On Thursday, 11 August 2022 at 13:43:10 UTC+2, richar...@gmail.com wrote:
> Which is why you need to be clear what domain you are talking about,
> especially if you are not talking about the domain that people will assume.
I have no way of knowing what "people" will assume. I am not a mind reader.

> That just shows that you believe it is ok to be deceptive by not being
> clear.
If your first conclusion is that I am being 'deceptive'; instead of you being presumptious then I have some really bad news for you.

There's a principle you should study; and learn to apply: https://en.wikipedia.org/wiki/Principle_of_charity

> The number, 0.9999... if not otherwise indicated by context, is a Real
> Number in the Real Number system.
Well, how about you just use a clearer notation!

>To later say you are talking about some other system *R, is just showing you are being deceptive.
See Principle of charity. You really need it.

> Virtually ANY statement can be proven or disproven if you allow it to be
> moved into an arbitrary logic system crafted for that purpose, so
> context is vital for communication.
I know that. It seems like you know that too. Why then are you so outraged by my theorems?

On Thursday, 11 August 2022 at 16:48:28 UTC+2, wyni...@gmail.com wrote:
> The video seems blocked to where I live.
OK... same video on YouTube: https://youtu.be/SoU2ePlqG5M

> I had skimmed a little what so called. "non-standard analysis", I did not like the impression read to me (too artificial).
It's Mathematics - everything is artificial!

There's no beauty here - only utility.

wij <wyniijj2@gmail.com> writes:

> The real number 0.999... is a number roughly
> A[0]=0
> A[n]=(A[n-1]+1)/2

Yes, roughly. Fortunately there is no need for rough analogies as
0.999... has a precise meaning already.

I'm curious... You posted some "proofs" with simple school-level
algebra errors. You ignored the replies. Why? Do you accept that your
algebra was wrong? You can accept that these arguments were wrong
without having to concede the main point.

--
Ben.

On Thursday, 11 August 2022 at 23:46:23 UTC+8, Ben Bacarisse wrote:
> wij <wyni...@gmail.com> writes:
>
> > The real number 0.999... is a number roughly
> > A[0]=0
> > A[n]=(A[n-1]+1)/2
> Yes, roughly. Fortunately there is no need for rough analogies as
> 0.999... has a precise meaning already.
>
> I'm curious... You posted some "proofs" with simple school-level
> algebra errors. You ignored the replies. Why? Do you accept that your
> algebra was wrong? You can accept that these arguments were wrong
> without having to concede the main point.
>
> --
> Ben.

Just point what is wrong. I am glad to know.
No need to show your idiotic 'smart' again and again.

On Thursday, 11 August 2022 at 23:33:05 UTC+8, Skep Dick wrote:
> On Thursday, 11 August 2022 at 16:48:28 UTC+2, wyni...@gmail.com wrote:
> > The video seems blocked to where I live.
> OK... same video on YouTube: https://youtu.be/SoU2ePlqG5M
>
> > I had skimmed a little what so called. "non-standard analysis", I did not like the impression read to me (too artificial).
> It's Mathematics - everything is artificial!
>
> There's no beauty here - only utility.

So, the next question is simplicity. I think my solution is the possibly simple
ones, easy to explain to computers.

wij <wyniijj2@gmail.com> writes:

> On Thursday, 11 August 2022 at 23:46:23 UTC+8, Ben Bacarisse wrote:
>> wij <wyni...@gmail.com> writes:
>>
>> > The real number 0.999... is a number roughly
>> > A[0]=0
>> > A[n]=(A[n-1]+1)/2
>> Yes, roughly. Fortunately there is no need for rough analogies as
>> 0.999... has a precise meaning already.
>>
>> I'm curious... You posted some "proofs" with simple school-level
>> algebra errors. You ignored the replies. Why? Do you accept that your
>> algebra was wrong? You can accept that these arguments were wrong
>> without having to concede the main point.
>>
>> --
>> Ben.
>
> Just point what is wrong. I am glad to know.

Two people pointed out the basic mistakes in the algebra. You ignored
both. I am curious as to why given you now claim that you'd be glad to
know?

I'm not going to go find the post, copy out what you write and then
repeat what I wrote just so you can ignore it again. I just want to
know why you ignored it originally.

--
Ben.

Skep Dick <skepdick22@gmail.com> writes:
> On Thursday, 11 August 2022 at 13:43:10 UTC+2, richar...@gmail.com wrote:
[...]
>> The number, 0.9999... if not otherwise indicated by context, is a Real
>> Number in the Real Number system.
> Well, how about you just use a clearer notation!

What clearer notation would you suggest?

My experience matches Richard's: the notation "0.9999..." refers to a
real number in ℝ unless otherwise specified. I, and most people, find
the existing notation perfectly clear. Anyone who means something else
by "0.9999..." needs to specify what they mean if they want to be
understood.

And since it's a real number in ℝ, the proof that it's equal to 1.0
applies.

Do you *not* assume that "0.9999..." refers to a real number in ℝ when
you see it without some other explanation?

I think most of us here understand and agree that 0.9999... is equal to
1.0 when interpreted in the real numbers, and may or may not be equal to
1.0 in some other system.

--
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 */

Skep Dick <skepdick22@gmail.com> writes:

> On Monday, 8 August 2022 at 15:16:39 UTC+2, Ben Bacarisse wrote:
>> Yes. For example 0.999... = 1/1.
>
> Ok. So it needs saying so I will say it. You are an ass.
>
> Few posts ago (on another thread) you were giving me a lecture about
> functions needing domains/context.

A few words words is not a lecture! In your case, there was no way to
determine the domain, but here there is. Wij is not making claims about
*R. He or she is claiming that "ordinary arithmetic" proves him or her
right.

> Whether 0.999... = 1/1 is a theorem or not absolutely depends on the
> number system. The domain of your symbols.

Yes (though that's a different use of the word). This is, of course,
the point I'm making. If Wij wants to dispute that 0.999... = 1 he or
she must explain what new meaning is being referred to. But cranks
never do that because learning about infinitesimal numbers is too much
work.

> It is a theorem in R.

Indeed.

> It isn’t a theorem in *R

Actually, I think it /is/ a theorem in *R isn't it? It's been a while,
but I remember series like this converge in *R just as the do in R. Is
there anyone here who knows about limits like this in *R (the
hyperreals) and can give the governing theorem? There will be some
convergence criterion theorem. I remember something to do with infinite
hyperinteger sums being approximately zero. Euler's criterion, I
think...

--
Ben.

Skep Dick <skepdick22@gmail.com> writes:

> On Tuesday, 9 August 2022 at 17:15:14 UTC+2, Ben Bacarisse wrote:
>> This is because 0.333... means
>>
>> lim(n->oo) Sum k=1,n (3/10^k)
>
> I notice that you think yourself very skilled in telling other people
> what stuff means.

Thank you (I suppose). It's better when people use agreed meanings.

--
Ben.

On 8/11/22 11:09 AM, wij wrote:
> On Thursday, 11 August 2022 at 19:43:10 UTC+8, richar...@gmail.com wrote:
>> On 8/11/22 4:50 AM, Skep Dick wrote:
>>> On Monday, 8 August 2022 at 15:16:39 UTC+2, Ben Bacarisse wrote:
>>>> Yes. For example 0.999... = 1/1.
>>>
>>> Ok. So it needs saying so I will say it. You are an ass.
>>>
>>> Few posts ago (on another thread) you were giving me a lecture about functions needing domains/context.
>>>
>>> Whether 0.999... = 1/1 is a theorem or not absolutely depends on the number system. The domain of your symbols.
>>>
>>> It is a theorem in R.
>>> It isn’t a theorem in *R
>>>
>>>
>> Which is why you need to be clear what domain you are talking about,
>> especially if you are not talking about the domain that people will assume.
>>
>> That just shows that you believe it is ok to be deceptive by not being
>> clear.
>>
>>
>> The number, 0.9999... if not otherwise indicated by context, is a Real
>> Number in the Real Number system. To later say you are talking about
>> some other system *R, is just showing you are being deceptive.
>>
>> Virtually ANY statement can be proven or disproven if you allow it to be
>> moved into an arbitrary logic system crafted for that purpose, so
>> context is vital for communication.
>
> Definition man, allow me to call you such (another meaning of definition is
> that your understanding stops there, you can't go anything beyond).
> Your R is only valid in 'standard + academic + examination' reinforced environments.
> 'Real number' is actually quite physical and global, in ancient time or present.
> If a theory of 'Real number' does not fit 'what is observed', it gets modified.
> There may be a standard R, like in physics there is a standard model, it is just
> a standardized resolution (AND, still in revision process) among many.
>
> The real number 0.999... is a number roughly
> A[0]=0
> A[n]=(A[n-1]+1)/2
>
> When n goes infinitely large. And it could be 'visualized' in thought logically.
> If possible, it could also be the experimental reality, like the scale marks.

Definitions are Definitions.

The "Real Number System" is a well defined entity, calling anything else
by that name is just a LIE.

If you want to talk about some other number system, go ahead, just use a
proper name for it, and make it clear what you are doing, or you are
being decietful.

The essence of communication is agreed definitions. To use words in a
manner that they are not agreed on, is to not be actually trying to
communicate.

On 8/11/22 11:29 AM, Skep Dick wrote:
> On Thursday, 11 August 2022 at 13:43:10 UTC+2, richar...@gmail.com wrote:
>> Which is why you need to be clear what domain you are talking about,
>> especially if you are not talking about the domain that people will assume.
> I have no way of knowing what "people" will assume. I am not a mind reader.

Then you fail the first step of communication, and thus fail to communicate.

>
>> That just shows that you believe it is ok to be deceptive by not being
>> clear.
> If your first conclusion is that I am being 'deceptive'; instead of you being presumptious then I have some really bad news for you.
>
> There's a principle you should study; and learn to apply: https://en.wikipedia.org/wiki/Principle_of_charity

I gave you charity at first. You then showed that you didn't care, and
just turned abusive.

Since YOU refuse to try to meet others interpretations, you lose the
right to claim yours are special.

You have proved what sort of person you are, and thus have lost the
right to charity.

>
>> The number, 0.9999... if not otherwise indicated by context, is a Real
>> Number in the Real Number system.
> Well, how about you just use a clearer notation!

What clear notation needs to be used? It is presumed that a number that
is written is part of the simplest number system that its representation
needs.

>
>> To later say you are talking about some other system *R, is just showing you are being deceptive.
> See Principle of charity. You really need it.

Maybe YOU need to use it.

>
>> Virtually ANY statement can be proven or disproven if you allow it to be
>> moved into an arbitrary logic system crafted for that purpose, so
>> context is vital for communication.
> I know that. It seems like you know that too. Why then are you so outraged by my theorems?
>
>

Because you refuse to put them into the context of the system they
belong in but claim they are part of a domain that they aren't in.

THAT makes them a LIE.

The fact that you ADMIT that you don't intend of following conventions,
says that nothing you say is apt to actually be meaningful, because you
won't label the system that it actually needs to be understood in.

On 8/11/22 8:41 AM, Skep Dick wrote:
> On Thursday, 11 August 2022 at 13:55:09 UTC+2, richar...@gmail.com wrote:
>> Except that you did it with non-convergent sums, I didn't it with a
>> finite value.
> So what? You did it with an infinite representation.
>
> If you are going to substitute a finite representation with an infinite one it's on you to prove that they are equivalent representations of the object.
>
>> 1/3 is a real
> Why do you say that?
>
> 1/3 ∈ ℚ
> 1/3 ∈ *R
> 1/3 ∈ R
>
> It's whatever you want it to be.
>
>> 1 + 2 + 3 + 4 + 5 .... is not, so you can't apply it there.
> That's a lot of talk what I can and can't do. Where's this rulebook of yours?

The value of 1 + 2 + 3 + 4 + 5 + ... does not result in a value that is
a Real Number.

So, when you are talking about things you SAY are Real Numbers, there is
no such value.

>
> You sure as hell haven't produces anything formal yet!
>
>> It is a well established property of infinite sums that many of the
>> conventional operations only "work" if the sum is in fact, convergent.
>> The thing you run into in your proof is that the your first line we get
>> the value of "infinity" for S.
>
> Which is a perfectly valid thing to do in some number systems.
> Why are you discriminating against those number systems?

Because, until specifically declaired, there are rules to determine the
assumed number system.

>
>
>> The problem is infinity-1 is the same as infinity (at least for some
>> versions of infinity), so everything breaks down.
> Not in my model. Maybe your model is incomplete?

Then your model isn't the Real Number System. If you have redefined
that, then your system just becomes a deception.

>
>> that handle the new values, like infinity, have this annoying problem of
>> losing characteristics that we like to assume we have.
> That's a really easy problem to solve! Stop making stupid assumptions.
>
>

Stop making statement that imply them then. I guess your GOAL is to be
ambiguous, and thus you are speaking deceptions.

You are just full of EGO and lack of concern about others, and thus
putting yourself outside of the community you seem to want to be part of.

On 8/11/22 11:01 AM, wij wrote:
> On Thursday, 11 August 2022 at 17:29:00 UTC+8, Skep Dick wrote:
>> On Tuesday, 9 August 2022 at 02:30:19 UTC+2, richar...@gmail.com wrote:
>>> On 8/8/22 8:27 AM, wij wrote:
>>>> If 0.999... is rational, then:
>>>> 0.999....= p/q (p,q∈ℕ)
>>>> <=> 0.999...*q=p
>>>> If 0.999...∈ℕ, there exist q∈ℕ such that 0.999...*q∈ℕ
>>>> since 0.999... is defined as infinite repeating, and q is finite,
>>>> but 0.999...*q is never finite.
>>>> Conclusion: Repeating decimals are irrational.
>>> Wrong, 9/9 can generate the pattern 0.9999...
>>>
>>> This can be proven by 9 = 3+3+3 and the assocative property thus 9/9 =
>>> (3+3+3)/9 = 3/9 + 3/9 + 3/9 = 0.3333... + 0.3333... + 0.3333... =
>>> 0.9999....
>> Ooooh! The associative property! I know how to abuse that too.
>>
>> S = 1 + 2 + 3 + 4 + 5 ...
>> S = 1 + (2+3+4) + (5+6+7) + (8+9+10)...
>> S-1 = 9 + 18 + 28 ...
>> S-1 = 9(1 + 2 + 3 ...)
>> S-1 = 9S
>> -8S = 1
>> S = -1/8
>> 1+2+3+4+5... = -1/8
>
> I think you should provide a solution to really solve the issue.
>
> My idea of infinity is simple. '∞' denotes a unique number like the i (unit of
> imaginary number).
>
> Definition of ∞:
> 1. ∀n∈ℕ, n<∞
> 2. The multiplicative inverse of ∞ is 1/∞, the additive inverse is -∞
>
> The meaning of ∞ in 'thinking' is merely (a process/procedure) 'never end'.
>
> I think I solved the basic 'paradoxes' of infinite series. The basics is that
> the addend of an infinite series cannot be rearranged.
> Everybody seems to agree this point, but really as did?, or I formalized the idea.
> Snippet from https://sourceforge.net/projects/cscall/files/MisFiles/NumberView-en.txt/download

Yes, you can start to build a number system like this, and in fact there
are a number of them based on slightly different details.

The key is that none of them are "The Real Number System", but an
expansion of it, and when you do this to express the concept of
"infinity" you tend to also lose some of the properties of the Real
Number system. (Which properties you lose depends on details of how you
flesh out the details of this new number).

Note, it takes some work to fully define how your "infinity" works, and
one of the problems is that some (many) definitions turn out to actually
end up with inconsistent systems (which is one of the reasons you lose
some of the normal basic properties, to eliminate those inconsistencies).

>
> +-----------------+
> | Infinite Series |
> +-----------------+
> Series::= S= Σ(n=0,k) a(n)= a(0)+ a(1)+ a(2) +... +a(k)
> a(n) is called the general term, addend, summand. n is referred as the
> index. Series S is the sum from the first term a(0) to the last term a(k).
> The sum of those first terms (n<k) is called the partial sum.
> "a(0)+...+a(k)" is called expanded form.
>
> Infinite Series::= If the series S refers to infinite terms (n=∞), S is called
> an infinite series. Note that there are infinite addend. The sum cannot be
> completed by enumeration (∞ means unreachable, by definition).
>
> In the concept that number-is-an-expression-of-computation, infinite series is
> a number, no such concern of converge/diverge (statement when number converges
> is a number, diverges is not, is self-controdictory). The computaion rule of
> infinite series is based on the expanded form and concepts mentioned above.
> Noteworthy difference is that the interpretation of "..." in the expanded form
> is a "fixed/unique" number of terms, i.e. "∞+1≠∞" (not the notion of Cantor's
> infinite correspondence).
>
> Arithmetic of expanded form:
> Ex1: Let S= Σ(n=0,∞) a^n = 1+a+a^2+...+a^∞)
> S= 1+a*(1+a+a^2+...+a^∞)- a*a^∞
> <=> S= 1+a*S-a^(∞+1)
> <=> S(1-a)=1-a^(∞+1)
> <=> S= (1-a^(∞+1))/(1-a)
>
> Ex2: Let S= Σ(n=1,∞) n = 1+2+3+...+n
> S= 1+2+3+...+n // (1)
> S= n+...+3+2+1 // (2)
> 2S= n*(n+1) // (1)+(2)
> <=> S= n*(n+1)/2
>
> ∴ Basically, formula for 'finite' series is applicable to infinite series.
> (note that mathematical inducion cannot prove such formulas because by
> definition, ∞ is unreachable by counting.)
>
> Rule: Handling of the expanded form of infinite series must list the last
> addend. Otherwise, the expanded form is ill-formed (obscure semantics and
> information being lost cannot conduct valid deduction).
>
> Ex.1 (the last addend is omitted):
> A=1+2+3+4+5+...
> =(1+2)+(3+4)+5+...
> =3+7+5+... // ill-formed, obscure semantics.
>
> Last addend listed:
> A=1+2+3+4+5+...+∞ // well-formed, the exanded form of Σ(n=1,∞) {n}
>
> Ex.2:
> S=1+2+4+8+... // ill-formed
> <=> S=1+2(1+2+4+8+...)
> <=> S=1+2S
> <=> S=-1
>
> Last addend listed:
> S=1+2+4+8+...+2^∞
> <=> S=1+2(1+2+4+...+2^(∞-1))
> <=> S=1+2S-2^(∞+1)
> <=> S=2^(∞+1)-1 // Lots of similar "magic calculation" deriving the result
> // S=-1 can be found in youtube. (the term containing the
> // last addend ∞ is ignored)
>
> Ex.3:
> "f(n)= Σ(k=0,n) 1/k! => f(∞)=e(The base of natural logarithm)"?
> We know for sure ∀n∈ℕ, f(n)∈ℚ. To get the result f(n)=e (f(n)∉ℚ), the only
> current option is n=∞. But the issue whether or not f(∞)=e (exact equal by
> definition) can only be decided via definition, e.g. e≡f(∞). Otherwise, we
> can only say f(∞)≈e. (In considering the definition of the equal sign '=',
> other forms of e are likely not mutually replaceable with f(∞))
>
> Ex.4: x= Σ(n=1,∞) 1/n²
> A common expression is x= Σ(n=1,∞) 1/n²= π²/6, therefore, π=√(6*x)
> The issue here is: Lots of π can be derived from various infinite serieses.
> But, according to the definition of '=', the result of mutual substitution
> may become inconsistent.
> For now, the uncontroversial definition of π is the ratio of the
> circumference of a circle to its diameter (no computable definition), it is
> more correct to use '≈'.
> Therefore, Σ(n=1,∞) 1/n² ≈ π²/6 is what it is.
>
> [Note1] "..." in expression is normally indeterminant, of vague semantic.
> "0.999..." is also indeterminant before the "..." is eliminated, the
> number "0.999..." represents is uncertain, must be removed to ensure
> what the number is.
> Ex1: Let x=0.999...
> 10*x= 9+x // This is the result of x after interpreted, not necessarily
> // the result followed from "x=0.999..."
> // This equation must be given to define x (eliminate the
> // ambiguous "...")
> Ex2: Let x=√(2+√(2+√(2+...))). Then, possible interpretation of x are:
> x=√(2+x)
> x=√(2+√(2+x))
> x=√(2+√(2+√(2+x)))
> ...
>
> 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...
>
> Let A=B
> <=> 1-1/2^∞= 1-1/10^∞ // converted from the formula of geometric series
> <=> 1/2^∞= 1/10^∞
> <=> 10^∞= 2^∞
> <=> 5^∞=1
> <=> false
>
> [Note2] Expanded form is prone to magic tricks, perhaps owing to conceptional
> generalization of visual illusion too easy to form. It is an error
> because the regrouping of the expanded form hides the fact that the
> original way of computation is reformulated.
> Ex: S can be the sum of any sequence of natural numbers.
> S= Σ(n=1,∞) n= 1+2+3+... =1+1+1+1+...= (1+1)+(1+1+1)+...
> = Σ(n=1,∞) n+1 // S is modified
>
> Axiom: Σ(n=0,∞) a(n)= a(0)+ Σ(n=1,∞) a(n)
> = a(∞)+ Σ(n=0,∞-1) a(n)
> Theorem1: Σ(n=0,∞) f(n) ± Σ(n=0,∞) g(n) = Σ(n=0,∞) f(n)±g(n)
> Theorem2: Σ(n=0,∞) c*f(n)= c*(Σ(n=0,∞) f(n))
> Proof: Omitted (Can be derived from the expanded form)
>
> Ex1: Σ 2*n =Σ (n+n) =Σ n + Σ n
> If Σ 2*n is said the sum of all even numbers, Σ n the sum of all natural
> numbers, the notion that the whole is greater than the part is conflicted
> by this rule (many paradoxical and current text book arithmetic have the
> same issue using Theorem2 like in Ex3).
> But, how do we express "the sum of even numbers"? Or Σ(n=0,∞/2) 2*n ?
> An idea that using C-language's for loop expression might solve this
> problem (or, at least, better than the traditional Σ notation):
> for(n=0;;++n) n; or f(n=0;;n+=2) n;
> Benefit of such a notation is 1.the symbol '∞' can be omitted 2. the
> meaning is more concrete, reducing mathematical imagination of 'Σ'.
>
> Temporary Conclusion: The essence of an infinite series may be a number whose
> computation never terminates because of infinite number of non-zero
> addends), or could be imagined as a 'running' number (density property
> requires the existence of such an 'irrational' number).
> ------------------------- End of Quote

On Friday, 12 August 2022 at 04:54:15 UTC+2, richar...@gmail.com wrote:
> On 8/11/22 11:29 AM, Skep Dick wrote:
> > On Thursday, 11 August 2022 at 13:43:10 UTC+2, richar...@gmail.com wrote:
> >> Which is why you need to be clear what domain you are talking about,
> >> especially if you are not talking about the domain that people will assume.
> > I have no way of knowing what "people" will assume. I am not a mind reader.
> Then you fail the first step of communication, and thus fail to communicate.

Is that like you failed to communicate 0.999...'s domain?
Or how you failed to communicate 3 and 9's domains.

Or are we only counting my communication failures but not yours?

> I gave you charity at first. You then showed that you didn't care, and
> just turned abusive.
I turned "abusive" and "stopped caring" the moment I realised you are uncharitable.

Which was roughly the moment you began insiting that you are "right" and other people are "wrong".

It was roughly the moment I realised that you don't know Mathematics is absolutely relative.

> Since YOU refuse to try to meet others interpretations, you lose the
> right to claim yours are special.
Wait. What?!? I never claimed that I am special. In fact! It is my primary axiom that there are NO privileged models/interpretations of computation!

You are the one gatekeeping YOUR interpretation.

> You have proved what sort of person you are, and thus have lost the
> right to charity.
You are equivocating "prove" you uncharitable twat!

The "sort of person I am" is beyond the techniques of Mathematics.

> What clear notation needs to be used?
So clarity in communication is no longer your goal? I thought so!

> is written is part of the simplest number system that its representation
> needs
Representations don't have needs. Humans have needs.

You are projecting needs onto your representations.

> >> To later say you are talking about some other system *R, is just showing you are being deceptive.
> > See Principle of charity. You really need it.
> Maybe YOU need to use it.
I am using it. That's why I am questioning your Mathematical dogma!

> Because you refuse to put them into the context of the system they
> belong in but claim they are part of a domain that they aren't in.
You fucking hypocrite!

WHere in this sentence did YOU put them in the context of the system they belong?!?

> This can be proven by 9 = 3+3+3 and the assocative property thus 9/9 =
> (3+3+3)/9 = 3/9 + 3/9 + 3/9 = 0.3333... + 0.3333... + 0.3333... =
> 0.9999....

> THAT makes them a LIE.
OK. Then I shall call you a Liar from now on.

> The fact that you ADMIT that you don't intend of following conventions.
There you go, being uncharitable again.

I have absolutely no idea whether "I am following conventions" or not!
I have no idea what YOUR cultural biases are - I am not a mind reader!

I am an autodidact - I rely on my intuition. That is to say - I am an intuitionist in the footsteps of Brouwer.
My intuition doesn't tell me which system it's operating in - if any!

In fact, the only time the question of systems/context even matters is when I encounter Mathematical statements which assault my intuitions.
Statements like "0.999... = 1". Or calculus done the epsilon-delta way.

> says that nothing you say is apt to actually be meaningful, because you
> won't label the system that it actually needs to be understood in.
That's just gaslighting! I can play the exact same game, you uncharitable ass.

You've said nothng meaningful every time you failed to label your system.

On Thursday, 11 August 2022 at 23:14:31 UTC+2, Ben Bacarisse wrote:
> Skep Dick <skepd...@gmail.com> writes:
>
> > On Tuesday, 9 August 2022 at 17:15:14 UTC+2, Ben Bacarisse wrote:
> >> This is because 0.333... means
> >>
> >> lim(n->oo) Sum k=1,n (3/10^k)
> >
> > I notice that you think yourself very skilled in telling other people
> > what stuff means.
> Thank you (I suppose). It's better when people use agreed meanings.
Oh, I disagree wholeheartedly. Negotiating disagreement in meanings is part of being a skilled communicator - we know a bunch of consensus protocols and they converge rapidly.

That's why you have all of those error-detection and error-correction facilities wired in your brain.
I would highly recommend you using them, but you seem far more interested in strongly-normalizing reductions than effective communication.

On Friday, 12 August 2022 at 05:00:23 UTC+2, richar...@gmail.com wrote:
> The value of 1 + 2 + 3 + 4 + 5 + ... does not result in a value that is
> a Real Number.
So what? If you want 1+2+3+4+5... to result in a value then DON'T use the Real Number System.

Use another system.

> So, when you are talking about things you SAY are Real Numbers, there is
> no such value.
I am not saying what they are or aren't. I am just manipulating symbols - I am computing!

Depending on the semantic properties I am interested in I may switch systems. So what?

> Because, until specifically declaired, there are rules to determine the
> assumed number system.
There are rules to mind-reading!?! Please could you explain those rules to a Turing Machine!

I would love to program via telepathy!

> Then your model isn't the Real Number System. If you have redefined
> that, then your system just becomes a deception.
I haven't redefined anything. I am just using symbols and constructions in a way that makes sense to me.

> Stop making statement that imply them then. I guess your GOAL is to be
> ambiguous, and thus you are speaking deceptions.
That is a wrong guess. But it's funny that this idea/goal should pop in in YOUR mind.

Maybe that's what YOU are doing? Are you trying to deceive other people?

After all - there's no empirical way to verify that ANYTHING you say is correct.

> You are just full of EGO and lack of concern about others, and thus
> putting yourself outside of the community you seem to want to be part of.
Are you psychoanalyzing yourself or...?

I have no ego. Which is why I am pointing out THAT Mathematics is relative.

There's no right and wrong. There's only right and wrong within the rules of a system.

But who created the system and why? Does their creation suit my purpose?

On 8/12/22 1:07 AM, Skep Dick wrote:
> On Friday, 12 August 2022 at 04:54:15 UTC+2, richar...@gmail.com wrote:
>> On 8/11/22 11:29 AM, Skep Dick wrote:
>>> On Thursday, 11 August 2022 at 13:43:10 UTC+2, richar...@gmail.com wrote:
>>>> Which is why you need to be clear what domain you are talking about,
>>>> especially if you are not talking about the domain that people will assume.
>>> I have no way of knowing what "people" will assume. I am not a mind reader.
>> Then you fail the first step of communication, and thus fail to communicate.
>
> Is that like you failed to communicate 0.999...'s domain?
> Or how you failed to communicate 3 and 9's domains.
>
> Or are we only counting my communication failures but not yours?

But I DID, by following the conventions.

IT isn't MY fault that you are ignorant of the standard
social-mathematical conventions.

Note, earlier in the conversation, and in the topic of the message, that
domain was actually specifically mentioned.

By making a rational/irrational comment, the domain being the Real is
made clear, as that is the smplest system that has both of them.

>
>> I gave you charity at first. You then showed that you didn't care, and
>> just turned abusive.
> I turned "abusive" and "stopped caring" the moment I realised you are uncharitable.

Nope, I pointed out that your statements were incorret in the impllied
system. I didn't say they couldn't be right if you actually specified a
domain, giving you the option to correct you statement and include the
domain.

YOUR reply was that you

>
> Which was roughly the moment you began insiting that you are "right" and other people are "wrong".

IF you ARE Right about something, you are right.

>
> It was roughly the moment I realised that you don't know Mathematics is absolutely relative.

So, you don't know that Truth is ABSOLUTE.

>
>> Since YOU refuse to try to meet others interpretations, you lose the
>> right to claim yours are special.
> Wait. What?!? I never claimed that I am special. In fact! It is my primary axiom that there are NO privileged models/interpretations of computation!
>
> You are the one gatekeeping YOUR interpretation.

WRONG.

>
>> You have proved what sort of person you are, and thus have lost the
>> right to charity.
> You are equivocating "prove" you uncharitable twat!
>
> The "sort of person I am" is beyond the techniques of Mathematics.

You are just proving the sort of person you are,

>
>> What clear notation needs to be used?
> So clarity in communication is no longer your goal? I thought so!
>
>> is written is part of the simplest number system that its representation
>> needs
> Representations don't have needs. Humans have needs.
>
> You are projecting needs onto your representations.
>
>>>> To later say you are talking about some other system *R, is just showing you are being deceptive.
>>> See Principle of charity. You really need it.
>> Maybe YOU need to use it.
> I am using it. That's why I am questioning your Mathematical dogma!
>
>> Because you refuse to put them into the context of the system they
>> belong in but claim they are part of a domain that they aren't in.
> You fucking hypocrite!
>
> WHere in this sentence did YOU put them in the context of the system they belong?!?
>
>> This can be proven by 9 = 3+3+3 and the assocative property thus 9/9 =
>> (3+3+3)/9 = 3/9 + 3/9 + 3/9 = 0.3333... + 0.3333... + 0.3333... =
>> 0.9999....
>
>> THAT makes them a LIE.
> OK. Then I shall call you a Liar from now on.
>
>> The fact that you ADMIT that you don't intend of following conventions.
> There you go, being uncharitable again.
>
> I have absolutely no idea whether "I am following conventions" or not!
> I have no idea what YOUR cultural biases are - I am not a mind reader!
>
> I am an autodidact - I rely on my intuition. That is to say - I am an intuitionist in the footsteps of Brouwer.
> My intuition doesn't tell me which system it's operating in - if any!
>
> In fact, the only time the question of systems/context even matters is when I encounter Mathematical statements which assault my intuitions.
> Statements like "0.999... = 1". Or calculus done the epsilon-delta way.
>
>> says that nothing you say is apt to actually be meaningful, because you
>> won't label the system that it actually needs to be understood in.
> That's just gaslighting! I can play the exact same game, you uncharitable ass.
>
> You've said nothng meaningful every time you failed to label your system.
>
>

On 8/12/22 1:42 AM, Skep Dick wrote:
> On Friday, 12 August 2022 at 05:00:23 UTC+2, richar...@gmail.com wrote:
>> The value of 1 + 2 + 3 + 4 + 5 + ... does not result in a value that is
>> a Real Number.
> So what? If you want 1+2+3+4+5... to result in a value then DON'T use the Real Number System.
>
> Use another system.

The actually USE the other system, but you need to specify it.

>
>> So, when you are talking about things you SAY are Real Numbers, there is
>> no such value.
> I am not saying what they are or aren't. I am just manipulating symbols - I am computing!
>
> Depending on the semantic properties I am interested in I may switch systems. So what?

If you don't define the system you are in, your symbols are meaningless.

That seems to be where you are stuck,

>
>> Because, until specifically declaired, there are rules to determine the
>> assumed number system.
> There are rules to mind-reading!?! Please could you explain those rules to a Turing Machine!
>
> I would love to program via telepathy!

Who needs mind-reading. That is YORU false assumption.

>
>> Then your model isn't the Real Number System. If you have redefined
>> that, then your system just becomes a deception.
> I haven't redefined anything. I am just using symbols and constructions in a way that makes sense to me.

And that is your problem, you should be using them in the way that makes
sense to the people you are talking about by being clear about the
system you are working in.

You are just proving your EGO problem.

>
>> Stop making statement that imply them then. I guess your GOAL is to be
>> ambiguous, and thus you are speaking deceptions.
> That is a wrong guess. But it's funny that this idea/goal should pop in in YOUR mind.
>
> Maybe that's what YOU are doing? Are you trying to deceive other people?
>
> After all - there's no empirical way to verify that ANYTHING you say is correct.
>
>> You are just full of EGO and lack of concern about others, and thus
>> putting yourself outside of the community you seem to want to be part of.
> Are you psychoanalyzing yourself or...?
>
> I have no ego. Which is why I am pointing out THAT Mathematics is relative.

So you are just ignorant.

>
> There's no right and wrong. There's only right and wrong within the rules of a system.

Incorrect. Yes, a system can define what it will treat as correct, but
there are fundamental rules that must be followed or the system is just
broken (and thus "incorrect")

>
> But who created the system and why? Does their creation suit my purpose?
>

That is one of the big questions.

On Friday, 12 August 2022 at 13:36:36 UTC+2, richar...@gmail.com wrote:
> > Or are we only counting my communication failures but not yours?
> But I DID, by following the conventions.
Precisely! You failed to communicate THAT you are following the convention.

> IT isn't MY fault that you are ignorant of the standard
> social-mathematical conventions.
It is your fault. You failed to communicate which convention you are using. Not me.

> Note, earlier in the conversation, and in the topic of the message, that
> domain was actually specifically mentioned.
> By making a rational/irrational comment, the domain being the Real is
> made clear, as that is the smplest system that has both of them.

What does that have to do with the point that the truth of 0.999... = 1 depends on an arbitrary choice?

It's true if you want it to be true.
It's false if you want it to be false.

What do you want it to be?

> >> I gave you charity at first. You then showed that you didn't care, and
> >> just turned abusive.
> > I turned "abusive" and "stopped caring" the moment I realised you are uncharitable.
> Nope, I pointed out that your statements were incorret in the impllied system.
See! You are uncharitable.

The statement is whatever we want it to be! You want it to be true. I want it to be false.

That doesn't make me incorrect. It makes you an ass.

Mathematics is relative!

>I didn't say they couldn't be right if you actually specified a
> domain, giving you the option to correct you statement and include the
> domain.
Idiot. Which part of choice-dependent truth is lost upon you?

> IF you ARE Right about something, you are right.
One more time - for the idiot in the classroom. There is no such thing as "right" or "wrong" in Mathematics!

0.999... = 1 is neither right nor wrong!

If you want to MAKE it wrong you use *R.
If you want to MAKE it right you use R.

> So, you don't know that Truth is ABSOLUTE.
Ahahahahahahahahahahahahahahahahaha!
Ahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahaha!
Ahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahaha!
Ahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahahaha!

Shame. Somebody doesn't understand Tarski's theorems.

https://en.wikipedia.org/wiki/Tarski%27s_undefinability_theorem
> > You are the one gatekeeping YOUR interpretation.
> WRONG.
There is no right and wrong in Mathematics.

> >> You have proved what sort of person you are, and thus have lost the
> >> right to charity.
> > You are equivocating "prove" you uncharitable twat!
> >
> > The "sort of person I am" is beyond the techniques of Mathematics.
> You are just proving the sort of person you are,
Q.E.D using the concept of "proof" outside of its applicable domain.

Does that make you an idiot? I wonder.

> >> What clear notation needs to be used?
> > So clarity in communication is no longer your goal? I thought so!
Q.E.D Ucharitable twat.

On Thu, 11 Aug 2022 07:43:06 -0400
Richard Damon <Richard@Damon-Family.org> wrote:

> On 8/11/22 4:50 AM, Skep Dick wrote:
> > On Monday, 8 August 2022 at 15:16:39 UTC+2, Ben Bacarisse wrote:
> >> Yes. For example 0.999... = 1/1.
> >
> > Ok. So it needs saying so I will say it. You are an ass.
> >
> > Few posts ago (on another thread) you were giving me a lecture
> > about functions needing domains/context.
> >
> > Whether 0.999... = 1/1 is a theorem or not absolutely depends on
> > the number system. The domain of your symbols.
> >
> > It is a theorem in R.
> > It isn’t a theorem in *R
> >
> >
>
> Which is why you need to be clear what domain you are talking about,
> especially if you are not talking about the domain that people will
> assume.
>
> That just shows that you believe it is ok to be deceptive by not
> being clear.
>
>
> The number, 0.9999... if not otherwise indicated by context, is a
> Real Number in the Real Number system. To later say you are talking
> about some other system *R, is just showing you are being deceptive.
>
> Virtually ANY statement can be proven or disproven if you allow it to
> be moved into an arbitrary logic system crafted for that purpose, so
> context is vital for communication.
>
>

0.999... = 1.0, proof:

S = 0.999...
S * 10 = 9.999...
S * 10 - S = 9.0
S * 9 = 9.0
S = 1.0
ergo 0.999... = 1.0 QED

/Flibble

On Friday, 12 August 2022 at 13:41:32 UTC+2, richar...@gmail.com wrote:
> > Use another system.
> The actually USE the other system, but you need to specify it.

I am USING the other system. And no - I don't have to fucking specify it.
I'll USE whichever damn system I want to use.

As long as it works.

> If you don't define the system you are in, your symbols are meaningless.
> That seems to be where you are stuck,
Ooooh! Are you sure you want to play that game?

If you don't define "Truth" then "Truth" is meaningless.
If you don't define "define" then "define" is meaningless.
If you don't define "meaningless" then "meaningless" is meaningless.

> Who needs mind-reading. That is YORU false assumption.
My assumption is neither true, nor false - it's just a fact.

It's a fact THAT I can't read your mind.
It's a fact THAT you failed to communicate which system you are using.

> And that is your problem, you should be using them in the way that makes
> sense to the people you are talking about by being clear about the
> system you are working in.
So when are you going to make clear which system of Truth you are working in?

> You are just proving your EGO problem.
In so far as one of us has an EGO problem. It's the guy who always has to be right...

> > I have no ego. Which is why I am pointing out THAT Mathematics is relative.
> So you are just ignorant.
Ahhh. The irony!

IF Mathematics is relative and you don't know that. Which one of us is ignorant?

Remind me again whether the truth of 0.999...= 1 is absolute; or relative..

> Incorrect.
You are incorrect about me being incorrect 😂😂😂😂

>Yes, a system can define what it will treat as correct, but
> there are fundamental rules that must be followed or the system is just
> broken (and thus "incorrect")
Shame. We have a fundamentalist on our hands.

> > But who created the system and why? Does their creation suit my purpose?
> >
> That is one of the big questions.
So you don't actually know the answer, but you blindly follow the rules?

Good computer!

On Friday, 12 August 2022 at 15:47:51 UTC+2, Mr Flibble wrote:
> 0.999... = 1.0, proof:
>
> S = 0.999...
> S * 10 = 9.999...
> S * 10 - S = 9.0
> S * 9 = 9.0
> S = 1.0
> ergo 0.999... = 1.0 QED
>
> /Flibble
if 0.999.. is convergent then the proof is valid.
if 0.999... is divergent then the proof is invalid.

Is 0.999... convergent or divergent?

That's undecidable. Subject to choice.

On Fri, 12 Aug 2022 06:58:27 -0700 (PDT)
Skep Dick <skepdick22@gmail.com> wrote:

> On Friday, 12 August 2022 at 15:47:51 UTC+2, Mr Flibble wrote:
> > 0.999... = 1.0, proof:
> >
> > S = 0.999...
> > S * 10 = 9.999...
> > S * 10 - S = 9.0
> > S * 9 = 9.0
> > S = 1.0
> > ergo 0.999... = 1.0 QED
> >
> > /Flibble
> if 0.999.. is convergent then the proof is valid.
> if 0.999... is divergent then the proof is invalid.
>
> Is 0.999... convergent or divergent?
>
> That's undecidable. Subject to choice.

Bullshit. 0.999... = 1.0 as I have just shown.

/Flibble

On Friday, 12 August 2022 at 16:04:33 UTC+2, Mr Flibble wrote:
> On Fri, 12 Aug 2022 06:58:27 -0700 (PDT)
> Skep Dick <skepd...@gmail.com> wrote:
>
> > On Friday, 12 August 2022 at 15:47:51 UTC+2, Mr Flibble wrote:
> > > 0.999... = 1.0, proof:
> > >
> > > S = 0.999...
> > > S * 10 = 9.999...
> > > S * 10 - S = 9.0
> > > S * 9 = 9.0
> > > S = 1.0
> > > ergo 0.999... = 1.0 QED
> > >
> > > /Flibble
> > if 0.999.. is convergent then the proof is valid.
> > if 0.999... is divergent then the proof is invalid.
> >
> > Is 0.999... convergent or divergent?
> >
> > That's undecidable. Subject to choice.
> Bullshit. 0.999... = 1.0 as I have just shown.

OK, genius.

S = 1 + 2 + 3 + 4...
S = 1 + (2 + 3 + 4) + (5 + 6 + 7)...
S = 1 + 9 + 18 + 27...
S = 1 + 9(1 + 2 + 3 + 4...)
S = 1 + 9S
S = -1/8

ergo 1 + 2 + 3 + 4... < 0

On Fri, 12 Aug 2022 07:11:37 -0700 (PDT)
Skep Dick <skepdick22@gmail.com> wrote:

> On Friday, 12 August 2022 at 16:04:33 UTC+2, Mr Flibble wrote:
> > On Fri, 12 Aug 2022 06:58:27 -0700 (PDT)
> > Skep Dick <skepd...@gmail.com> wrote:
> >
> > > On Friday, 12 August 2022 at 15:47:51 UTC+2, Mr Flibble wrote:
> > > > 0.999... = 1.0, proof:
> > > >
> > > > S = 0.999...
> > > > S * 10 = 9.999...
> > > > S * 10 - S = 9.0
> > > > S * 9 = 9.0
> > > > S = 1.0
> > > > ergo 0.999... = 1.0 QED
> > > >
> > > > /Flibble
> > > if 0.999.. is convergent then the proof is valid.
> > > if 0.999... is divergent then the proof is invalid.
> > >
> > > Is 0.999... convergent or divergent?
> > >
> > > That's undecidable. Subject to choice.
> > Bullshit. 0.999... = 1.0 as I have just shown.
>
> OK, genius.
>
> S = 1 + 2 + 3 + 4...
> S = 1 + (2 + 3 + 4) + (5 + 6 + 7)...
> S = 1 + 9 + 18 + 27...
> S = 1 + 9(1 + 2 + 3 + 4...)
> S = 1 + 9S
> S = -1/8
>
> ergo 1 + 2 + 3 + 4... < 0
>

false analogy strawman logical fallacy QED

/Flibble