On Thursday, 25 August 2022 at 13:17:05 UTC+1, skepd...@gmail.com wrote:
> On Thursday, 25 August 2022 at 13:51:27 UTC+2, Ben Bacarisse wrote:
> > The infinite sequence of symbols is not in doubt. Even wij has said as
> > much. The question is why everyone with an oh-so-clever alternative
> > meaning won't say more than this trivial remark about the symbols. What
> > are the rules the govern arithmetic with these sequences? Or, if you
> > can't do arithmetic with them, what /can/ be done with them?
> I don't understand your question - it's too vague/imprecise.
>
We've got the sequence 0.999... with the nines going on forever.
Now we double it. So obviously we obtain
1.999... followed by an 8? Or do we say that since the 9s go on forever,
the 8 never exists?
There's not necessarily a "right" answer. It depends which relationships you
wish to preseve with your rules for arithetic, and which you are prepared to
sacrifice.

On Thursday, 25 August 2022 at 13:41:35 UTC+2, richar...@gmail.com wrote:
> > https://en.wikipedia.org/wiki/Universe_(mathematics)
> But, at least in general, the Part is not the Whole.
No idea what that implies.

> Also, in general, Rules don't need "Precedence", that only needs to come
> if they have special interactions.
>
> For instance, the Rules:
>
> x + 0 == x
That's not a rule. That's a proposition. And I have no idea whether you mean x + (0 == x) OR (x + 0) == (x)

> x * 1 == x
That's also a proposition. And I have no idea whether you mean x * (1 == x) OR (x * 1) == (x)

> Have no need to be ordered. Yes, we have a rule that says if not
> otherwise indicated (typeically by parenthesis) and we have a multply
> operation and an addition operation, like x * y + z, we interprete that
> as wanting to do the multiply first, but that is in a different type of
> rule.
Fucking shit-for-brains idiot.

BODMAS doesn't tell you the precedence of ==

Is it EBODMAS ?
Is it BEODMAS ?
Is it BOEDMAS ?
Is it BODMEAS ?
Is it BODMAES ?
Is it BODMASE ?

On Thursday, 25 August 2022 at 13:41:35 UTC+2, richar...@gmail.com wrote:
> On 8/25/22 3:39 AM, Skep Dick wrote:
> >>> One question a time. You don't realize you are asking for the rule of the universe.
> >> The Reals (aka The Real Numbers) are NOT "The Universe".
> > Shit for brains. The Reals are IN a Universe.
> >
> > Your Universe has objects. Some of those objects are Rules. And one particular object must be your Rule Precedence Rule: THE rule which determines rule precedence.
> >
> > https://en.wikipedia.org/wiki/Universe_(mathematics)
> But, at least in general, the Part is not the Whole.
>
> Also, in general, Rules don't need "Precedence", that only needs to come
> if they have special interactions.
>
> For instance, the Rules:
>
> x + 0 == x
>
> and
>
> x * 1 == x
>
>
> Have no need to be ordered. Yes, we have a rule that says if not
> otherwise indicated (typeically by parenthesis) and we have a multply
> operation and an addition operation, like x * y + z, we interprete that
> as wanting to do the multiply first, but that is in a different type of
> rule.
Here you go, shit-for-brains...

def values(x):
return {
'x + (0 == x)': x + (0 == x),
'(x + 0) == (x)' : (x + 0) == (x),
'x * (1 == 0)' : x * (1 == 0),
'(x * 1) == 0': (x * 1) == 0
}

In [2]: values(0)
Out[2]:
{'x + (0 == x)': 1,
'(x + 0) == (x)': True,
'x * (1 == 0)': 0,
'(x * 1) == 0': True}

In [3]: values(1)
Out[3]:
{'x + (0 == x)': 1,
'(x + 0) == (x)': True,
'x * (1 == 0)': 0,
'(x * 1) == 0': False}

In [4]: values(2)
Out[4]:
{'x + (0 == x)': 2,
'(x + 0) == (x)': True,
'x * (1 == 0)': 0,
'(x * 1) == 0': False}

In [5]: values(3)
Out[5]:
{'x + (0 == x)': 3,
'(x + 0) == (x)': True,
'x * (1 == 0)': 0,
'(x * 1) == 0': False}

Skep Dick <skepdick22@gmail.com> writes:

> On Thursday, 25 August 2022 at 13:51:27 UTC+2, Ben Bacarisse wrote:
>> The infinite sequence of symbols is not in doubt. Even wij has said as
>> much. The question is why everyone with an oh-so-clever alternative
>> meaning won't say more than this trivial remark about the symbols. What
>> are the rules the govern arithmetic with these sequences? Or, if you
>> can't do arithmetic with them, what /can/ be done with them?
>
> I don't understand your question - it's too vague/imprecise.

Can you are least answer the question you asked me? Or was that just
for show?

> Can you formalize it?
>
>> Indeed. Why won't you say? I think wij is hoping that someone else
>> will come up with the meaning he imagines, but it seems even you won't
>> help him or her out.
> Ditto.

Despite your deceptive editing, most readers will remember that this was
your question, not mine.

--
Ben.

On Thursday, 25 August 2022 at 18:07:27 UTC+2, Ben Bacarisse wrote:
> Skep Dick <skepd...@gmail.com> writes:
>
> > On Thursday, 25 August 2022 at 13:51:27 UTC+2, Ben Bacarisse wrote:
> >> The infinite sequence of symbols is not in doubt. Even wij has said as
> >> much. The question is why everyone with an oh-so-clever alternative
> >> meaning won't say more than this trivial remark about the symbols. What
> >> are the rules the govern arithmetic with these sequences? Or, if you
> >> can't do arithmetic with them, what /can/ be done with them?
> >
> > I don't understand your question - it's too vague/imprecise.
> Can you are least answer the question you asked me? Or was that just
> for show?
> > Can you formalize it?
> >
> >> Indeed. Why won't you say? I think wij is hoping that someone else
> >> will come up with the meaning he imagines, but it seems even you won't
> >> help him or her out.
> > Ditto.
> Despite your deceptive editing, most readers will remember that this was
> your question, not mine.

Despite your accusation of deception, most readers might bother to actually read back and see that it wasn't my question...

Here is my post:

> Of course I know what I mean when I write "...".
>I mean the exact thing that everyone means - an infinite sequence off the symbol preceding "...".
> x = 0.999...
> 999... * x = 999.... * 0.999...
> Now what?

It contains TWO questions (for those who can't tell the difference between judgmental and propositional equality)

First QUESTION: 999... * x = 999.... * 0.999...
Second QUESTION: Now what?

But perhaps it shall become clearer to you... Is the TYPE x = (999.... * 0.999...)/999... " inhabited ?

Skep Dick <skepdick22@gmail.com> writes:

> On Thursday, 25 August 2022 at 18:07:27 UTC+2, Ben Bacarisse wrote:
>> Skep Dick <skepd...@gmail.com> writes:
>>
>> > On Thursday, 25 August 2022 at 13:51:27 UTC+2, Ben Bacarisse wrote:
>> >> The infinite sequence of symbols is not in doubt. Even wij has said as
>> >> much. The question is why everyone with an oh-so-clever alternative
>> >> meaning won't say more than this trivial remark about the symbols. What
>> >> are the rules the govern arithmetic with these sequences? Or, if you
>> >> can't do arithmetic with them, what /can/ be done with them?
>> >
>> > I don't understand your question - it's too vague/imprecise.
>> Can you are least answer the question you asked me? Or was that just
>> for show?
>> > Can you formalize it?
>> >
>> >> Indeed. Why won't you say? I think wij is hoping that someone else
>> >> will come up with the meaning he imagines, but it seems even you won't
>> >> help him or her out.
>> > Ditto.
>> Despite your deceptive editing, most readers will remember that this was
>> your question, not mine.
>
> Despite your accusation of deception, most readers might bother to
> actually read back and see that it wasn't my question...
>
> Here is my post:
>
>> Of course I know what I mean when I write "...".
>>I mean the exact thing that everyone means - an infinite sequence off the symbol preceding "...".
>> x = 0.999...
>> 999... * x = 999.... * 0.999...
>> Now what?
>
> It contains TWO questions (for those who can't tell the difference
> between judgmental and propositional equality)

English has marker to distinguish between the two.

> First QUESTION: 999... * x = 999.... * 0.999...
> Second QUESTION: Now what?

So, will you answer it? And if not, why not?

> But perhaps it shall become clearer to you... Is the TYPE x =
> (999.... * 0.999...)/999... " inhabited ?

I don't understand your question - it's too vague/imprecise. Can you
formalize it?

--
Ben.

On Thursday, 25 August 2022 at 18:21:52 UTC+2, Ben Bacarisse wrote:
> Skep Dick <skepd...@gmail.com> writes:
> English has marker to distinguish between the two.
Indeed! But Mathematics doesn't. A total faux-pas on behalf of Mathematicians.

> So, will you answer it? And if not, why not?
Because it's undecidable! Exactly like the question x = x.

The value of that expression is whatever the decision-procedure decides it is.

> I don't understand your question - it's too vague/imprecise. Can you
> formalize it?
At this point I am not really sure formalization will help us out of this mess...

You think "x=x" is a statement, not a question.

On Tuesday, 23 August 2022 at 07:27:20 UTC+2, wyni...@gmail.com wrote:

> Intuitively, SumOfEvenNum = Σ(n=0,∞) 2*n

As others have pointed out, (in standard mathematics)
'oo' is *not* a number, and the above is not "intuitive" but
rather an abbreviation for the mathematical definition
which is (using ASCII):

Sum_{n=0}^oo f(n) := Lim_{N->oo} Sum_{n=0}^N f(n).

The same goes with the notation for infinite unions
and intersections, and similar: where you see 'oo' that
is an abbreviation for some limit.

> If ∞ is some kind of whole number, Is ∞ an even number?

As said, standardly 'oo' indeed is not a number, just a
short-hand for taking a limit, or the result of taking a
limit where the limit diverges, as in lim_{n->oo} n = oo.

HTH,

Julio

On 8/25/2022 11:49 AM, Julio Di Egidio wrote:
> On Tuesday, 23 August 2022 at 07:27:20 UTC+2, wyni...@gmail.com wrote:
>
>> Intuitively, SumOfEvenNum = Σ(n=0,∞) 2*n
>
> As others have pointed out, (in standard mathematics)
> 'oo' is *not* a number, and the above is not "intuitive" but
> rather an abbreviation for the mathematical definition
> which is (using ASCII):
>
> Sum_{n=0}^oo f(n) := Lim_{N->oo} Sum_{n=0}^N f(n).
>
> The same goes with the notation for infinite unions
> and intersections, and similar: where you see 'oo' that
> is an abbreviation for some limit.
>
>> If ∞ is some kind of whole number, Is ∞ an even number?
>
> As said, standardly 'oo' indeed is not a number, just a
> short-hand for taking a limit, or the result of taking a
> limit where the limit diverges, as in lim_{n->oo} n = oo.
I think that if you use a standard epsilon/delta definition of limit,
you will find that, in the case you discuss above, there isn't a limit.
Note that I said using the standard definition. Do you have some
alternate definition of limit and/or the notation you used?
--
Jeff Barnett

On Thursday, 25 August 2022 at 21:38:19 UTC+2, Jeff Barnett wrote:
> On 8/25/2022 11:49 AM, Julio Di Egidio wrote:
> > On Tuesday, 23 August 2022 at 07:27:20 UTC+2, wyni...@gmail.com wrote:
> >
> >> Intuitively, SumOfEvenNum = Σ(n=0,∞) 2*n
> >
> > As others have pointed out, (in standard mathematics)
> > 'oo' is *not* a number, and the above is not "intuitive" but
> > rather an abbreviation for the mathematical definition
> > which is (using ASCII):
> >
> > Sum_{n=0}^oo f(n) := Lim_{N->oo} Sum_{n=0}^N f(n).
> >
> > The same goes with the notation for infinite unions
> > and intersections, and similar: where you see 'oo' that
> > is an abbreviation for some limit.
> >
> >> If ∞ is some kind of whole number, Is ∞ an even number?
> >
> > As said, standardly 'oo' indeed is not a number, just a
> > short-hand for taking a limit, or the result of taking a
> > limit where the limit diverges, as in lim_{n->oo} n = oo.
>
> I think that if you use a standard epsilon/delta definition of limit,
> you will find that, in the case you discuss above, there isn't a limit.
> Note that I said using the standard definition. Do you have some
> alternate definition of limit and/or the notation you used?

You and your gang of retarded cunts just talk nonsense.

Stop spamming the Usenet, go to the fucking pub...

*Plonk*

Julio

Julio Di Egidio <julio@diegidio.name> writes:

> You and your gang of retarded cunts just talk nonsense.
>
> Stop spamming the Usenet, go to the fucking pub...

Ah, there it is! I thought for a moment someone was impersonating you.

--
Ben.

On Thursday, 25 August 2022 at 22:36:34 UTC+2, Ben Bacarisse wrote:
> Julio Di Egidio <ju...@diegidio.name> writes:
>
> > You and your gang of retarded cunts just talk nonsense.
> >
> > Stop spamming the Usenet, go to the fucking pub...
>
> Ah, there it is! I thought for a moment someone was impersonating you.

Your retarded bullshit and lies instead will never change.

ESAD, you and the whole indecent band-wagon.

*Plonk*

Julio

On Thursday, 25 August 2022 at 19:49:56 UTC+2, Julio Di Egidio wrote:
> On Tuesday, 23 August 2022 at 07:27:20 UTC+2, wyni...@gmail.com wrote:
>
> > Intuitively, SumOfEvenNum = Σ(n=0,∞) 2*n
> As others have pointed out, (in standard mathematics)
> 'oo' is *not* a number, and the above is not "intuitive" but
> rather an abbreviation for the mathematical definition
> which is (using ASCII):
>
> Sum_{n=0}^oo f(n) := Lim_{N->oo} Sum_{n=0}^N f(n).
>
> The same goes with the notation for infinite unions
> and intersections, and similar: where you see 'oo' that
> is an abbreviation for some limit.
>
> > If ∞ is some kind of whole number, Is ∞ an even number?
>
> As said, standardly 'oo' indeed is not a number, just a
> short-hand for taking a limit, or the result of taking a
> limit where the limit diverges, as in lim_{n->oo} n = oo.

Up. Fuckers...

Julio

On 8/25/2022 2:36 PM, Ben Bacarisse wrote:
> Julio Di Egidio <julio@diegidio.name> writes:
>
>> You and your gang of retarded cunts just talk nonsense.
>>
>> Stop spamming the Usenet, go to the fucking pub...
>
> Ah, there it is! I thought for a moment someone was impersonating you.

I think we may be talking to a badly written script; certainly not a
rational being. Think of Eliza with "plonk" and so on randomly inserted
into the response patterns. There's nothing in the responses that shows
any grasp of what it's responding to. Eliza had a built in move the the
"Julio" agent was developed without: in addition to forming an immediate
response such as "how does the rest of the family feel" keyed off a word
like aunt, it could later take a response such as "how does your aunt
have to say" and randomly toss it out. It gave the eerie feeling of
sentience in the agent and that's what's missing here.
--
Jeff Barnett

Jeff Barnett <jbb@notatt.com> writes:

> On 8/25/2022 2:36 PM, Ben Bacarisse wrote:
>> Julio Di Egidio <julio@diegidio.name> writes:
>>
>>> You and your gang of retarded cunts just talk nonsense.
>>>
>>> Stop spamming the Usenet, go to the fucking pub...
>> Ah, there it is! I thought for a moment someone was impersonating you.
>
> I think we may be talking to a badly written script; certainly not a
> rational being. Think of Eliza with "plonk" and so on randomly
> inserted into the response patterns. There's nothing in the responses
> that shows any grasp of what it's responding to.

Actually, I have had interesting technical exchanges with JDE. He is
knowledgeable about (at least) EcmaScript and Prolog, but even then it
only took a message or two for the expletives and the sadly rhetorical
plonk to surface.

--
Ben.

Julio Di Egidio <julio@diegidio.name> writes:
> On Thursday, 25 August 2022 at 22:36:34 UTC+2, Ben Bacarisse wrote:
>> Julio Di Egidio <ju...@diegidio.name> writes:
>>
>> > You and your gang of retarded cunts just talk nonsense.
>> >
>> > Stop spamming the Usenet, go to the fucking pub...
>>
>> Ah, there it is! I thought for a moment someone was impersonating you.
>
> Your retarded bullshit and lies instead will never change.
>
> ESAD, you and the whole indecent band-wagon.
>
> *Plonk*
>
> Julio

Thanking you for making it clear so quickly and emphatically that I
never need to pay attention to you.

--
Keith Thompson (The_Other_Keith) Keith.S.Thompson+u@gmail.com
Working, but not speaking, for Philips
void Void(void) { Void(); } /* The recursive call of the void */

On Friday, 26 August 2022 at 00:04:21 UTC+2, Keith Thompson wrote:
> Julio Di Egidio <ju...@diegidio.name> writes:
> > On Thursday, 25 August 2022 at 22:36:34 UTC+2, Ben Bacarisse wrote:
> >> Julio Di Egidio <ju...@diegidio.name> writes:
> >>
> >> > You and your gang of retarded cunts just talk nonsense.
> >> >
> >> > Stop spamming the Usenet, go to the fucking pub...
> >>
> >> Ah, there it is! I thought for a moment someone was impersonating you.
> >
> > Your retarded bullshit and lies instead will never change.
> >
> > ESAD, you and the whole indecent band-wagon.
> >
> > *Plonk*
> >
> > Julio
> Thanking you for making it clear so quickly and emphatically that I
> never need to pay attention to you.

Look, you aren't worth much paying-attention-to either, but you never seem to indicate that overtly.

If anything - you are an ass for making other people having to spend time figuring it out.

On Thursday, 25 August 2022 at 19:49:56 UTC+2, Julio Di Egidio wrote:
> On Tuesday, 23 August 2022 at 07:27:20 UTC+2, wyni...@gmail.com wrote:
>
> > Intuitively, SumOfEvenNum = Σ(n=0,∞) 2*n
> As others have pointed out, (in standard mathematics)
> 'oo' is *not* a number, and the above is not "intuitive" but
> rather an abbreviation for the mathematical definition
> which is (using ASCII):
>
> Sum_{n=0}^oo f(n) := Lim_{N->oo} Sum_{n=0}^N f(n).
>
> The same goes with the notation for infinite unions
> and intersections, and similar: where you see 'oo' that
> is an abbreviation for some limit.
>
> > If ∞ is some kind of whole number, Is ∞ an even number?
>
> As said, standardly 'oo' indeed is not a number, just a
> short-hand for taking a limit, or the result of taking a
> limit where the limit diverges, as in lim_{n->oo} n = oo.

Up. Fuckers...

Julio

Skep Dick <skepdick22@gmail.com> writes:

> At this point I am not really sure formalization will help us out of
> this mess...

It's your mess. I am quite content with the conventional interpretation
of 0.999... You, I think, don't want to agree that 0.999... = 1 but you
can't say anything useful about what else it might mean. All you've
done in fire questions at me as if I should be able to tell you what you
mean.

--
Ben.

On Friday, 26 August 2022 at 02:16:18 UTC+2, Ben Bacarisse wrote:
> Skep Dick <skepd...@gmail.com> writes:
>
> > At this point I am not really sure formalization will help us out of
> > this mess...
> It's your mess. I am quite content with the conventional interpretation
> of 0.999... You, I think, don't want to agree that 0.999... = 1 but you
> can't say anything useful about what else it might mean. All you've
> done in fire questions at me as if I should be able to tell you what you
> mean.
What is it that you don't understand about expressions of the form "x = y".

In the most pedestrian understanding (Clasical logic) such expressions could mean true; or they could mean false.

And so it goes for "0.999... = 1". It could mean true; or it could mean false.

Obviously, I've made it clear that when I say "0.999... = 1" I mean false and when I say "0.999... + ε = 1" I mean true.

Where have I ever asked you to tell me what I mean? I am asking you to tell me what you mean by ""0.999... = 1" !

Skep Dick <skepdick22@gmail.com> writes:

> On Friday, 26 August 2022 at 02:16:18 UTC+2, Ben Bacarisse wrote:
>> Skep Dick <skepd...@gmail.com> writes:
>>
>> > At this point I am not really sure formalization will help us out of
>> > this mess...
>> It's your mess. I am quite content with the conventional interpretation
>> of 0.999... You, I think, don't want to agree that 0.999... = 1 but you
>> can't say anything useful about what else it might mean. All you've
>> done in fire questions at me as if I should be able to tell you what you
>> mean.
>
> What is it that you don't understand about expressions of the form "x = y".
>
> In the most pedestrian understanding (Clasical logic) such expressions
> could mean true; or they could mean false.
>
> And so it goes for "0.999... = 1". It could mean true; or it could
> mean false.
>
> Obviously, I've made it clear that when I say "0.999... = 1" I mean
> false and when I say "0.999... + ε = 1" I mean true.
>
> Where have I ever asked you to tell me what I mean? I am asking you to
> tell me what you mean by ""0.999... = 1" !

Maybe wait until sober before posting?

--
Ben.

On Friday, 26 August 2022 at 02:38:23 UTC+2, Ben Bacarisse wrote:
> Skep Dick <skepd...@gmail.com> writes:
>
> > On Friday, 26 August 2022 at 02:16:18 UTC+2, Ben Bacarisse wrote:
> >> Skep Dick <skepd...@gmail.com> writes:
> >>
> >> > At this point I am not really sure formalization will help us out of
> >> > this mess...
> >> It's your mess. I am quite content with the conventional interpretation
> >> of 0.999... You, I think, don't want to agree that 0.999... = 1 but you
> >> can't say anything useful about what else it might mean. All you've
> >> done in fire questions at me as if I should be able to tell you what you
> >> mean.
> >
> > What is it that you don't understand about expressions of the form "x = y".
> >
> > In the most pedestrian understanding (Clasical logic) such expressions
> > could mean true; or they could mean false.
> >
> > And so it goes for "0.999... = 1". It could mean true; or it could
> > mean false.
> >
> > Obviously, I've made it clear that when I say "0.999... = 1" I mean
> > false and when I say "0.999... + ε = 1" I mean true.
> >
> > Where have I ever asked you to tell me what I mean? I am asking you to
> > tell me what you mean by ""0.999... = 1" !
> Maybe wait until sober before posting?

I am pretty sure that when I sober up I'll ask you exactly the same thing....

Probably because I see "0.999... = 1" as a proposition with an unspecified semantic value and you don't.

Skep Dick <skepdick22@gmail.com> writes:

> On Friday, 26 August 2022 at 02:38:23 UTC+2, Ben Bacarisse wrote:
>> Skep Dick <skepd...@gmail.com> writes:
>>
>> > On Friday, 26 August 2022 at 02:16:18 UTC+2, Ben Bacarisse wrote:
>> >> Skep Dick <skepd...@gmail.com> writes:
>> >>
>> >> > At this point I am not really sure formalization will help us out of
>> >> > this mess...
>> >> It's your mess. I am quite content with the conventional interpretation
>> >> of 0.999... You, I think, don't want to agree that 0.999... = 1 but you
>> >> can't say anything useful about what else it might mean. All you've
>> >> done in fire questions at me as if I should be able to tell you what you
>> >> mean.
>> >
>> > What is it that you don't understand about expressions of the form "x = y".
>> >
>> > In the most pedestrian understanding (Clasical logic) such expressions
>> > could mean true; or they could mean false.
>> >
>> > And so it goes for "0.999... = 1". It could mean true; or it could
>> > mean false.
>> >
>> > Obviously, I've made it clear that when I say "0.999... = 1" I mean
>> > false and when I say "0.999... + ε = 1" I mean true.
>> >
>> > Where have I ever asked you to tell me what I mean? I am asking you to
>> > tell me what you mean by ""0.999... = 1" !
>> Maybe wait until sober before posting?
>
> I am pretty sure that when I sober up I'll ask you exactly the same thing...
>
> Probably because I see "0.999... = 1" as a proposition with an
> unspecified semantic value and you don't.

Maybe tomorrow you will remember why I declined to explain this entirely
conventional piece of notation to you.

--
Ben.

On Friday, 26 August 2022 at 01:49:56 UTC+8, ju...@diegidio.name wrote:
> On Tuesday, 23 August 2022 at 07:27:20 UTC+2, wyni...@gmail.com wrote:
>
> > Intuitively, SumOfEvenNum = Σ(n=0,∞) 2*n
> As others have pointed out, (in standard mathematics)
> 'oo' is *not* a number, and the above is not "intuitive" but
> rather an abbreviation for the mathematical definition
> which is (using ASCII):
>
> Sum_{n=0}^oo f(n) := Lim_{N->oo} Sum_{n=0}^N f(n).
>
> The same goes with the notation for infinite unions
> and intersections, and similar: where you see 'oo' that
> is an abbreviation for some limit.
>
> > If ∞ is some kind of whole number, Is ∞ an even number?
>
> As said, standardly 'oo' indeed is not a number, just a
> short-hand for taking a limit, or the result of taking a
> limit where the limit diverges, as in lim_{n->oo} n = oo.
>
> HTH,
>
> Julio

Read again what you wrote "lim_{n->oo} n = oo"
You said: ...'oo' indeed is not a number, just a short-hand for taking a
limit, or the result of taking a limit where the limit diverges,
That is convenient excuse to refute "oo".

Can you read it backward: "oo = lim_{n->oo} n"? What does this mean?

n approaches c infinitely but never equals to c (this is probably in an older?
definition of limit, people keeps re-phrasing in different ways, but the
essence is no different).
=> the limit of n is c // no problem
=> n=c // very problematic (invalid deduction, actually)

https://groups.google.com/g/comp.theory/c/Px5i7DAd0Vs talked about the
illogic of limit theory and ambiguous use of infinity.

On Friday, 26 August 2022 at 08:16:18 UTC+8, Ben Bacarisse wrote:
> Skep Dick <skepd...@gmail.com> writes:
>
> > At this point I am not really sure formalization will help us out of
> > this mess...
> It's your mess. I am quite content with the conventional interpretation
> of 0.999... You, I think, don't want to agree that 0.999... = 1 but you
> can't say anything useful about what else it might mean. All you've
> done in fire questions at me as if I should be able to tell you what you
> mean.
>
> --
> Ben.

As said. 0.999... or "Repeating decimal" suffer from pattern interpretation problems:
(1) 0.999...= 0.(9) = 0.(99)= 0.(999)
(2) 0.999...= 0.((9)(99)) // Andy Walker provided such interpretation
(3) 1-1/∞= 0.999...
1-2/∞= 0.999...
1-3/2^∞= 0.999...
1-4/10^∞= 0.999...
(4) 0.999...= 0.9 + 0.999 + 0.99 + 0.9999 +...
= 0.4+0.5 + 0.444+0.555 +...
= Σ(n=1,∞) f(n) // this f(n) can be nearly anything and yields different result.

See the snippet [Infinite series] in previous post about re-grouping/
re-arrange issues of infinite series.
(5) More interpretations are possible

Which one does "0.999..." really mean? Note that these expressions eventually
will be translated to procedure/operation of natural numbers and then, physical
entities.

As to possible point of current discussion, a consensus that "Repeating decimal
does not specify a unique entity" should be established.
However, such expressions "1-1/∞" or "1-1/10^∞" or "∑(n=1,∞) 9/10^n" can specify
a unique entity, because elements in these expressions can be defined.

As to whether "1-1/2^∞" and "1-1/10^∞" are equal or not, from the snippet:
Ex3: "0.999..." usual 'repeating decimal' cannot denote a unique number.
Let A= Σ(n=1,∞) 1/2^n = 0.999...
B= Σ(n=1,∞) 9/10^n = 0.999...

Assume A=B
<=> 1-1/2^∞= 1-1/10^∞ // converted from the formula of geometric series
<=> 1/2^∞= 1/10^∞
<=> 5^∞=1
<=> false

Conclusion: A and B denote different numbers. (a physical device computing
the truth value of A=B is a deterministic process, yields false, no way 'equal').