On Friday, 26 August 2022 at 14:39:36 UTC+2, richar...@gmail.com wrote:
> > So you don't have (Mathematical) object in your system?
> >
> > https://en.wikipedia.org/wiki/Mathematical_object
> >
> > Fucking idiot.
> So, WHICH definition of "Object" are you using. You seem to keep
> changing it.
I am not using any "definition" of object. Moron. I am just USING the concept of an object.

There's absoluteley no need to define it! Every child understands the condept intuitivley.

An object is an object is an object. Everything is an object.

> You are now the one being inconsistent.
I have told you this a dozen times already!!! I am consistently inconsistent!

It's not really my fault that you can't decide whether that amounts to consistency; or inconsistency.

> Mathematical Objects are not the exact same thing as the objects of a
> programming language.
In so far as they are conceptual - there is absolutely NO difference.

But if you want to - you are welcome to treat ALL objects as first class citizens in some programming language.

> But you don't seem to be able to test the "type" of a object to use the
> appropriate definition to go with it.
The fuck? You said the context/domain is defined.

+(x:ℝ, x:ℝ) -> y:ℝ

> 5.25 can be a Real Number
So you don't know what you are representing with with those symbols?

> ∞ is the symbol that represents infinity, which ISN'T a 'value' in the
> Real Number System, but can be use in a few special situations.
So it's half-pregnant when it needs to be?

> > What I am DOING is trying to figure out HOW you are doing arithmetic with "Real numbers" which are NOT computationally defined.
> Who says they aren't computationally defined?
Who says they are?

> The definition of how you do arithmetic with the Reals is all in the
> body of knowledge that is out there, and is too vast to just post in an
> usenet posting.
Body of knowledge or body of bullshit?

If arithmetic with infinite-precision (why does this even need saying?) Real Numbers is computable then you've solved the halting problem.

On 8/26/22 8:43 AM, Skep Dick wrote:
> On Friday, 26 August 2022 at 14:27:52 UTC+2, richar...@gmail.com wrote:
>>> Jesus fucking christ. I am asking you if 0.999... == 1 is a theorem, or if the negation of 0.999... == 1 is a theorem in your system.
>>>
>>> Why can't you tell me?
>> In The Real Number System, it would be a theorem.
> Holy fucking shitballs you imprecise moron! They are BOTH theorems! I am asking you WHICH "it" is YOUR theorem.

Your context evaluator is obviously broken, as BY DEFINITON in the real
Number system 0.999... == 1 is the Theorem.

>
> is "IT" the theorem ( 0.999... == 1); or is is "IT" the theorem not(0.999... == 1)
>
> Can you bind "IT" to a value!?!
>
>
>> The question comes
>> will wij admit they are working in The Real Number System, and thus need
>> to accept that fact, and that other things they are trying to do aren't
>> allowed, or will the admit they aren't working in The Real Number System.
> Shit-for-brains fucking idiot. You are constantly doing things which are "not allowed" IN The Real Number System.
>
> You are doing arithmetic in R. Which is "not allowed".

Doing arithmetic on ∞ is not allowed in R, since ∞ is not an element in R,

>
> Does that mean you are lying about working in The Real Number System?
>
>>> I always start with theorems first.
>> Hard to work with a Theorem if you don't know the system it is supposed
>> to be part of.
> Nothing hard about it! It's exactly how the Real World works!
>
> I don't need to know which universe I am in, in order to accept gravity as a theorem.
>
>>> Which has what to do with anything?
>> Truth.
> Truth? Is that like God?
>
> Are we in alt.religion or comp.theory ?!?!

On Friday, 26 August 2022 at 14:44:08 UTC+2, Ben Bacarisse wrote:
> So you still want me to waste time typing out standard material from
> goodness know how many sources? No. Go read them.
Fucking idiot. Nobody is asking you to post "standard material" or ANY material.

I am asking you to identify WHICH standard you think is THE standard.

Because I've read material, and I've read material - and there's no fucking standard! There are just echo chambers.

> If you don't know what 0.999... = 1 means, you know where you can find
> out.
Fucking idiot! Of courseI know what it means in gneral! It means a Boolean!

But I am not interested in general answers, I am looking for the particular and precis answer. I am looking for the Boolean value YOU have assigned to it,
and of course I know where I can find that out. The location of that information is in YOUR head. That is PRECISELY why I am asking YOU.

> The question is what /you/ mean. That will remain a mystery because you
> won't say more than report, as stated, silly uncontested facts like
> "0.999... + epsilon = 1" is true.
What the fuck?! I have told you over and over what /I/ mean!

I have assigned the Boolean value "True" to the type "0.999... + epsilon = 1". That's precisly what it means!

"0.999... + epsilon = 1" means True:Boolean

Do you even understand what you are asking?!?

On 8/26/22 8:53 AM, Skep Dick wrote:
> On Friday, 26 August 2022 at 14:39:36 UTC+2, richar...@gmail.com wrote:
>>> So you don't have (Mathematical) object in your system?
>>>
>>> https://en.wikipedia.org/wiki/Mathematical_object
>>>
>>> Fucking idiot.
>> So, WHICH definition of "Object" are you using. You seem to keep
>> changing it.
> I am not using any "definition" of object. Moron. I am just USING the concept of an object.
>
> There's absoluteley no need to define it! Every child understands the condept intuitivley.
>
> An object is an object is an object. Everything is an object.

So, you can't define it?

>
>> You are now the one being inconsistent.
> I have told you this a dozen times already!!! I am consistently inconsistent!
>
> It's not really my fault that you can't decide whether that amounts to consistency; or inconsistency.

Nope, you are just inconsistent so your logic system is worthless.

PERIOD.

>
>> Mathematical Objects are not the exact same thing as the objects of a
>> programming language.
> In so far as they are conceptual - there is absolutely NO difference.
>
> But if you want to - you are welcome to treat ALL objects as first class citizens in some programming language.

And what language is that?

I think you will find you just defined your system to blow up.

I guess is has in it the set of all sets that don't contain themselves.

And thus has "blown itself up"

FAIL.

>
>> But you don't seem to be able to test the "type" of a object to use the
>> appropriate definition to go with it.
> The fuck? You said the context/domain is defined.
>
> +(x:ℝ, x:ℝ) -> y:ℝ

Right, and ∞ is NOT an element of the Reals, so that doesn't define what
you meant by +(x, ∞)

>
>> 5.25 can be a Real Number
> So you don't know what you are representing with with those symbols?
>
>> ∞ is the symbol that represents infinity, which ISN'T a 'value' in the
>> Real Number System, but can be use in a few special situations.
> So it's half-pregnant when it needs to be?
>
>>> What I am DOING is trying to figure out HOW you are doing arithmetic with "Real numbers" which are NOT computationally defined.
>> Who says they aren't computationally defined?
> Who says they are?
>
>> The definition of how you do arithmetic with the Reals is all in the
>> body of knowledge that is out there, and is too vast to just post in an
>> usenet posting.
> Body of knowledge or body of bullshit?
>
> If arithmetic with infinite-precision (why does this even need saying?) Real Numbers is computable then you've solved the halting problem.

On Friday, 26 August 2022 at 14:56:46 UTC+2, richar...@gmail.com wrote:
> On 8/26/22 8:43 AM, Skep Dick wrote:
> > On Friday, 26 August 2022 at 14:27:52 UTC+2, richar...@gmail.com wrote:
> >>> Jesus fucking christ. I am asking you if 0.999... == 1 is a theorem, or if the negation of 0.999... == 1 is a theorem in your system.
> >>>
> >>> Why can't you tell me?
> >> In The Real Number System, it would be a theorem.
> > Holy fucking shitballs you imprecise moron! They are BOTH theorems! I am asking you WHICH "it" is YOUR theorem.
> Your context evaluator is obviously broken, as BY DEFINITON in the real
> Number system 0.999... == 1 is the Theorem.
> >
> > is "IT" the theorem ( 0.999... == 1); or is is "IT" the theorem not(0.999... == 1)
> >
> > Can you bind "IT" to a value!?!
> >
> >
> >> The question comes
> >> will wij admit they are working in The Real Number System, and thus need
> >> to accept that fact, and that other things they are trying to do aren't
> >> allowed, or will the admit they aren't working in The Real Number System.
> > Shit-for-brains fucking idiot. You are constantly doing things which are "not allowed" IN The Real Number System.
> >
> > You are doing arithmetic in R. Which is "not allowed".
> Doing arithmetic on ∞ is not allowed in R, since ∞ is not an element in R,

Doing ANY operations on infinite precision numbers is also not allowed in R.. Because you can't perform infinite number of steps in finite time.

This is not a limit of Turing machines.
This is alimit of humans in a time-bound Universe.

On Friday, 26 August 2022 at 15:09:47 UTC+2, richar...@gmail.com wrote:
> > An object is an object is an object. Everything is an object.
> So, you can't define it?
I did define it! Recursively! Which part of my definition are you struggling with?

> > It's not really my fault that you can't decide whether that amounts to consistency; or inconsistency.
> Nope, you are just inconsistent so your logic system is worthless.
Your logic can't tell THAT I am consistently inconsisteent.

Now THAT's worthless.
> > But if you want to - you are welcome to treat ALL objects as first class citizens in some programming language.
> And what language is that?
The programming language in which ALL mathematical objects are first class citizens.
> I think you will find you just defined your system to blow up.
Not possible. My system doesn't admit the principle of explosion.

Alrady explained it to you. A bunch of times.

> I guess is has in it the set of all sets that don't contain themselves.
> And thus has "blown itself up"
> FAIL.
You intentionally admit principles which blow up your system on trivialities !?!

If you pulled that stunt when designing industrial systems you'd be thrown in prison!

Oh wait.. you DO admit principlees which blow up your system. You already admitted that your system does "if x is ∞ then..."

https://en.wikipedia.org/wiki/Curry's_paradox

It's a shame that you have accepted sucha stupid, explosive principle as a foundation of a system...
Not smart. Not smart at all..

> > +(x:ℝ, x:ℝ) -> y:ℝ
> Right, and ∞ is NOT an element of the Reals, so that doesn't define what
> you meant by +(x, ∞)
Hypocrite.

If x is an element of the Reals you still haven't defined what you mean by lim(x -> ∞)f(x)

On Friday, 26 August 2022 at 14:10:16 UTC+1, skepd...@gmail.com wrote:
> On Friday, 26 August 2022 at 14:56:46 UTC+2, richar...@gmail.com wrote:
> > On 8/26/22 8:43 AM, Skep Dick wrote:
> > > On Friday, 26 August 2022 at 14:27:52 UTC+2, richar...@gmail.com wrote:
> > >>> Jesus fucking christ. I am asking you if 0.999... == 1 is a theorem, or if the negation of 0.999... == 1 is a theorem in your system.
> > >>>
> > >>> Why can't you tell me?
> > >> In The Real Number System, it would be a theorem.
> > > Holy fucking shitballs you imprecise moron! They are BOTH theorems! I am asking you WHICH "it" is YOUR theorem.
> > Your context evaluator is obviously broken, as BY DEFINITON in the real
> > Number system 0.999... == 1 is the Theorem.
> > >
> > > is "IT" the theorem ( 0.999... == 1); or is is "IT" the theorem not(0.999... == 1)
> > >
> > > Can you bind "IT" to a value!?!
> > >
> > >
> > >> The question comes
> > >> will wij admit they are working in The Real Number System, and thus need
> > >> to accept that fact, and that other things they are trying to do aren't
> > >> allowed, or will the admit they aren't working in The Real Number System.
> > > Shit-for-brains fucking idiot. You are constantly doing things which are "not allowed" IN The Real Number System.
> > >
> > > You are doing arithmetic in R. Which is "not allowed".
> > Doing arithmetic on ∞ is not allowed in R, since ∞ is not an element in R,
> Doing ANY operations on infinite precision numbers is also not allowed in R. Because you can't perform infinite number of steps in finite time.
>
acos(sqrt(2)) = PI/4
You can prove that geometrically (draw a right angled triangle with unit small sides. It's an isosceles triangle because the
small sides are of equal length, and the angle between them is a right angle. So the other two angles must be PI/4).

The numbers are irrational (the sides of the triangle are not ratios of each other, and the angle isn't a ratio of the angle an
arc subtends with two radii of its own length). But we can specify them exactly.

On Friday, 26 August 2022 at 15:39:16 UTC+2, malcolm.ar...@gmail.com wrote:
> acos(sqrt(2)) = PI/4
> You can prove that geometrically (draw a right angled triangle with unit small sides. It's an isosceles triangle because the
> small sides are of equal length, and the angle between them is a right angle. So the other two angles must be PI/4).
>
> The numbers are irrational (the sides of the triangle are not ratios of each other, and the angle isn't a ratio of the angle an
> arc subtends with two radii of its own length). But we can specify them exactly.
Which has what to do with arithmetic on real numbers?

On 8/26/22 9:10 AM, Skep Dick wrote:
> On Friday, 26 August 2022 at 14:56:46 UTC+2, richar...@gmail.com wrote:
>> On 8/26/22 8:43 AM, Skep Dick wrote:
>>> On Friday, 26 August 2022 at 14:27:52 UTC+2, richar...@gmail.com wrote:
>>>>> Jesus fucking christ. I am asking you if 0.999... == 1 is a theorem, or if the negation of 0.999... == 1 is a theorem in your system.
>>>>>
>>>>> Why can't you tell me?
>>>> In The Real Number System, it would be a theorem.
>>> Holy fucking shitballs you imprecise moron! They are BOTH theorems! I am asking you WHICH "it" is YOUR theorem.
>> Your context evaluator is obviously broken, as BY DEFINITON in the real
>> Number system 0.999... == 1 is the Theorem.
>>>
>>> is "IT" the theorem ( 0.999... == 1); or is is "IT" the theorem not(0.999... == 1)
>>>
>>> Can you bind "IT" to a value!?!
>>>
>>>
>>>> The question comes
>>>> will wij admit they are working in The Real Number System, and thus need
>>>> to accept that fact, and that other things they are trying to do aren't
>>>> allowed, or will the admit they aren't working in The Real Number System.
>>> Shit-for-brains fucking idiot. You are constantly doing things which are "not allowed" IN The Real Number System.
>>>
>>> You are doing arithmetic in R. Which is "not allowed".
>> Doing arithmetic on ∞ is not allowed in R, since ∞ is not an element in R,
>
> Doing ANY operations on infinite precision numbers is also not allowed in R. Because you can't perform infinite number of steps in finite time.
>
> This is not a limit of Turing machines.
> This is alimit of humans in a time-bound Universe.

Nope.

Nothing says that operations on the Reals need to give the full results
in finite time/steps.

That is just a limitation of YOUR domain.

On 8/26/22 9:08 AM, Skep Dick wrote:
> On Friday, 26 August 2022 at 14:44:08 UTC+2, Ben Bacarisse wrote:
>> So you still want me to waste time typing out standard material from
>> goodness know how many sources? No. Go read them.
> Fucking idiot. Nobody is asking you to post "standard material" or ANY material.
>
> I am asking you to identify WHICH standard you think is THE standard.
>
> Because I've read material, and I've read material - and there's no fucking standard! There are just echo chambers.
>
>> If you don't know what 0.999... = 1 means, you know where you can find
>> out.
> Fucking idiot! Of courseI know what it means in gneral! It means a Boolean!
>
> But I am not interested in general answers, I am looking for the particular and precis answer. I am looking for the Boolean value YOU have assigned to it,
> and of course I know where I can find that out. The location of that information is in YOUR head. That is PRECISELY why I am asking YOU.
>
>> The question is what /you/ mean. That will remain a mystery because you
>> won't say more than report, as stated, silly uncontested facts like
>> "0.999... + epsilon = 1" is true.
> What the fuck?! I have told you over and over what /I/ mean!
>
> I have assigned the Boolean value "True" to the type "0.999... + epsilon = 1". That's precisly what it means!
>
> "0.999... + epsilon = 1" means True:Boolean
>
> Do you even understand what you are asking?!?
>
>

So, since "epsilon" is NOT part of the "Real Number System", you are
clearly not working with that system, even though that was the system
that wij claimed to have been working on wheen he started.

He, of course, was making a similar mistake.

On 8/26/22 9:22 AM, Skep Dick wrote:
> On Friday, 26 August 2022 at 15:09:47 UTC+2, richar...@gmail.com wrote:
>>> An object is an object is an object. Everything is an object.
>> So, you can't define it?
> I did define it! Recursively! Which part of my definition are you struggling with?
>
>>> It's not really my fault that you can't decide whether that amounts to consistency; or inconsistency.
>> Nope, you are just inconsistent so your logic system is worthless.
> Your logic can't tell THAT I am consistently inconsisteent.
>
> Now THAT's worthless.
>
>>> But if you want to - you are welcome to treat ALL objects as first class citizens in some programming language.
>> And what language is that?
> The programming language in which ALL mathematical objects are first class citizens.
>
>> I think you will find you just defined your system to blow up.
> Not possible. My system doesn't admit the principle of explosion.

Then it doesn't support the principle of LOGIC.

>
> Alrady explained it to you. A bunch of times.

As you have amply demonstrated.

You system is consistently WORTHLESS because it doesn't have a
foundation to stand on.
>
>> I guess is has in it the set of all sets that don't contain themselves.
>> And thus has "blown itself up"
>> FAIL.
> You intentionally admit principles which blow up your system on trivialities !?!
>
> If you pulled that stunt when designing industrial systems you'd be thrown in prison!
>
> Oh wait.. you DO admit principlees which blow up your system. You already admitted that your system does "if x is ∞ then..."
>
> https://en.wikipedia.org/wiki/Curry's_paradox

So, you don't understand Curry's paradox.

I never said that x was defined as if x then ... so t doesn't fit the
definition.

>
> It's a shame that you have accepted sucha stupid, explosive principle as a foundation of a system...
> Not smart. Not smart at all..
>
>>> +(x:ℝ, x:ℝ) -> y:ℝ
>> Right, and ∞ is NOT an element of the Reals, so that doesn't define what
>> you meant by +(x, ∞)
> Hypocrite.
>
> If x is an element of the Reals you still haven't defined what you mean by lim(x -> ∞)f(x)

Obviously you lie, because I have. To repeat it:

lim(x -> ∞) f(x) means L if and only if there exists an L in the Reals
that for any e in the Reals > 0 we can find an X in the Real such that:

| f(x) - L | < e for all x > X

IF that is true, then L is the value of lim(x->∞) f(x)

If there is no such L, then the limit doesn't exist.

On Friday, 26 August 2022 at 18:33:52 UTC+8, Ben Bacarisse wrote:
> wij <wyni...@gmail.com> writes:
>
> > 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.
> >>
> >
> > As said. 0.999... or "Repeating decimal" suffer from pattern
> > interpretation problems:
> Only here. The meaning of ... after digits is almost universally
> agreed. So much so that other notations should be used for any other
> meaning.

Do you agree that derivation like this is not a proof?
(high schools use such deductions to 'prove' repeating decimals are rational).

Proof: 1=0.999...
x=0.999...
10x= 9.999...
10x= 9+x
9x=9
x=1

> > (1) 0.999...= 0.(9) = 0.(99)= 0.(999)
> Yes.

You should say no. They are not what "∑(n=1,∞) 9/10^n)" mean.

> > (2) 0.999...= 0.((9)(99)) // Andy Walker provided such
> > interpretation
> No. Just write 0.((9)(99)) if that's what you mean (and explain the
> concept either in terms of games or order relations).
The example is given by Andy. It could be valid to mean something.

> > (3) 1-1/∞= 0.999...
>
> Introducing a new number called ∞ by which one can divide other numbers
> does not produce any clarity. It produces even more ambiguity. What I
> would like to see from a "alterntivist" is clarity. If that requires a
> new number, so be it, but the set of numbers needs to be defined along
> with the operations on those.

The symbol ∞ I use is perfectly defined, not like yours.

> > 1-2/∞= 0.999...
> > 1-3/2^∞= 0.999...
> > 1-4/10^∞= 0.999...
> Without further explanation I will conclude that n/∞ = 0 and that n/k^∞
> = 0. That does not sound very useful, but what else can I conclude from
> your lack of explanation?

You are using your ambiguous ∞ again. You have no unambiguous base to say
"n/∞ = 0" or "n/k^∞= 0" (details had been discussed in another post). In this
case, n/∞ = 0 <=> n= ∞*0 <=> n=0. n has to be 0, not any number. In the
examples above, like 1-1/2^∞= 0.999..., n is not 0.

> | (4) 0.999...= 0.9 + 0.09+ 0.009 + 0.0009+ ...
> | = 0.09 + 0.9 + 0.0009 + 0.009+ ...
> | = 0.04+0.05 + 0.4+0.5+ 0.0004+0.0005+ 0.004+0.005+....
> | = 0.44+0.55 + 0.0044+0.0055+...
> = 1.
> | = 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.
> No. See any good textbook on how to calculate these limits.

The limit theory perfectly says THE LIMIT of lim(x->c) f(x) is L, why you
keep pretending I don't know limit better than you do? I am questioning f(c)=L (EQUAL), like
1/∞= 2/∞= 3/∞. Do all graph of n/x join at any remote point at infinite remote
point? There is no value x in ℝ such that 1/x=2/x=3/x, not even ∞ (not even valid
in your math.). I don't think you can find any valid logic except brainlessly reciting the
limit theory, as so far exhibited.

> > (5) More interpretations are possible
> *Sigh* I'd like to see just /one/ alternative interpretation. All
> anyone posts is bad algebra and one-line hints. Do the work. Define
> your extension to the reals and explain how algebra is to be done in
> this new set.

I don't see you really understand algebra.

> > Which one does "0.999..." really mean?
> 0.999... means lim(k->oo) Sum(k=1,n) 9/10^k. That limit is 1. It will
> mean that even if you stop being lazy and define what you want it to
> mean. All you will have done is add confusion. You should define (for
> example) 0.999___ and then you can prove that 0.999... =/= 0.999___.

It is you who are lazy, just reciting textbook to pass exam. for ???.

> > 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.
> You are not a dictator. You can't take away the meaning I (and vast
> numbers of boring old mathematicians) give to the symbols 0.999... Even
> when your great work is published it will (for a century or so at least)
> still mean lim(k->oo) Sum(k=1,n) 9/10^k.
>
> You can introduce ambiguity by not using the symbols like the rest of
> us, or you can be a proper mathematician and introduce an unambiguous
> way to say what you want. Of course, not only is that real work, you
> also have the up-hill struggle to persuade anyone to be interested.

Let's see. I estimate it won't take long. Because I try to be reasonable.

> > 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.
> If only! Yes they /can/ be defined. I just wish someone would get off
> their... er, I mean, stop prevaricating and do the work to define them
> and their operations.

A= Σ(n=1,∞) 1/2^n = 0.999... Agree?
If you really understand algebra, A!=B is logically unavoidable.

> > 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
> Or, more simply, prove that A = B = 1.
> > <=> 1-1/2^∞= 1-1/10^∞ // converted from the formula of geometric series
> > <=> 1/2^∞= 1/10^∞
> > <=> 5^∞=1
> > <=> false
> Not with the conventional meanings of any of these symbols.

I just use a perfectly defined symbol '∞', nothing more.
If you really understand algebra, the definition of '∞' is sufficient:
1. ∀n∈ℕ, n<∞
2. The multiplicative inverse of ∞ is 1/∞, the additive inverse is -∞

> > 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').
> Conclusion: you don't know what the symbols mean and you don't dare
> define new ones with the meaning you;d like them to have.
>
> --
> Ben.

The meaning the symbol ∞ used by you (and in textbook) is vague, all you
can say is "it is a concept", "it does not exist"..., nothing very significant.

On Friday, 26 August 2022 at 14:44:29 UTC+1, skepd...@gmail.com wrote:
> On Friday, 26 August 2022 at 15:39:16 UTC+2, malcolm.ar...@gmail.com wrote:
> > acos(sqrt(2)) = PI/4
> > You can prove that geometrically (draw a right angled triangle with unit small sides. It's an isosceles triangle because the
> > small sides are of equal length, and the angle between them is a right angle. So the other two angles must be PI/4).
> >
> > The numbers are irrational (the sides of the triangle are not ratios of each other, and the angle isn't a ratio of the angle an
> > arc subtends with two radii of its own length). But we can specify them exactly.
> Which has what to do with arithmetic on real numbers?
>
You said that no "operations" could be performed on irrationals of infinite precision.
So I gave an example of an operation. We've got one irrational (root 2) and one operation
(arc cosine) and, if we're working in radians, we obtain another irrational (PI/4). These are
exact.

On Friday, 26 August 2022 at 22:32:18 UTC+8, malcolm.ar...@gmail.com wrote:
> On Friday, 26 August 2022 at 14:44:29 UTC+1, skepd...@gmail.com wrote:
> > On Friday, 26 August 2022 at 15:39:16 UTC+2, malcolm.ar...@gmail.com wrote:
> > > acos(sqrt(2)) = PI/4
> > > You can prove that geometrically (draw a right angled triangle with unit small sides. It's an isosceles triangle because the
> > > small sides are of equal length, and the angle between them is a right angle. So the other two angles must be PI/4).
> > >
> > > The numbers are irrational (the sides of the triangle are not ratios of each other, and the angle isn't a ratio of the angle an
> > > arc subtends with two radii of its own length). But we can specify them exactly.
> > Which has what to do with arithmetic on real numbers?
> >
> You said that no "operations" could be performed on irrationals of infinite precision.
> So I gave an example of an operation. We've got one irrational (root 2) and one operation
> (arc cosine) and, if we're working in radians, we obtain another irrational (PI/4). These are
> exact.

Just comment. I don't get the point what you two are talking about.
The definition of pi is defined as the ratio of the circumference and diameter
of a circle. No other definition can 'exactly' define the value of pi.
Many irrationals can only be expressed like e, pi, sqrt(2), atan(1),...
My point is that if '∞' not defined, many existing irrationals are difficult to
talk about. e.g. many infinite series whose limit is pi but the 'value' of those
expressions are themselves, another irrational (endless process), not exactly pi.

On 8/26/22 11:38 AM, wij wrote:
> On Friday, 26 August 2022 at 22:32:18 UTC+8, malcolm.ar...@gmail.com wrote:
>> On Friday, 26 August 2022 at 14:44:29 UTC+1, skepd...@gmail.com wrote:
>>> On Friday, 26 August 2022 at 15:39:16 UTC+2, malcolm.ar...@gmail.com wrote:
>>>> acos(sqrt(2)) = PI/4
>>>> You can prove that geometrically (draw a right angled triangle with unit small sides. It's an isosceles triangle because the
>>>> small sides are of equal length, and the angle between them is a right angle. So the other two angles must be PI/4).
>>>>
>>>> The numbers are irrational (the sides of the triangle are not ratios of each other, and the angle isn't a ratio of the angle an
>>>> arc subtends with two radii of its own length). But we can specify them exactly.
>>> Which has what to do with arithmetic on real numbers?
>>>
>> You said that no "operations" could be performed on irrationals of infinite precision.
>> So I gave an example of an operation. We've got one irrational (root 2) and one operation
>> (arc cosine) and, if we're working in radians, we obtain another irrational (PI/4). These are
>> exact.
>
> Just comment. I don't get the point what you two are talking about.
> The definition of pi is defined as the ratio of the circumference and diameter
> of a circle. No other definition can 'exactly' define the value of pi.
> Many irrationals can only be expressed like e, pi, sqrt(2), atan(1),...
> My point is that if '∞' not defined, many existing irrationals are difficult to
> talk about. e.g. many infinite series whose limit is pi but the 'value' of those
> expressions are themselves, another irrational (endless process), not exactly pi.

What you seem to miss is tha "Infinite Sums" are defined by limit
theory. Thus, while at any finite stage, there total sum will not be
exactly pi, the final limit will be.

This is in fact, the nature of all the irrationals, we may not be able
to get an exact value in finite time, but their definition converges in
the limit to the exact value.

Some, like sqrt(2) have a "finite represention" in that computational
form, and we can perhaps do exact algerbra based on that form, but to
get a numeric "digits" representation is only available in the limit.

There are many series/sums that can be show DO exactly represent pi "in
the limit" which is the DEFINITION (in the Reals) of those series/sums.

On Friday, 26 August 2022 at 16:38:49 UTC+1, wyni...@gmail.com wrote:
> On Friday, 26 August 2022 at 22:32:18 UTC+8, malcolm.ar...@gmail.com wrote:
> > On Friday, 26 August 2022 at 14:44:29 UTC+1, skepd...@gmail.com wrote:
> > > On Friday, 26 August 2022 at 15:39:16 UTC+2, malcolm.ar...@gmail.com wrote:
> > > > acos(sqrt(2)) = PI/4
> > > > You can prove that geometrically (draw a right angled triangle with unit small sides. It's an isosceles triangle because the
> > > > small sides are of equal length, and the angle between them is a right angle. So the other two angles must be PI/4).
> > > >
> > > > The numbers are irrational (the sides of the triangle are not ratios of each other, and the angle isn't a ratio of the angle an
> > > > arc subtends with two radii of its own length). But we can specify them exactly.
> > > Which has what to do with arithmetic on real numbers?
> > >
> > You said that no "operations" could be performed on irrationals of infinite precision.
> > So I gave an example of an operation. We've got one irrational (root 2) and one operation
> > (arc cosine) and, if we're working in radians, we obtain another irrational (PI/4). These are
> > exact.
> Just comment. I don't get the point what you two are talking about.
> The definition of pi is defined as the ratio of the circumference and diameter
> of a circle. No other definition can 'exactly' define the value of pi.
> Many irrationals can only be expressed like e, pi, sqrt(2), atan(1),...
> My point is that if '∞' not defined, many existing irrationals are difficult to
> talk about. e.g. many infinite series whose limit is pi but the 'value' of those
> expressions are themselves, another irrational (endless process), not exactly pi.
>
e to the PI i equals minus one (Euler's identity). So if we can agree on e, i, and minus
one, then that gives us another definition of PI.
Whilst normally e is defined in terms of infinite series, it can also be defined as the
value for which the differential of e^x (taking tiny steps in x) is e^x.

However there is no finite sum of rationals which yields an irrational. So if you're
teaching mathematics, you need to make sure that there's at least a rudimentary
understanding of infinity before you introduce the concept of irrational numbers.

On Friday, 26 August 2022 at 23:38:49 UTC+8, wij wrote:
> On Friday, 26 August 2022 at 22:32:18 UTC+8, malcolm.ar...@gmail.com wrote:
> > On Friday, 26 August 2022 at 14:44:29 UTC+1, skepd...@gmail.com wrote:
> > > On Friday, 26 August 2022 at 15:39:16 UTC+2, malcolm.ar...@gmail.com wrote:
> > > > acos(sqrt(2)) = PI/4
> > > > You can prove that geometrically (draw a right angled triangle with unit small sides. It's an isosceles triangle because the
> > > > small sides are of equal length, and the angle between them is a right angle. So the other two angles must be PI/4).
> > > >
> > > > The numbers are irrational (the sides of the triangle are not ratios of each other, and the angle isn't a ratio of the angle an
> > > > arc subtends with two radii of its own length). But we can specify them exactly.
> > > Which has what to do with arithmetic on real numbers?
> > >
> > You said that no "operations" could be performed on irrationals of infinite precision.
> > So I gave an example of an operation. We've got one irrational (root 2) and one operation
> > (arc cosine) and, if we're working in radians, we obtain another irrational (PI/4). These are
> > exact.
> Just comment. I don't get the point what you two are talking about.
> The definition of pi is defined as the ratio of the circumference and diameter
> of a circle. No other definition can 'exactly' define the value of pi.
> Many irrationals can only be expressed like e, pi, sqrt(2), atan(1),...
> My point is that if '∞' not defined, many existing irrationals are difficult to
> talk about. e.g. many infinite series whose limit is pi but the 'value' of those
> expressions are themselves, another irrational (endless process), not exactly pi.

For those who doubt the result of calculus is refuted, not exactly.
The derivative result involving power function is checked exact, exponential and
trigonometric functions are still questionable (but the error is infinitesimal,
most engineering problems don't need to worry much).

On Friday, 26 August 2022 at 17:26:18 UTC+1, wyni...@gmail.com wrote:
> On Friday, 26 August 2022 at 23:38:49 UTC+8, wij wrote:
> > On Friday, 26 August 2022 at 22:32:18 UTC+8, malcolm.ar...@gmail.com wrote:
> > > On Friday, 26 August 2022 at 14:44:29 UTC+1, skepd...@gmail.com wrote:
> > > > On Friday, 26 August 2022 at 15:39:16 UTC+2, malcolm.ar...@gmail.com wrote:
> > > > > acos(sqrt(2)) = PI/4
> > > > > You can prove that geometrically (draw a right angled triangle with unit small sides. It's an isosceles triangle because the
> > > > > small sides are of equal length, and the angle between them is a right angle. So the other two angles must be PI/4).
> > > > >
> > > > > The numbers are irrational (the sides of the triangle are not ratios of each other, and the angle isn't a ratio of the angle an
> > > > > arc subtends with two radii of its own length). But we can specify them exactly.
> > > > Which has what to do with arithmetic on real numbers?
> > > >
> > > You said that no "operations" could be performed on irrationals of infinite precision.
> > > So I gave an example of an operation. We've got one irrational (root 2) and one operation
> > > (arc cosine) and, if we're working in radians, we obtain another irrational (PI/4). These are
> > > exact.
> > Just comment. I don't get the point what you two are talking about.
> > The definition of pi is defined as the ratio of the circumference and diameter
> > of a circle. No other definition can 'exactly' define the value of pi.
> > Many irrationals can only be expressed like e, pi, sqrt(2), atan(1),...
> > My point is that if '∞' not defined, many existing irrationals are difficult to
> > talk about. e.g. many infinite series whose limit is pi but the 'value' of those
> > expressions are themselves, another irrational (endless process), not exactly pi.
> For those who doubt the result of calculus is refuted, not exactly.
> The derivative result involving power function is checked exact, exponential and
> trigonometric functions are still questionable (but the error is infinitesimal,
> most engineering problems don't need to worry much).
>
Euler's number is the number you obtain when something grows in proportion to its
size, or to say the same thing in a different manner, changes rate of change by its
rate of change.

On 8/26/22 12:26 PM, wij wrote:
> On Friday, 26 August 2022 at 23:38:49 UTC+8, wij wrote:
>> On Friday, 26 August 2022 at 22:32:18 UTC+8, malcolm.ar...@gmail.com wrote:
>>> On Friday, 26 August 2022 at 14:44:29 UTC+1, skepd...@gmail.com wrote:
>>>> On Friday, 26 August 2022 at 15:39:16 UTC+2, malcolm.ar...@gmail.com wrote:
>>>>> acos(sqrt(2)) = PI/4
>>>>> You can prove that geometrically (draw a right angled triangle with unit small sides. It's an isosceles triangle because the
>>>>> small sides are of equal length, and the angle between them is a right angle. So the other two angles must be PI/4).
>>>>>
>>>>> The numbers are irrational (the sides of the triangle are not ratios of each other, and the angle isn't a ratio of the angle an
>>>>> arc subtends with two radii of its own length). But we can specify them exactly.
>>>> Which has what to do with arithmetic on real numbers?
>>>>
>>> You said that no "operations" could be performed on irrationals of infinite precision.
>>> So I gave an example of an operation. We've got one irrational (root 2) and one operation
>>> (arc cosine) and, if we're working in radians, we obtain another irrational (PI/4). These are
>>> exact.
>> Just comment. I don't get the point what you two are talking about.
>> The definition of pi is defined as the ratio of the circumference and diameter
>> of a circle. No other definition can 'exactly' define the value of pi.
>> Many irrationals can only be expressed like e, pi, sqrt(2), atan(1),...
>> My point is that if '∞' not defined, many existing irrationals are difficult to
>> talk about. e.g. many infinite series whose limit is pi but the 'value' of those
>> expressions are themselves, another irrational (endless process), not exactly pi.
>
> For those who doubt the result of calculus is refuted, not exactly.
> The derivative result involving power function is checked exact, exponential and
> trigonometric functions are still questionable (but the error is infinitesimal,
> most engineering problems don't need to worry much).

Nope, there derivative results of the trigonometric functions IS exact
(at least if you are talking in the domain of R, or possible R^N, like
the complex numbers).

The key is that if you are seeing infinitesimals, you have left the
concept of the Reals, as infinitesimals are not part of the Real Number
System.

Note, that as normally used, "Calculus" is a math field defined on the
Real Number Field (or with simple extension, the Complex Numbers or
Vectors in R^N)

Since it works by "defining" operations with a specific class of
infinitesimals that do not leave its operations, there are difficulties
with trying to combine it with other extensions to the Real Number
System that also add infinities and infinitesimals.

wij <wyniijj2@gmail.com> writes:

> On Friday, 26 August 2022 at 18:33:52 UTC+8, Ben Bacarisse wrote:
>> wij <wyni...@gmail.com> writes:
>>
>> > 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.
>> >>
>> >
>> > As said. 0.999... or "Repeating decimal" suffer from pattern
>> > interpretation problems:
>> Only here. The meaning of ... after digits is almost universally
>> agreed. So much so that other notations should be used for any other
>> meaning.
>
> Do you agree that derivation like this is not a proof?
> (high schools use such deductions to 'prove' repeating decimals are
> rational).

What a shame. But it's irrelevant to the discussion here.

> Proof: 1=0.999...
> x=0.999...
> 10x= 9.999...
> 10x= 9+x
> 9x=9
> x=1

Eh? The fact that 0.999... = 1 comes from (a) defining field in
question (the reals), (b) defining what the ... means (an infinite sum),
(c) defining what an infinite sum is (the limit of the sequence on
partial sums), and finally, showing that the limit of the sum in
question is 1.

>> > (1) 0.999...= 0.(9) = 0.(99)= 0.(999)
>> Yes.
>
> You should say no. They are not what "∑(n=1,∞) 9/10^n)" mean.

They all mean the same. The ()s denote repetition of digits. They have
no effect on how the sum of digits is determined.

>> > (2) 0.999...= 0.((9)(99)) // Andy Walker provided such
>> > interpretation
>> No. Just write 0.((9)(99)) if that's what you mean (and explain the
>> concept either in terms of games or order relations).
>
> The example is given by Andy. It could be valid to mean something.

Not my concern. Cranks often misrepresent what others have said and I
am not going to defend something I never said.

>> > (3) 1-1/∞= 0.999...
>>
>> Introducing a new number called ∞ by which one can divide other numbers
>> does not produce any clarity. It produces even more ambiguity. What I
>> would like to see from a "alterntivist" is clarity. If that requires a
>> new number, so be it, but the set of numbers needs to be defined along
>> with the operations on those.
>
> The symbol ∞ I use is perfectly defined, not like yours.

Yet I have not see a definition of it from you. Why is that?

>> > 1-2/∞= 0.999...
>> > 1-3/2^∞= 0.999...
>> > 1-4/10^∞= 0.999...
>> Without further explanation I will conclude that n/∞ = 0 and that n/k^∞
>> = 0. That does not sound very useful, but what else can I conclude from
>> your lack of explanation?
>
> You are using your ambiguous ∞ again.

Don't be silly. It's not "my" ∞. You used it in a context in which I
can determine that the sub-expression (e.g. 3/∞) is zero. You give no
meaning for 3/∞ other than it must be zero, since you now know that
0.999... = 1. I will make any deductions I like based on the fact that
0.999... = 1 so you really should start using some new notation what
whatever it is you want to be "not quite 1".

>> | (4) 0.999...= 0.9 + 0.09+ 0.009 + 0.0009+ ...
>> | = 0.09 + 0.9 + 0.0009 + 0.009+ ...
>> | = 0.04+0.05 + 0.4+0.5+ 0.0004+0.0005+ 0.004+0.005+....
>> | = 0.44+0.55 + 0.0044+0.0055+...
>> = 1.
>> | = 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.
>> No. See any good textbook on how to calculate these limits.
>
> The limit theory perfectly says THE LIMIT of lim(x->c) f(x) is L, why you
> keep pretending I don't know limit better than you do?

You don't know how to define the other sort of limit. It's staggering
that you will accuse several people who appear to have degrees in
mathematics of not knowing how limits are defined simply because you
think there is only one.

> I am questioning f(c)=L (EQUAL),

No one is talking about such a limit. Pick up a book. Learn about the
asymptotic limit and then start being more respectful of the years some
people have put into learning about this material.

> like 1/∞= 2/∞= 3/∞. Do all graph of
> n/x join at any remote point at infinite remote point? There is no
> value x in ℝ such that 1/x=2/x=3/x, not even ∞ (not even valid in your
> math.).

Indeed. So whatever is you meant by ∞ when you wrote that 1-2/∞=
0.999... was not in ℝ. Will you ever say what it is? I doubt it. That
would involve doing some real work.

> I don't think you can find any valid logic except brainlessly
> reciting the limit theory, as so far exhibited.

Yes, I am stuck having to report on the result of four centuries of
mathematical investigation into the reals, limits and calculus.

>> > (5) More interpretations are possible
>> *Sigh* I'd like to see just /one/ alternative interpretation. All
>> anyone posts is bad algebra and one-line hints. Do the work. Define
>> your extension to the reals and explain how algebra is to be done in
>> this new set.
>
> I don't see you really understand algebra.

Of course you don't.

>> > Which one does "0.999..." really mean?
>> 0.999... means lim(k->oo) Sum(k=1,n) 9/10^k. That limit is 1. It will
>> mean that even if you stop being lazy and define what you want it to
>> mean. All you will have done is add confusion. You should define (for
>> example) 0.999___ and then you can prove that 0.999... =/= 0.999___.
>
> It is you who are lazy, just reciting textbook to pass exam. for ???.

But I am not claiming anything new or interesting. Should I join the
massed ranks of cranks that post here and make something up, just so you
can't call me lazy? No, that would be daft. So, yes, I will be lazy.
I will continue to recite the accumulated understanding I got from my
many years of education.

>> > 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.
>> You are not a dictator. You can't take away the meaning I (and vast
>> numbers of boring old mathematicians) give to the symbols 0.999... Even
>> when your great work is published it will (for a century or so at least)
>> still mean lim(k->oo) Sum(k=1,n) 9/10^k.
>>
>> You can introduce ambiguity by not using the symbols like the rest of
>> us, or you can be a proper mathematician and introduce an unambiguous
>> way to say what you want. Of course, not only is that real work, you
>> also have the up-hill struggle to persuade anyone to be interested.
>
> Let's see. I estimate it won't take long. Because I try to be
> reasonable.

No, refusing to say what you mean is not reasonable.

>> > 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.
>> If only! Yes they /can/ be defined. I just wish someone would get off
>> their... er, I mean, stop prevaricating and do the work to define them
>> and their operations.

Still no definition of what you mean of course.

> A= Σ(n=1,∞) 1/2^n = 0.999... Agree?

Yes, because 0.999... = Σ(n=1,∞) 9/10^n = 1.

> If you really understand algebra, A!=B is logically unavoidable.

The B you defined before: B= Σ(n=1,∞) 9/10^n, has the same sum.

Ultimately, there is no getting around this basic disagreement. And if
you knew how to find the sum (i.e. the limit of the sequence of partial
sums) you would know that the sums are equal. This is an argument on
the level of 2+2 != 1+3. The truth of the matter follows from the
conventional meaning of the symbols.

>> > 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
>> Or, more simply, prove that A = B = 1.
>> > <=> 1-1/2^∞= 1-1/10^∞ // converted from the formula of geometric series
>> > <=> 1/2^∞= 1/10^∞
>> > <=> 5^∞=1
>> > <=> false
>> Not with the conventional meanings of any of these symbols.
>
> I just use a perfectly defined symbol '∞', nothing more.

Ben Bacarisse <ben.usenet@bsb.me.uk> writes:
> wij <wyniijj2@gmail.com> writes:
[...]
>> I just use a perfectly defined symbol '∞', nothing more.
>
> Ah. You think that's a definition. I see the problem. It isn't.
>
>> If you really understand algebra, the definition of '∞' is sufficient:
>> 1. ∀n∈ℕ, n<∞
>> 2. The multiplicative inverse of ∞ is 1/∞, the additive inverse is
>> -∞
>
> Even this is not a definition. Have you read anything about extensions
> to the reals? That would show you how this sort of thing needs to be
> defined. (And why are you talking about ℕ?)
[...]

A couple of weeks ago, I asked wij whether they were talking about the
hyperreals or not. They weren't even able to answer that. That's about
where I gave up.

Part of the discussion:

I wrote:
>> If ∞-(x+1) < ∞-x, then you have multiple infinite values, even if you
>> only use the term "∞" to refer to one of them.
>>
>> More concretely, you seem to be saying that ∞-1 and ∞-2 are distinct
>> values. They're clearly both infinite, right? But neither of them is
>> equal to ∞?
>>
>> Certainly there are systems in which that's all true -- but I don't know
>> what system you're working with.
>>
>> If you're talking about hyperreals, you can save a lot of time and
>> effort by saying so. Likewise if you're talking about some other well
>> defined system in which ∞ is treated as a unique number. There are a
>> number of such systems.
>> [...]

wig replied:
> I read your reply many times and still not sure what it means.
> IIUC, the concern of naming issue depends on how things develop.

I would have though that "Are you talking about hypperreals or not?"
(which is a *slight* simplification of what I wrote) would be an easy
question to answer.

--
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 8/26/22 5:59 PM, Keith Thompson wrote:
> Ben Bacarisse <ben.usenet@bsb.me.uk> writes:
>> wij <wyniijj2@gmail.com> writes:
> [...]
>>> I just use a perfectly defined symbol '∞', nothing more.
>>
>> Ah. You think that's a definition. I see the problem. It isn't.
>>
>>> If you really understand algebra, the definition of '∞' is sufficient:
>>> 1. ∀n∈ℕ, n<∞
>>> 2. The multiplicative inverse of ∞ is 1/∞, the additive inverse is
>>> -∞
>>
>> Even this is not a definition. Have you read anything about extensions
>> to the reals? That would show you how this sort of thing needs to be
>> defined. (And why are you talking about ℕ?)
> [...]
>
> A couple of weeks ago, I asked wij whether they were talking about the
> hyperreals or not. They weren't even able to answer that. That's about
> where I gave up.
>
> Part of the discussion:
>
> I wrote:
>>> If ∞-(x+1) < ∞-x, then you have multiple infinite values, even if you
>>> only use the term "∞" to refer to one of them.
>>>
>>> More concretely, you seem to be saying that ∞-1 and ∞-2 are distinct
>>> values. They're clearly both infinite, right? But neither of them is
>>> equal to ∞?
>>>
>>> Certainly there are systems in which that's all true -- but I don't know
>>> what system you're working with.
>>>
>>> If you're talking about hyperreals, you can save a lot of time and
>>> effort by saying so. Likewise if you're talking about some other well
>>> defined system in which ∞ is treated as a unique number. There are a
>>> number of such systems.
>>> [...]
>
> wig replied:
>> I read your reply many times and still not sure what it means.
>> IIUC, the concern of naming issue depends on how things develop.
>
> I would have though that "Are you talking about hypperreals or not?"
> (which is a *slight* simplification of what I wrote) would be an easy
> question to answer.
>

I think that wij ultimate doesn't understand the various Trans-Finite
number systems, but just wants to work in some system call "The Reals"
that happens to have infinites added to them.

Skep Dick <skepdick22@gmail.com> writes:

> On Friday, 26 August 2022 at 14:44:08 UTC+2, Ben Bacarisse wrote:
>> So you still want me to waste time typing out standard material from
>> goodness know how many sources? No. Go read them.
>
> Fucking idiot. Nobody is asking you to post "standard material" or ANY
> material.

That's good.

> I am asking you to identify WHICH standard you think is THE standard.

Limits in real analysis. Do you mean to say you've been commenting on
an infinite sum without knowing what such things "usually" mean? Why
would you say anything about a topic when you don't know the standard
meanings?

>> If you don't know what 0.999... = 1 means, you know where you can find
>> out.
>
> Fucking idiot! Of courseI know what it means in gneral! It means a
> Boolean!

No. I seriously doubt you don't know what it means, but if you don't
why did you ever think it was reasonable to talk about the subject?

> But I am not interested in general answers, I am looking for the
> particular and precis answer. I am looking for the Boolean value YOU
> have assigned to it, and of course I know where I can find that
> out. The location of that information is in YOUR head. That is
> PRECISELY why I am asking YOU.

OK. But I don't have to play that game do I?

The big picture here is that I am not trying to persuade you of
anything. You can find out how an infinite sum of digit values is
defined if you really don't know (which I doubt). If you never get to
know what I mean, well, fine. Why should I care?

>> The question is what /you/ mean. That will remain a mystery because you
>> won't say more than report, as stated, silly uncontested facts like
>> "0.999... + epsilon = 1" is true.
>
> What the fuck?! I have told you over and over what /I/ mean!
>
> I have assigned the Boolean value "True" to the type "0.999... +
> epsilon = 1". That's precisly what it means!
>
> "0.999... + epsilon = 1" means True:Boolean

So what? Since 0.999... = 1 of course 0.999... + epsilon = 1 is true
(technically satisfiable). Of course that's not what you mean, but you
dare not say more since you fear being too clearly wrong.

> Do you even understand what you are asking?!?

More to the point, do you even know what you are saying?

--
Ben.

Skep Dick <skepdick22@gmail.com> writes:

> On Friday, 26 August 2022 at 12:33:52 UTC+2, Ben Bacarisse wrote:
>> Conclusion: you don't know what the symbols mean and you don't dare
>> define new ones with the meaning you;d like them to have.
>
> Yeeep. Drunk me was 100% right. We have a priest/zealot in the house!

More wine? Attempts to insult me don't later the facts. If you want to
know what I mean the information is readily available on the web. Any
one who would like to know what /you/ mean gets called a priest. So be
it, but we still don't know what you mean. And I suspect we never will.

> Nor could he even tell you what ∞ and "->" denote in the expression
> lim(k -> ∞)

I could, but I won't, because it's standard and available in any course
on real analysis. It's a troll move to get me to waste time telling you
things you should have learnt before commenting on this topic. But I
think the tread is working out just fine for you, no?

--
Ben.

On Saturday, 27 August 2022 at 01:59:19 UTC+2, Ben Bacarisse wrote:
> More wine? Attempts to insult me don't later the facts.
I don't have to insult you. You insult yourself by appealing to "facts" in Mathematics.

There are cultural trends and fads, sure - but facts? Heh!

>If you want to know what I mean the information is readily available on the web.
That is soooo peculiar to me, the location of YOUR meaning is NOT in your own head, but on the web?!?

Wow! Bourbaki really were right - you morons have totally debased meaning in Mathematics.

>Any one who would like to know what /you/ mean gets called a priest. So be
> it, but we still don't know what you mean. And I suspect we never will.
The confusion is all yours. There are multiple possible theories of formal semantics you see.

Or maybe you don't see.

> I could, but I won't, because it's standard and available in any course on real analysis.
OH! You mean the coursework that has been bullshiting us about epsilon-delta calculus for centuries?

No thanks. Liebnitz and Newton (actual Mathematicians) did it much better than the abstract academic monkeys.

>It's a troll move to get me to waste time telling you things you should have learnt before commenting on this topic.
I did learn them. And right after my Mathematic class I went to Physics class. And guess what? Apparently Physicists don't care about epsilon-delta. They never left the universe of infinitesimals - physicists just differentiate anywhere, everywhere, whenever they like.

>But I think the tread is working out just fine for you, no?
If by "fine" you mean your utmost refusal to tell me which theory of meaning you subscribe to... then sure.