
Russell sank it with a version of "Russell's paradox", then, after ZFC
after the Cantor's Mengenlehre or set theory, blessed ZFC after having
an "ordinary" omega, ignoring Burali-Forti's "paradox" and so on.
That "blessing" is a "curse" as the only axioms of ZFC what "wish away",
or define as not sets, what would be sets, are the axioms of regularity a.k.a
well-foundedness, and, for omega that an inductive set exist: that a necessarily
"ordinary" infinite inductive set exists and is defined as a constant.
(That otherwise would just be a result of quantification, extra-, ordinary.)

Then, that there only truisms and only validities are well-formed in a
Comenius language, the "Liar paradox" just falls out as a prototype of
fallacy, what that any contradiction is as so simply reduced to it.

Russell convinced Zermelo and Fraenkel to "ignore their dark
or non-well-founded if not as inconsistent multiplicities, what
otherwise would be sets". If you're interested in both ordinary/well-founded
and extraordinary/non-well-founded sets as result from theory, you might
learn some things for example about Aczel and his theories.

Of course if you're not interested in foundations there are of course
platforms with fundamental theorems for usual objects. But, a true
foundations includes all the mathematics, so, that's the interest of foundations.

On Friday, September 10, 2021 at 1:01:47 PM UTC-7, FromTheRafters wrote:
> Serg io explained on 9/10/2021 :
> > On 9/10/2021 8:19 AM, WM wrote:
> >> Greg Cunt schrieb am Donnerstag, 9. September 2021 um 15:51:46 UTC+2:
> >>> On Thursday, September 9, 2021 at 3:03:01 PM UTC+2, WM wrote:
> >>>
> >>>> Because we or our ancestors have constructed them without rows and
> >>>> vertices.
> >>> Where did they construct them?
> >>
> >> On many occasions. Counting sheep for intance.
> >
> > One must align all identified sheeps to be counted (including the last one)
> > into rows and vertices (not columns) pointed to magnetic north. When that is
> > done, then you count each sheep once, once thou shall countith said sheep,
> > not twice, but only once. Remember to increase the count by 1 each time; not
> > 1,1,1,1,1,1... but 1,2,3,4,5,6...
> >
> >>
> >>> Where can we find them?
> >>
> >> In school books for instance.
> >
> > there are lots of books on "how to count rocks", and "how to count sheeps
> > using rocks".
> Sadly, none for teaching rocks how to do math.

Not many people know a fundamental difference between numbering
and counting, that there is one, and that though often effectively the
same, make for quite different frameworks of ordinals about cardinals
and cardinals about ordinals.

Many people took the line that "numbering is counting", but really
they learned about a simple machine with a temporal store and
a stack machine of sorts of the ball-and-vase variety, left all
underdefined, for those not interested in foundations.

Compared to that each sheep has a name....

On 9/10/2021 4:01 PM, FromTheRafters wrote:
> Serg io explained on 9/10/2021 :

>> there are lots of books on "how to count rocks", and
>> "how to count sheeps using rocks".
>
> Sadly, none for teaching rocks how to do math.

Here's how rocks (ie, trolls) do math on Discworld:
| | He could hear the jody Detritus had taught them.
| Somehow, you could tell it was made up by a troll:
| | "Now we sing dis stupid song!
| Sing it as we run along!
| Why we sing dis we don't know!
| We can't make der words rhyme prop'ly!"
| | "Sound off!"
| | "One! Two!
| | "Sound off!"
| | "Many!Lots!"
| | "Sound off!"
| | "Er...what?"
| -- _Night Watch_ Terry Pratchett

On Friday, September 10, 2021 at 2:48:34 PM UTC-7, Ross A. Finlayson wrote:
> On Friday, September 10, 2021 at 11:45:16 AM UTC-7, Serg io wrote:
> > On 9/10/2021 9:45 AM, Ross A. Finlayson wrote:
> > > On Friday, September 10, 2021 at 3:15:23 AM UTC-7, FromTheRafters wrote:
> > >> Ross A. Finlayson was thinking very hard :
> > >>> On Thursday, September 9, 2021 at 7:25:37 PM UTC-7, FromTheRafters wrote:
> > >>>> Gus Gassmann pretended :
> > >>>>> On Thursday, 9 September 2021 at 18:07:28 UTC-3, FromTheRafters wrote:
> > >>>>>> Serg io was thinking very hard :
> > >>>>>>> On 9/9/2021 8:01 AM, WM wrote:
> > >>>>>>>> zelos...@gmail.com schrieb am Donnerstag, 9. September 2021 um 07:03:00
> > >>>>>>>> UTC+2:
> > >>>>>>>>> onsdag 8 september 2021 kl. 21:38:49 UTC+2 skrev WM:
> > >>>>>>>>>> Jim Burns schrieb am Mittwoch, 8. September 2021 um 00:33:30 UTC+2:
> > >>>>>>>>>>
> > >>>>>>>>>>> If there is no last end segment of all end segments,
> > >>>>>>>>>>> then the intersection of all end segments is
> > >>>>>>>>>> Then there is no "all endsegments". "All" can only be proved by
> > >>>>>>>>>> showing the last.
> > >>>>>>>>>>
> > >>>>>>>>> Where does it say that "all" must mean a last?
> > >>>>>>>>
> > >>>>>>>> In linear order nobody should believe the claim of all without being
> > >>>>>>>> shown the last element.
> > >>>>>>>
> > >>>>>>>
> > >>>>>>> all natural numbers => 1,2,3,...
> > >>>>>>>
> > >>>>>>> so according to WM do not believe in Natural Numbers unless WM can show
> > >>>>>>> you the Last one.
> > >>>>>> Sure, there's the last one, this current one, and the next one.
> > >>>>>
> > >>>>> Cool. So, in an inductive set it should indeed be sufficient to be shown
> > >>>>> the last one, because you then have this current one, as well as the next
> > >>>>> one! Is that what the great perfessor is taking about?
> > >>>> Who knows what he's talking about, he hasn't made any sense for
> > >>>> decades.
> > >>>
> > >>>
> > >>> It's always "infinite induction exhausts" never satisfying related rates
> > >>> problems or the countable and uncountable in functional analysis and
> > >>> infinite domains.
> > >>>
> > >>> (WM is _plainly_ mostly Hodges' hopeless and sometimes "infinite integers
> > >>> as discredited as possible".)
> > >>>
> > >>> Is it a paradox that the differential via countable additivity both
> > >>> integrates under any continuous functions but there are uncountably many
> > >>> points on it?
> > >>>
> > >>> Is it not because there aren't uncountably partitions of the unit interval
> > >>> because each would contain a rational?
> > >>>
> > >>> Doesn't well-ordering the reals have a subset that is well-ordering
> > >>> uncountably many, in their order?
> > >>>
> > >>>
> > >>> Counterexamples....
> > >>>
> > >>>
> > >>> I know what's he's talking about, just doing it wrong, not enough, and the
> > >>> wrong way.
> > >> Yeah, I guess it is easy to know what he is talking about when you
> > >> consider his goal is to use his misunderstandings about "series" to
> > >> show Cantor's diagonal method of 'listing; the rationals is flawed
> > >> because Cantor ignores WM's 'Dark Numbers' which he says cannot be
> > >> mapped because they can't be exactly expressed as a finite sequence.
> > >>
> > >> He tries to shoehorn in some 'Dark Numbers' into ZFC and when it
> > >> doesn't work he exclaims "ZFC is inconsistent" because it ignores his
> > >> "Dark Numbers".
> > >
> > > Yeah that's wrong, given usual formalisms and facts like "irrational numbers
> > > exist and are dense in the reals", the antidiagonal argument, nested intervals
> > > and other results in topology of numbers about uncountability. That said, the
> > > rationals are HUGE in a sense, i.e. in a usual sense much larger a "set" than
> > > the integers, a set in th etopology of the numbers, in all the supersets of the
> > > rationals and the integers as a subset, of the rationals, by their values.
> > what ?
> > >
> > > Many people have a number model of values with attributes of being integer,
> > > rational, real, ..., for each value, and that R > Q > N means subset and also size.
> > > (In those labels of those sets under that extensionality.) For many people R-values
> > > is enough numbers for the purposes of scalars in vector spaces.
> > What ?
> > >
> > > Then, for something like "ZF is inconsistent for example according to Russell
> > > a model of it as a set contains itself so it's not consistent its axioms those
> > > that restrict comprehension i.e. well-foundedness and 'ordinary' omega".
> > > is a way to re-frame usual paradoxes as what arrived at those axioms already.
> > Buzz word BOT spew.
> > >
> > > What theorists would have not exist....
> > >
> "Rationals HUGE" is a reference to Harvey Friedman ideas that include
> that "though countable, the rationals are HUGE".
>
> You might find more of his posts on FOM, where, of course, FOM is
> an initialism for "Foundations of Mathematics".
>
> https://cs.nyu.edu/pipermail/fom/
>
>
> Most people's model of numbers is integer part and non-integer part,
> being totally ordered in the integer and non-integer part and about
> that in the theory of vector spaces, there is the scalar, and, real
> numbers as values are the scalar values, and rationals have thier
> integer part and non-integer part as real numbers, and of course integers
> have their integer parts, making for the simplest model of numbers
> most understood by everybody in the world.
>
> If you've never studied well-orderings of the reals, it's an interesting
> thing about that any set in ZFC has a well-ordering, but, nobody can come
> up with an example for the reals, without, more than less having their
> integer parts well-ordered and non-integer parts well-ordered.
>
>
>
>
>
> When it comes to bots, it's pretty simple that anybody with a usual
> working knowledge and some time spent in writing chat-bots, could
> make quite a few, basically populating the chat with spew. (I am not one.)
>
> Of course, it's not expected they're particularly sophisticated or flexible,
> and, when given inputs what make them thrash because they don't have
> much the apparatus of holistic opinion, they are farmed out massive wide
> in parallel then the ones that start thinking get culled and the ones that
> amuse the bot-swarm sock-puppeteer get re-inflicted on sci.amth.
> (Bot's a bot, other bots are bots, some bots are bots, all bots are bots.)
>
> (The "bot fly" is a particularly gruesome insect.)
>
> If you don't know the history of Gottlob Frege and his Grundgesetze,
> it was an effort in fundamental logic about the end of the 19'th century.
> Russell sank it with a version of "Russell's paradox", then, after ZFC
> after the Cantor's Mengenlehre or set theory, blessed ZFC after having
> an "ordinary" omega, ignoring Burali-Forti's "paradox" and so on.
> That "blessing" is a "curse" as the only axioms of ZFC what "wish away",
> or define as not sets, what would be sets, are the axioms of regularity a.k.a
> well-foundedness, and, for omega that an inductive set exist: that a necessarily
> "ordinary" infinite inductive set exists and is defined as a constant.
> (That otherwise would just be a result of quantification, extra-, ordinary.)
>
>
> Then, that there only truisms and only validities are well-formed in a
> Comenius language, the "Liar paradox" just falls out as a prototype of
> fallacy, what that any contradiction is as so simply reduced to it.
>
>
> Russell convinced Zermelo and Fraenkel to "ignore their dark
> or non-well-founded if not as inconsistent multiplicities, what
> otherwise would be sets". If you're interested in both ordinary/well-founded
> and extraordinary/non-well-founded sets as result from theory, you might
> learn some things for example about Aczel and his theories.
>
> Of course if you're not interested in foundations there are of course
> platforms with fundamental theorems for usual objects. But, a true
> foundations includes all the mathematics, so, that's the interest of foundations.
>
>
> Which for me started as interest in continuity what resulted
> research in foundations.
>
> Frege's is a remarkable effort and for most people would suffice for most things.

On Friday, September 10, 2021 at 10:37:04 PM UTC+2, WM wrote:
> Greg Cunt schrieb am Freitag, 10. September 2021 um 19:00:59 UTC+2:
> > On Friday, September 10, 2021 at 6:52:16 PM UTC+2, WM wrote:
> > > Greg Cunt schrieb am Freitag, 10. September 2021 um 18:49:34 UTC+2:

A simple an trivial fact (outside of crank town):

> > > > The intersection of (the set of) all endsegments is empty.
> > > >
> > > Actually it is the minimum endsegment.
> > >
> > The MINIMAL ENDSEGMENT??? Huh???!!!
> >
> > There IS NO MINIMAL ENDSEGMENT,
> >
> If all endsegments have card aleph_0, then all are minimal.

LOOK, YOU FUCKING IDIOT, if you are (just) referring to the cardinal numbers of the end segments, then the endsegements are NOT ORDERED (this way). Hence talking about "minimal" endsegments is NONSENSE in this case.

Hint: The definition E <= E' :<-> card(E) <= card(E') DOESN'T define an order on the set of endsegments.

> > Hint: For all n e IN: E(n+1) c E(n) & E(n+1) =/= E(n).

The ORDER we consider in this context AND *YOU* ARE REFERRING TO with your "inclusion monotony" mantra is given by THE SUBSET-RELATION.

Hence THERE'S NO (c-)MINIMAL endsegment, you silly asshole!

FUCK YOU, Mucke!

On 9/10/2021 12:52 PM, WM wrote:
> Greg Cunt schrieb
> am Freitag, 10. September 2021 um 18:49:34 UTC+2:
>> On Friday, September 10, 2021 at 6:26:12 PM UTC+2,
>> WM wrote:

>>> As long as the endsegments are infinite,
>>> the intersection is infinite too.
>>
>> Actually, the intersection of (the set of) all endsegments
>> is empty.
>
> Actually it is the minimum endsegment.
> If all endsegments are infinite,

If all end segments are infinite,
then each end segment is followed by at least one end segment.

Therefore,
if all end segments are infinite,
then there is no last end segment.

If the intersection of all end segments is an end segment,
then there is a last end segment.

If there is no last end segment.
then the intersection of all end segments is not an end segment,

Therefore,
if all end segments are infinite,
then the intersection of all end segments is not an end segment.

The intersection of closed upwards sets is closed upwards.

The intersection of all end segments (which are closed upwards) is
either an end segment (if it's not empty),
or the empty set (if it's empty).

If all end segments are infinite,
then the intersection of all end segments is
either an end segment or the empty set, and is not an end segment.

Therefore,
if all end segments are infinite,
then the intersection of all end segments is the empty set.

> If all endsegments are infinite,
> the minimum endsegment is infinite too.

If all end segments are infinite,
then the intersection of all end segments is the empty set.

On Friday, September 10, 2021 at 3:19:39 PM UTC-7, Greg C wrote:

If you wouldn't mind moderating your language,
there are polite people present.

Not that you must count yourself among them....

Otherwise it's like one of those crazy cat or dog people
screeching at their animal and making everybody disgusted.

(And there's nothing anybody needs from your help to
refute the little troll Muckenheim.)

Christ, where's Virgil when he'd be better.

(Anonymity turns some people into the crude.)

It's like a bum yelling at a fire hydrant.

Anyways if you ever wonder whether the number theory
has that there's a point at infinity and a fixed point and
otherwise that there's a usual notion that N is compact: it's so.

A usual fact what troll-kickers are usually bereft of....

I.e., I can usually write whatever WM says in much stronger terms,
and, if you wonder why topology put (countable) ultrafilters atop
a means for countable saturation in a topos over the uncountable,
it's an end-run about what otherwise would only be a sticking point.

On Friday, September 10, 2021 at 5:35:51 PM UTC-3, WM wrote:
> William schrieb am Freitag, 10. September 2021 um 20:19:16 UTC+2:
> > On Friday, September 10, 2021 at 1:26:12 PM UTC-3, WM wrote:
> > > William schrieb am Freitag, 10. September 2021 um 16:47:24 UTC+2:
> > > > On Friday, September 10, 2021 at 10:18:07 AM UTC-3, WM wrote:
> > > > > William schrieb am Donnerstag, 9. September 2021 um 15:46:00 UTC+2:
> > > > > > On Thursday, September 9, 2021 at 10:09:49 AM UTC-3, WM wrote:
> > > > > > > No [single element of the sequence] can cause a finite intersection
> > > > > >
> > > > > > True. A finite intersection is a property of the sequence, not a property of an element of the sequence.
> > > > > The sequence is inclusion monotonic. Therefore its intersection cannot be empty if no endsegment is empty.
> > > > No, the intersection, a property of the sequence, cannot be empty if no endsegment is empty and there is a last endsegment.
> > > >
> > > The latter clause is irrelevant. As long as the endsegments are infinite, the intersection is infinite too.
> > Indeed. "As long" , so for every finite initial subsequence of the sequence, the intersection is not empty. However, we are considering a property, not of every finite initial subsequence, but a property of the sequence.
> [The endless sequence] consist of only finite initial subsequences.

An endless sequence consists of an infinite number of finite sequences. An infinite sequence has properties that no finite sequence has.

You are fond of the argument:

every finite initial sequence of X has property Y.
I can construct X from an infinite number of finite intitial sequences.
X has property Y

Too bad it is a load of dingo kidneys

--
William Hughes

On Saturday, September 11, 2021 at 1:43:09 AM UTC+2, Ross A. Finlayson wrote:
> On Friday, September 10, 2021 at 3:19:39 PM UTC-7, Greg C wrote:

I'm glad, you are doing fine these days, Ross. A clear and crisp message. :-)

On Friday, September 10, 2021 at 6:01:01 PM UTC-7, Greg Cunt wrote:
> On Saturday, September 11, 2021 at 1:43:09 AM UTC+2, Ross A. Finlayson wrote:
> > On Friday, September 10, 2021 at 3:19:39 PM UTC-7, Greg C wrote:
> I'm glad, you are doing fine these days, Ross. A clear and crisp message. :-)

Why that's kind as thing as one might note, if trivial or wrong.

Thank you so much for speaking and reading in English,
though it might not be your first language.

If you bother to read the charter, it's a part of the charter
that usually the e-mail or real identity of the person, is
what posts to usenet.

Also just as I must ask, speaking English and including for
example having a computer to look up words, Greg, I can't
help but notice that your name Greg C*** collides with the
Eniglish word, C***, that disgusts half the people and disgusts
the other half from disgusting the first half, that you might
put a fair note "here's the clan crest and family and line of C***",
helping to dismabiguate the poor reader not knowing the
language of "though I post through Google Groups and my
identity is opaque, and I used to post as 'me' to confuse people,
really perhaps it was because my real name is a source of offense".

So, I kind of appreciate your sentiment, I do, I appreciate your sentiment.
Please pick a new name if you're not using your real one, unless you don't
know enough English to really understand that what you are doing is wrong.

Or share us, please, let's see, what English names are bad words,
Smythe? No, ..., Gibbons? Uh, ... Ponfrey?

C***?

Cook?

Of course, in any language, any bad words, there is another language,
where the word is a word, not a bad word, and, somebody's name.

Here though everybody knows enough English to know the seven banned words.

Good luck meeting mister right, Frank Cook.

Bonne chance!

Of course these are not bad words....

Well, then, thanks Greg C., I hope that helps clear this up.

On Thursday, August 26, 2021 at 7:12:25 AM UTC-7, Serg io wrote:
> On 8/26/2021 7:54 AM, WM wrote:
> > Greg Cunt schrieb am Mittwoch, 25. August 2021 um 23:42:58 UTC+2:
> >> On Wednesday, August 25, 2021 at 10:42:20 PM UTC+2, WM wrote:
> >>> William schrieb am Mittwoch, 25. August 2021 um 14:54:01 UTC+2:
> >>>> On Wednesday, August 25, 2021 at 9:26:53 AM UTC-3, WM wrote:
> >>>>>
> >>>>> What about the first unit fraction when starting from 0?
> >>>>>
> >>>> This does not exist.
> >>>>
> >>> What about the first that exists?
> >> Holy shit!
> >
> > Does none exist?
> >
> > Regards, WM
> >
> none exist.
>
> proof;
>
> 1. assume k is the first unit fraction in [0,1]
>
> 2. however k/2 is closer to 0, therfore now first
>
> 3. Assumption is proven false.
>
> 4 there is no number that is "first" unit fraction.

This is an example framed for example "iota-sums",
instead of "iota-multiples", that "first unit fractions exist",
or don't, that the multiple unit fractions make the unit,
usually it's accumulated under the function in "iota-multiples",
from least to last all of them the one, while, it's "iota-sums",
that don't accumulate. However, under a framework for example
where it is only being held up, under the case otherwise after sums,
is an example of the maintenance of the arithmetic, of the iota-values,
where usually iota-multiples is the mode of either the multiplication
or the summation that add up to one, as for whether in the algebra
what models it, for example either one or the other has the simple bound.

This is the simple way iota-sums, infinitely-many, and iota-multiples, times infinity,
make for a writing of infinitesimals with arithmetic the operations "+" and "*".

In summary....

Greg Cunt schrieb am Freitag, 10. September 2021 um 22:57:57 UTC+2:
> On Friday, September 10, 2021 at 10:29:35 PM UTC+2, WM wrote:

> > > > stepwise loss ∀k ∈ ℕ: E(k+1) = E(k) \ {k}..
> > it is the definition of the endsegments.
> "it"? What?

See first line above.

> | If the intersection is not infinite, then there must be a first infinite endsegment with finite intersection because
> | of stepwise loss ∀k ∈ ℕ: E(k+1) = E(k) \ {k}
> ?
>
> Well, little wonder. Since the claim is false.

The claim is the definition of endsegments. If you cannot accept it, then you have in mind other objects which you erroneously denote as endsegments.
>
Regards, WM

Jim Burns schrieb am Samstag, 11. September 2021 um 00:51:17 UTC+2:

> if all end segments are infinite,
> then there is no last end segment.

Then there is an infinite set of natural nunbers remaining in all endsegments forever. This is an infinite intersection.

Regards, WM

WM pretended :
> Greg Cunt schrieb am Freitag, 10. September 2021 um 22:57:57 UTC+2:
>> On Friday, September 10, 2021 at 10:29:35 PM UTC+2, WM wrote:
>
>>>>> stepwise loss ∀k ∈ ℕ: E(k+1) = E(k) \ {k}.
>>> it is the definition of the endsegments.
>> "it"? What?
>
> See first line above.
>
>>> If the intersection is not infinite, then there must be a first infinite
>>> endsegment with finite intersection because of stepwise loss ∀k ∈ ℕ:
>>> E(k+1) = E(k) \ {k}
>> ?
>>
>> Well, little wonder. Since the claim is false.
>
> The claim is the definition of endsegments. If you cannot accept it, then you
> have in mind other objects which you erroneously denote as endsegments.

Where in the definition is the 'stepwise' part necessary? It is just
your mental block again.

*ALL* k in N have FISONs ending with k and infinite endsegments
starting with k + 1 -- there is no need to add a stepwise character to
the mental process of considering *ALL* of something.

William schrieb am Samstag, 11. September 2021 um 02:18:54 UTC+2:
> On Friday, September 10, 2021 at 5:35:51 PM UTC-3, WM wrote:
> > William schrieb am Freitag, 10. September 2021 um 20:19:16 UTC+2:

> > [The endless sequence] consist of only finite initial subsequences.
>
> An endless sequence consists of an infinite number of finite sequences. An infinite sequence has properties that no finite sequence has.
>
> You are fond of the argument:

Every infinite endsegment has an infinite intersection with all its predecessors. If the infinite sequence has only infinite endsegments, then this cannot change and does not change.

If you claim that a sequence of only infinite endsegments has an empty intersection, then this is nonsense and not useful to continue this discussion. It is enough for me to have forced you matheologians to make nonsense claims.

Regards, WM

On 9/10/2021 3:36 PM, WM wrote:
> Greg Cunt schrieb am Freitag, 10. September 2021 um 19:00:59 UTC+2:
>> On Friday, September 10, 2021 at 6:52:16 PM UTC+2, WM wrote:
>>> Greg Cunt schrieb am Freitag, 10. September 2021 um 18:49:34 UTC+2:
>>>> On Friday, September 10, 2021 at 6:26:12 PM UTC+2, WM wrote:
>>>>>
>>>>> As long as the endsegments are infinite, the intersection is infinite too.
>>>>>
>>>> Actually, the intersection of (the set of) all endsegments is empty.
>>>>
>>> Actually it is the minimum endsegment.
>> The MINIMAL ENDSEGMENT??? Huh???!!!
>>
>> There IS NO MINIMAL ENDSEGMENT,
>
> If all endsegments have card aleph_0, then all are minimal.
>
>> Hint: For all n e IN: E(n+1) c E(n) & E(n+1) =/= E(n).
>
> Hint cardinality is same.
>
> Regards, WM
>

NEW ONES !!!

Minimal Ants
Minimal Ants of the empty endsegment

Minimal Ants that hint cardinality

On 9/10/2021 5:19 PM, Greg Cunt wrote:
> On Friday, September 10, 2021 at 10:37:04 PM UTC+2, WM wrote:
>> Greg Cunt schrieb am Freitag, 10. September 2021 um 19:00:59 UTC+2:
>>> On Friday, September 10, 2021 at 6:52:16 PM UTC+2, WM wrote:
>>>> Greg Cunt schrieb am Freitag, 10. September 2021 um 18:49:34 UTC+2:
>
> A simple an trivial fact (outside of crank town):
>
>>>>> The intersection of (the set of) all endsegments is empty.
>>>>>
>>>> Actually it is the minimum endsegment.
>>>>
>>> The MINIMAL ENDSEGMENT??? Huh???!!!
>>>
>>> There IS NO MINIMAL ENDSEGMENT,
>>>
>> If all endsegments have card aleph_0, then all are minimal.
>
> LOOK, YOU FUCKING IDIOT, if you are (just) referring to the cardinal numbers of the end segments, then the endsegements are NOT ORDERED (this way). Hence talking about "minimal" endsegments is NONSENSE in this case.
>
> Hint: The definition E <= E' :<-> card(E) <= card(E') DOESN'T define an order on the set of endsegments.
>
>>> Hint: For all n e IN: E(n+1) c E(n) & E(n+1) =/= E(n).
>
> The ORDER we consider in this context AND *YOU* ARE REFERRING TO with your "inclusion monotony" mantra is given by THE SUBSET-RELATION.
>
> Hence THERE'S NO (c-)MINIMAL endsegment, you silly asshole!
>
> FUCK YOU, Mucke!
>

Excluded inclusion monotony Ants

Ross A. Finlayson wrote:

> On Thursday, August 26, 2021 at 7:12:25 AM UTC-7, Serg io wrote:
>> 4 there is no number that is "first" unit fraction.
>
> This is an example framed for example "iota-sums",
> instead of "iota-multiples", that "first unit fractions exist", or
> don't, that the multiple unit fractions make the unit, usually it's
> accumulated under the function in "iota-multiples",

biden, "we need to protect the vaccinated from the unvaccinated".

*boooong!!*

On 9/10/2021 5:51 PM, Jim Burns wrote:
> On 9/10/2021 12:52 PM, WM wrote:
>> Greg Cunt schrieb
>> am Freitag, 10. September 2021 um 18:49:34 UTC+2:
>>> On Friday, September 10, 2021 at 6:26:12 PM UTC+2,
>>> WM wrote:
>
>>>> As long as the endsegments are infinite,
>>>> the intersection is infinite too.
>>>
>>> Actually, the intersection of (the set of) all endsegments
>>> is empty.
>>
>> Actually it is the minimum endsegment.
>> If all endsegments are infinite,
>
> If all end segments are infinite,
> then each end segment is followed by at least one end segment.

yes and yes

>
> Therefore,
> if all end segments are infinite,
> then there is no last end segment.

agree

>
>
> If the intersection of all end segments is an end segment,
> then there is a last end segment.

why would the intersection be an end segment ?

there is no last endsegment.

>
> If there is no last end segment.
> then the intersection of all end segments is not an end segment,

provide a showing or proof.
(ez to prove it is empty)

>
> Therefore,
> if all end segments are infinite,
> then the intersection of all end segments is not an end segment.

you skip a step, show the intersection is empty, then show it cannot be an endsegment.

>
>
> The intersection of closed upwards sets is closed upwards.
>
> The intersection of all end segments (which are closed upwards) is
> either an end segment (if it's not empty),
> or the empty set (if it's empty).
>
> If all end segments are infinite,
> then the intersection of all end segments is
> either an end segment or the empty set, and is not an end segment.
>
> Therefore,
> if all end segments are infinite,
> then the intersection of all end segments is the empty set.
>
>> If all endsegments are infinite,
>> the minimum endsegment is infinite too.
>
> If all end segments are infinite,
> then the intersection of all end segments is the empty set.
>

On 9/11/2021 8:05 AM, WM wrote:
> Jim Burns schrieb am Samstag, 11. September 2021 um 00:51:17 UTC+2:
>
>
>> if all end segments are infinite,
>> then there is no last end segment.
>
> Then there is an infinite set of natural nunbers remaining in all endsegments forever. This is an infinite intersection.
>
> Regards, WM
>

Wrong on the intersection again.

On 9/11/2021 8:55 AM, Loy Gue wrote:
> Ross A. Finlayson wrote:
>
>> On Thursday, August 26, 2021 at 7:12:25 AM UTC-7, Serg io wrote:
>>> 4 there is no number that is "first" unit fraction.
>>
>> This is an example framed for example "iota-sums",
>> instead of "iota-multiples", that "first unit fractions exist", or
>> don't, that the multiple unit fractions make the unit, usually it's
>> accumulated under the function in "iota-multiples",
>
> biden, "we need to protect the vaccinated from the unvaccinated".
>
> *boooong!!*
>

Joe Biden the Fuck-Up.