Finally the discussion is over: S = Lim S is a bad definition.

[John Gabriel]

Finally the discussion is over: S = Lim S is a bad definition.

https://www.youtube.com/watch?v=NBOs-Xf_UIg

Comments are unwelcome and will be ignored.

Posted on this newsgroup in the interests of public education and to eradicate ignorance and stupidity from mainstream mythmatics.

gils...@gmail.com (MIT)
huiz...@psu.edu (HARVARD)
and...@mit.edu (MIT)
david....@math.okstate.edu (David Ullrich)
djo...@clarku.edu
mar...@gmail.com

[burs...@gmail.com]

Since math did work with you, maybe try something else?
How about cheese rolling, maybe you can excel there?

Cheese Rolling 2017 at Cooper's Hill
https://www.youtube.com/watch?v=pK1j06Gjp94

[burs...@gmail.com]

Could be a nice addition to the stupidity award you won here:
https://groups.google.com/d/msg/sci.math/bgU-4JWvHbY/0OECkpHlBgAJ

[j4n bur53]

Or if you use the new mongo lingo of bird brain
John Gabriel, you can also call it "not determinable".
doesn't matter how you call it, a sequence is not
the same as a value, but Euler clearly didn't use

sequence notation in his public tailored publication,
he used the infinite sum notation, thats John Gabriels
error, that he thinks the following is not a
limit notation, but a sequence notation:

a1 + a2 + a3 + ...

Here you find a nice publication by Euler, where
he indeed mentions a sequence, and he uses this notation:

(1), (2), (3), ...
E334 -- Recherches generales sur la mortalite et
la multiplication du genre humain
http://eulerarchive.maa.org//docs/originals/E334.pdf

So the difference is that he uses a comma in the
above, and not a summation sign. It is not the case
that mathematicians only wrote up sequences after
Euler, sequence notation existed already during times

of Euler. And clearly there is no Euler blunder S=Lim S,
this is complete bird bran John Gabriel nonsense,
to denote a sequence, Euler would have used the comma.
BTW in the same paper E334, you later find

also sum instead of comma, so Euler was even able
to use sequence and series side by side.

Am Dienstag, 3. Oktober 2017 23:51:43 UTC+2 schrieb burs...@gmail.com:
> limit, since {an} or (an) wants to
> indicate a multiplicity of values, but

John Gabriel schrieb:

[Me]

On Wednesday, October 4, 2017 at 12:03:53 AM UTC+2, John Gabriel wrote:

> Finally the discussion is over

Was there ever a discussion?

> S = Lim S is

nonsense. Right. But this was clear from the beginning.

[j4n bur53]

BTW: It took me 2 minutes to find a sequence notation
in the works of Euler, maybe further examples can
be found. I used this website:

In 1910 and 1913, Swedish Mathematician Gustav
Eneström completed a comprehensive survey of
Euler's works. He counted and enumerated 866
distinct works, including books, journal articles,
and some letters he deemed to be especially important.
Each of these was assigned a number, from E1 to
E866, which is now referred to as the "Eneström
number." Most historical scholars today use
Eneström numbers to identify Euler's
writings quickly."
http://eulerarchive.maa.org/index/enestrom.html

The sequence notation I found is not perfect,
since later in his paper he stops with his
mortality considerations at age=100.

But I guess everybody gets the idea...?!

j4n bur53 schrieb:

[j4n bur53]

Well you have to account for bird brain John Gabriels
incapacitation, in that he has zero brains, so

everything is probably foggy for him. His shoes,
his toothbrush, math, Euler, etc..

Me schrieb:

[j4n bur53]

One more example, comma, on the first page:
http://eulerarchive.maa.org//docs/originals/E449.pdf

j4n bur53 schrieb:

[j4n bur53]

I didn't pay attention frankly over the last months.
You are still doing new videos? What for?

Like 1 year ago you had only 198 subscribers,
now you have only 198 subscribers. What happened?

John Gabriel schrieb:

[j4n bur53]

Did you gas your students, like Hitler, or what?

j4n bur53 schrieb:

[Dan Christensen]

On Tuesday, October 3, 2017 at 6:03:53 PM UTC-4, John Gabriel wrote:
> Finally the discussion is over: S = Lim S is a bad definition.
>

Yup, that was your biggest blunder yet, Troll Boy. And that's saying a LOT!

You mistakenly attributed "S = Lim S" to Euler, but when I confronted you with the evidence, even you had to concede, "Of course he [Euler] did not write 'Lim S'... He did not talk about S." (May 27, 2017)

A sane person would have apologized for the error and left it that. But not you, eh, Troll Boy?


Dan

Download my DC Proof 2.0 software at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com

[John Gabriel]

On Tuesday, 3 October 2017 18:24:16 UTC-4, Me wrote:
> On Wednesday, October 4, 2017 at 12:03:53 AM UTC+2, John Gabriel wrote:
>
> > Finally the discussion is over
>
> Was there ever a discussion?

No. I was right all along. It was a very dumb definition by Euler.

>
> > S = Lim S is
>
> nonsense. Right. But this was clear from the beginning.

Yes. Of course S = Lim S is nonsense. So why do you still believe in it?

[burs...@gmail.com]

So if 0.999... <> 1, do we have:

0.999... < 1

Or rather?

0.999... > 1

[burs...@gmail.com]

So whats this Gabriel number:

lim n->oo 0.999...9995 = ?
\---n---/

[burs...@gmail.com]

Well its the mean value between 0.999... and 1.0.
Look if we have a and b, the mean value is (a+b)/2:

a b (a+b)/2
0.9 1.0 0.95
0.99 1.00 0.995
0.999 1.000 0.9995
0.9999 1.0000 0.99995
Etc..

If 0.999... <> 1, then also 0.999... <> 0.999...9995
and then also 0.999...9995 <> 1.

And so on, as soon 0.999... <> 1, there are miriad
other numbers inbetween.

My suggestion: Don't do this nonsense, just interpret
0.999... as limit. Then you can also interpret

0.999..9995 as limit, namely this charming limit,
the following summands summed up to finity:

0.5
0.45
0.045
0.0045
...

Guess what is the result?

1/2+sum_i=1^n (45/10^(i+1)) = 1/2 + (1 - 10^(-n))/2

lim n->oo 1/2 + (1 - 10^(-n))/2 = 1

[burs...@gmail.com]

But if you plot the two series, 0.999... and 0.999...9995
you will see that neither of them is below the other,
there is always one summand that makes it bigger:

0.999... 0.999...9995
0.9
0.95
0.99
0.995
0.999
0.9995
Etc..

So we can only conclude Eulers series are brilliant,
interpreting a1+a2+a3+... as lim n->oo sum an, is
the only viable way,

any non-standard numbers with 0.999... != 1 dont
make any sense, they dont obey the standard laws
of algebra and blow up the

number space with a lot of cripples.

[Zelos Malum]

Whats that ugly shit on the upper right? Looks like el chubacabra

and you still aren't fucking getting the definition.

[John Gabriel]

On Tuesday, 3 October 2017 20:32:47 UTC-4, burs...@gmail.com wrote:
> Well its the mean value between 0.999... and 1.0.

What are you saying you baboon, what are you mumbling about? You can only calculate an arithmetic mean between well formed numbers you moron! 0.999... is NOT a number of any kind. It represents a SERIES. If you define it stupidly as Euler did to be equal to its limit, then you are taking the mean of 1 and 1. There is nothing to do you HUGE APE!!!!

Grow a brain. You sit pounding out your brain farts on sci.math. Get a job idiot!!!!! No one will hire you once they read the crap you write here.

<6 year old rant>

[John Gabriel]

On Tuesday, 3 October 2017 23:07:23 UTC-4, Zelos Malum wrote:
> Whats that ugly shit on the upper right? Looks like el chubacabra

You probably look like shit and that's why you are deluded into thinking you have this "mysterious air" about you. I laughed so much when I saw that in your profile on mathstackexchange. Too scared to show the world what a dipshit you look like eh? Chuckle. My guess is you are fat, freckled and screaming ugly.

> and you still aren't fucking getting the definition.

No one understands definitions like I do you fuckwad! I was the first to devise a set of guidelines while gorillas like you have eat their shit.

https://www.youtube.com/watch?v=oAQubtm-IPg

[burs...@gmail.com]

el cubacabra muito coco loco wrote:

"You can only calculate an arithmetic mean
between well formed numbers you moron!
0.999... is NOT a number of any kind.
It represents a SERIES. If you define
it stupidly as Euler did to be equal
to its limit, then you are taking the
mean of 1 and 1."

Well then, why is 0.999... <> 1 in the first place?

[John Gabriel]

On Wednesday, 4 October 2017 05:54:28 UTC-4, burs...@gmail.com wrote:
> el cubacabra muito coco loco wrote:
>
> "You can only calculate an arithmetic mean
> between well formed numbers you moron!
> 0.999... is NOT a number of any kind.
> It represents a SERIES. If you define
> it stupidly as Euler did to be equal
> to its limit, then you are taking the
> mean of 1 and 1."
>
> Well then, why is 0.999... <> 1 in the first place?

Why should it be? Just because Euler defined it that way???!!!

[Zelos Malum]

Den onsdag 4 oktober 2017 kl. 11:33:07 UTC+2 skrev John Gabriel:
> On Tuesday, 3 October 2017 23:07:23 UTC-4, Zelos Malum wrote:
> > Whats that ugly shit on the upper right? Looks like el chubacabra
>
> You probably look like shit and that's why you are deluded into thinking you have this "mysterious air" about you. I laughed so much when I saw that in your profile on mathstackexchange. Too scared to show the world what a dipshit you look like eh? Chuckle. My guess is you are fat, freckled and screaming ugly.

Why would I show my picture all over the place? I have no inclination of doing it as it serves no purpose. Maybe I am ugly, maybe I am not. You are definately it and showing it to the world and what is worse for you is that you are ugly AND stupid. If I am ugly, I am just ugly, but very smart.

>No one understands definitions like I do you fuckwad! I was the first to devise a set of guidelines while gorillas like you have eat their shit.

You don't understand it AT ALL! that is the issue and that is why you think you can push it over. Because all you got is a strawman.

>No one understands definitions like I do you fuckwad! I was the first to devise a set of guidelines while gorillas like you have eat their shit.

If euler defined it or not is irrelevant, we do not care about the name but the structure itself and in real numbers, in all of their definitions, 0.999... must equal 1, there cannot be any other way for it to be.

[7777777]

torstai 5. lokakuuta 2017 8.44.17 UTC+3 Zelos Malum kirjoitti:
> 0.999... must equal 1, there cannot be any other way for it to be.

fail.

in real numbers 0.(9) is not equal to 1.

[FromTheRafters]

After serious thinking 7777777 wrote :

Yes, it is. If it and zero were two different real numbers, there would
be at least one more real number sitting between them.

See the density property of the reals.

[John Gabriel]

On Thursday, 5 October 2017 01:44:17 UTC-4, Zelos Malum wrote:
> Den onsdag 4 oktober 2017 kl. 11:33:07 UTC+2 skrev John Gabriel:
> > On Tuesday, 3 October 2017 23:07:23 UTC-4, Zelos Malum wrote:
> > > Whats that ugly shit on the upper right? Looks like el chubacabra
> >
> > You probably look like shit and that's why you are deluded into thinking you have this "mysterious air" about you. I laughed so much when I saw that in your profile on mathstackexchange. Too scared to show the world what a dipshit you look like eh? Chuckle. My guess is you are fat, freckled and screaming ugly.
>
> Why would I show my picture all over the place?

Because ugly people are jealous of others. You are ugly both outside and inside. If you show your photo, everyone will see that you are a troll.

> If I am ugly, I am just ugly, but very smart.

Chuckle. You are one of the biggest morons I have tried to educate.

You understand nothing you dipshit. You can't even grasp the simplest definitions. You are an absolute delusional idiot.

> I was the first to devise a set of guidelines while gorillas like you have eat their shit.
>
> You don't understand it AT ALL! that is the issue and that is why you think you can push it over. Because all you got is a strawman.

Bla, bla, bla. Nah Uh and objections can be shoved up your fat arse. Your assertions are nothing but pooh.

>
> >No one understands definitions like I do you fuckwad! I was the first to devise a set of guidelines while gorillas like you have eat their shit.
>
> If euler defined it or not is irrelevant,

It is a fact that you need to acknowledge and it MATTERS a hell of a lot!

> we do not care about the name but the structure itself and in real numbers, in all of their definitions, 0.999... must equal 1,

MUST??!!! Fail you moron. Fail.

> there cannot be any other way for it to be.

It cannot be and I am changing this bullshit! You will comply withe me moron!!!!

[Zelos Malum]

Incorrect, as per usual. It is trivial to prove it using dedekinds, cauchy or any number of other methods.

[Dan Christensen]

On Wednesday, October 4, 2017 at 6:32:50 AM UTC-4, John Gabriel wrote:
> On Wednesday, 4 October 2017 05:54:28 UTC-4, burs...@gmail.com wrote:
> > el cubacabra muito coco loco wrote:
> >
> > "You can only calculate an arithmetic mean
> > between well formed numbers you moron!
> > 0.999... is NOT a number of any kind.
> > It represents a SERIES. If you define
> > it stupidly as Euler did to be equal
> > to its limit, then you are taking the
> > mean of 1 and 1."
> >
> > Well then, why is 0.999... <> 1 in the first place?
>
> Why should it be? Just because Euler defined it that way???!!!
>

Well, Troll Boy, why don't you show the world how it is possible to do science and engineering even better if we ban the use of 0, negative numbers, pi, root 2 (and all other irrational numbers), 0.333... , 0.999... (and all other repeating decimals), and all axioms and all rules of logic (and whatever else you may have banned lately because you couldn't shoehorn it into your goofy system). If you thought your Wacky New Calclueless was a hard sell...

What a moron.

[John Gabriel]

On Tuesday, 3 October 2017 18:03:53 UTC-4, John Gabriel wrote:
> Finally the discussion is over: S = Lim S is a bad definition.
>
> https://www.youtube.com/watch?v=NBOs-Xf_UIg
>
> Comments are unwelcome and will be ignored.
>
> Posted on this newsgroup in the interests of public education and to eradicate ignorance and stupidity from mainstream mythmatics.
>
> gils...@gmail.com (MIT)
> huiz...@psu.edu (HARVARD)
> and...@mit.edu (MIT)
> david....@math.okstate.edu (David Ullrich)
> djo...@clarku.edu
> mar...@gmail.com

The conclusion is that Euler's definition is ill-formed and the orangutans of the past 300 years have shame written all over their stupid faces.

[Mr Sawat Layuheem]

เมื่อ วันพฤหัสบดีที่ 5 ตุลาคม ค.ศ. 2017 18 นาฬิกา 20 นาที 43 วินาที UTC+7, John Gabriel เขียนว่า:

https://www.facebook.com/photo.php?fbid=883010801853912&set=a.397252653763065.1073741825.100004350013006&type=3&theater

[Dan Christensen]

On Thursday, October 5, 2017 at 7:20:43 AM UTC-4, John Gabriel wrote:

> The conclusion is that Euler's definition is ill-formed and the orangutans of the past 300 years have shame written all over their stupid faces.

No, the conclusion is that John "Troll Boy" Gabriel has much egg on this face for this, the biggest blunder of his trolling career: Deliberately misquoting Euler and being caught out again and again. What a moron.

[Markus Klyver]

0.999... is a short hand for an infinite sum which we define as the limit of a finite sum as the number of terms approaches infinity.

Den torsdag 5 oktober 2017 kl. 08:01:05 UTC+2 skrev 7777777:
> torstai 5. lokakuuta 2017 8.44.17 UTC+3 Zelos Malum kirjoitti:
> > 0.999... must equal 1, there cannot be any other way for it to be.
>
> fail.
>
> in real numbers 0.(9) is not equal to 1.

It indeed does. Or how do you define 0.(9)?

[John Gabriel]

On Thursday, 5 October 2017 09:44:43 UTC-4, Markus Klyver wrote:
> Den onsdag 4 oktober 2017 kl. 11:27:43 UTC+2 skrev John Gabriel:
> > On Tuesday, 3 October 2017 20:32:47 UTC-4, burs...@gmail.com wrote:
> > > Well its the mean value between 0.999... and 1.0.
> >
> > What are you saying you baboon, what are you mumbling about? You can only calculate an arithmetic mean between well formed numbers you moron! 0.999... is NOT a number of any kind. It represents a SERIES. If you define it stupidly as Euler did to be equal to its limit, then you are taking the mean of 1 and 1. There is nothing to do you HUGE APE!!!!
> >
> > Grow a brain. You sit pounding out your brain farts on sci.math. Get a job idiot!!!!! No one will hire you once they read the crap you write here.
> >
> > <6 year old rant>
>

> 0.999... is a short hand for an infinite sum (S = 0.9+0.09+0.009+...) which we define as the limit of a finite sum (Lim S = Lim {n \to \infty} 1-10^(-n)) as the number of terms approaches infinity.

Yes, S = Lim S. Clear as water.

It is an ill-formed definition because S is NOT the same as Lim S.

How about this definition: Mercedes = cheese cake.

Do you think it is well formed?

[Dan Christensen]

On Thursday, October 5, 2017 at 1:22:37 PM UTC-4, John Gabriel wrote:

> >
> > 0.999... is a short hand for an infinite sum (S = 0.9+0.09+0.009+...) which we define as the limit of a finite sum (Lim S = Lim {n \to \infty} 1-10^(-n)) as the number of terms approaches infinity.
>
> Yes, S = Lim S. Clear as water.
>

Wrong again, Troll Boy. That should be:

S = Lim(n-->oo): S_n

where S_n = 1 - 1/10^n (the nth partial sum)

S_1 = 0.9
S_2 = 0.99
S_3 = 0.999

and so on.

[Dan Christensen]

On Thursday, October 5, 2017 at 2:22:40 PM UTC-4, Dan Christensen wrote:
> On Thursday, October 5, 2017 at 1:22:37 PM UTC-4, John Gabriel wrote:
>
> > >
> > > 0.999... is a short hand for an infinite sum (S = 0.9+0.09+0.009+...) which we define as the limit of a finite sum (Lim S = Lim {n \to \infty} 1-10^(-n)) as the number of terms approaches infinity.
> >
> > Yes, S = Lim S. Clear as water.
> >
>
> Wrong again, Troll Boy. That should be:
>
> S = Lim(n-->oo): S_n
>
> where S_n = 1 - 1/10^n (the nth partial sum)
>
> S_1 = 0.9
> S_2 = 0.99
> S_3 = 0.999
>
> and so on.

Or equivalently, S_n = Sum(k=1,n): 9/10^k

[John Gabriel]

Also, consider that you don't have a unique decimal representation of any number if you define the series to be the limit. For example, both of the following series have the same limit:

0.999... = 9/10 + 9/100 + ...
0.875... = 1/2 + 1/4 + 1/8 + ...

So if we define them both as 1, then 0.999... = 1 and 0.875... = 1. How do we identify what series we are dealing with if we only have the limit? There are innumerably many series with the same limit of 1.

On the one hand you berate the limit and on the other hand you invoke it. What is more important, the series or its limit? You seem to think the limit does not matter and then you go right ahead and DEFINE the series to be equal to its limit?! Isn't that stupid?

A series is NOT a LIMIT. In fact, no matter if you could hypothetically sum all the terms of 3/10 + 3/100 + ..., you would never arrive at 1/3 because 1/3 is not measurable in base 10.

Do you understand that expression "measurable in base 10"? It means expressing any rational number using a given base. There is no fraction p/q such that q=10^n with n integer and p/q = 1/3. It's impossible my little stupid. There is a theorem stating this. You defining S = Lim S goes against the theorem. You just can't use ill-formed definitions. They break everything.

Get it?

[burs...@gmail.com]

Thats a little bit far fetched.

Decimal representation is a more narrow notion than series.
Decimal repreentations are only series of the form:

d0.d1 d2 d3 .... with di in {0,..,9}

Or if you want you can write it:

d0 + d1/10 + d2/100 + d3/1000 + ...

You "decimal" means 10, so this a base 10 digit series.
On the otherhand this one here is not a decimal, base 10,
representation:

1/2 + 1/4 + 1/8 + ... = 1

Got it?

[burs...@gmail.com]

Now there is a simple proof, that every Cauchy sequence
is equivalent to at least one decimal representation.

The decimal representation is simply
the limit of the sequence:

bk = floor(a*10^k)*10^(-k)

But the above would be circular, since "a" above is the
real number corresponding to the Cauchy sequence we

want to decimally represent. Can we extract the decimal
representation from a Cauchy sequence without the

detour of a real? Since the sequence converges, we
have a function N(e) such that:

forall n>=N(e) |an-a| < e

When can we use aj instaed of a to compute bk? We
need to assure the following where fk=bk*10^k and
fk is an integer:

fk =< a*10^k < fk

fk =< aj*10^k < fk

Use fk=floor(aj*10^k) and compute the distance:

d = min(aj*10^k-fk,fk+1-aj*10^k)

And check:

j>=N(d)

Always increment j, but increment k when the
check succeeds. Does it work?

[John Gabriel]

On Thursday, 5 October 2017 15:09:12 UTC-4, burs...@gmail.com wrote:
> That ...

> You "decimal" means 10, so this a base 10 digit series.
> On the otherhand this one here is not a decimal, base 10,
> representation:
>
> 1/2 + 1/4 + 1/8 + ... = 1

5/10 + 25/100 + 125/1000 + .... = 1

That's decimal you baboon!!!

[Dan Christensen]

So, NOT 0.875... as you originally claimed. Whew! I thought we were going to have to ban converging series now. Or did I miss that decree?

[Markus Klyver]

Den torsdag 5 oktober 2017 kl. 19:22:37 UTC+2 skrev John Gabriel:
> On Thursday, 5 October 2017 09:44:43 UTC-4, Markus Klyver wrote:
> > Den onsdag 4 oktober 2017 kl. 11:27:43 UTC+2 skrev John Gabriel:
> > > On Tuesday, 3 October 2017 20:32:47 UTC-4, burs...@gmail.com wrote:
> > > > Well its the mean value between 0.999... and 1.0.
> > >
> > > What are you saying you baboon, what are you mumbling about? You can only calculate an arithmetic mean between well formed numbers you moron! 0.999... is NOT a number of any kind. It represents a SERIES. If you define it stupidly as Euler did to be equal to its limit, then you are taking the mean of 1 and 1. There is nothing to do you HUGE APE!!!!
> > >
> > > Grow a brain. You sit pounding out your brain farts on sci.math. Get a job idiot!!!!! No one will hire you once they read the crap you write here.
> > >
> > > <6 year old rant>
> >
> > 0.999... is a short hand for an infinite sum (S = 0.9+0.09+0.009+...) which we define as the limit of a finite sum (Lim S = Lim {n \to \infty} 1-10^(-n)) as the number of terms approaches infinity.
>
> Yes, S = Lim S. Clear as water.
>
> It is an ill-formed definition because S is NOT the same as Lim S.
>
> How about this definition: Mercedes = cheese cake.
>
> Do you think it is well formed?
>
> >
> > Den torsdag 5 oktober 2017 kl. 08:01:05 UTC+2 skrev 7777777:
> > > torstai 5. lokakuuta 2017 8.44.17 UTC+3 Zelos Malum kirjoitti:
> > > > 0.999... must equal 1, there cannot be any other way for it to be.
> > >
> > > fail.
> > >
> > > in real numbers 0.(9) is not equal to 1.
> >
> > It indeed does. Or how do you define 0.(9)?

What's S and Lim S? You haven't actually defined what they mean. If S is the value of the series, then no, we don't define the value of the series as the limit of the value of the series.

Den torsdag 5 oktober 2017 kl. 20:46:07 UTC+2 skrev John Gabriel:
> On Thursday, 5 October 2017 13:22:37 UTC-4, John Gabriel wrote:
> > On Thursday, 5 October 2017 09:44:43 UTC-4, Markus Klyver wrote:
> > > Den onsdag 4 oktober 2017 kl. 11:27:43 UTC+2 skrev John Gabriel:
> > > > On Tuesday, 3 October 2017 20:32:47 UTC-4, burs...@gmail.com wrote:
> > > > > Well its the mean value between 0.999... and 1.0.
> > > >
> > > > What are you saying you baboon, what are you mumbling about? You can only calculate an arithmetic mean between well formed numbers you moron! 0.999... is NOT a number of any kind. It represents a SERIES. If you define it stupidly as Euler did to be equal to its limit, then you are taking the mean of 1 and 1. There is nothing to do you HUGE APE!!!!
> > > >
> > > > Grow a brain. You sit pounding out your brain farts on sci.math. Get a job idiot!!!!! No one will hire you once they read the crap you write here.
> > > >
> > > > <6 year old rant>
> > >
> > > 0.999... is a short hand for an infinite sum (S = 0.9+0.09+0.009+...) which we define as the limit of a finite sum (Lim S = Lim {n \to \infty} 1-10^(-n)) as the number of terms approaches infinity.
> >
> > Yes, S = Lim S. Clear as water.
> >
> > It is an ill-formed definition because S is NOT the same as Lim S.
> >
> > How about this definition: Mercedes = cheese cake.
> >
> > Do you think it is well formed?
> >
> > >
> > > Den torsdag 5 oktober 2017 kl. 08:01:05 UTC+2 skrev 7777777:
> > > > torstai 5. lokakuuta 2017 8.44.17 UTC+3 Zelos Malum kirjoitti:
> > > > > 0.999... must equal 1, there cannot be any other way for it to be.
> > > >
> > > > fail.
> > > >
> > > > in real numbers 0.(9) is not equal to 1.
> > >
> > > It indeed does. Or how do you define 0.(9)?
>

> Also, consider that you don't have a unique decimal representation of any number if you define the series to be the limit. For example, both of the following series have the same limit:
>
> 0.999... = 9/10 + 9/100 + ...
> 0.875... = 1/2 + 1/4 + 1/8 + ...
>
> So if we define them both as 1, then 0.999... = 1 and 0.875... = 1. How do we identify what series we are dealing with if we only have the limit? There are innumerably many series with the same limit of 1.
>
> On the one hand you berate the limit and on the other hand you invoke it. What is more important, the series or its limit? You seem to think the limit does not matter and then you go right ahead and DEFINE the series to be equal to its limit?! Isn't that stupid?
>
> A series is NOT a LIMIT. In fact, no matter if you could hypothetically sum all the terms of 3/10 + 3/100 + ..., you would never arrive at 1/3 because 1/3 is not measurable in base 10.
>
> Do you understand that expression "measurable in base 10"? It means expressing any rational number using a given base. There is no fraction p/q such that q=10^n with n integer and p/q = 1/3. It's impossible my little stupid. There is a theorem stating this. You defining S = Lim S goes against the theorem. You just can't use ill-formed definitions. They break everything.
>
> Get it?

That is not how decimal expansions are defined. You can't just shop off a series and write 0.875... = 1/2 + 1/4 + 1/8 + ..., because you as the number of terms grows you will surpass 0.875 and the digits will not match. We use base-10, and hence 0.875... = 8/10 + 7/100 + 5/1000 + ...

A series is defined as the limit of ITS PARTIAL SUMS. It is NOT defined as ITS OWN LIMIT. That's nonsense and an other strawman from your side. Put this madness down. You are either choosing not to listen to anything we explain, or you don't care. Summing "an infinite amount of terms" is defined as taking a limit.

The theorem you keep referring to only applies to finite decimal expansions.

Den torsdag 5 oktober 2017 kl. 22:52:59 UTC+2 skrev John Gabriel:
> On Thursday, 5 October 2017 15:09:12 UTC-4, burs...@gmail.com wrote:
> > That ...
>
>
> > You "decimal" means 10, so this a base 10 digit series.
> > On the otherhand this one here is not a decimal, base 10,
> > representation:
> >
> > 1/2 + 1/4 + 1/8 + ... = 1
>
> 5/10 + 25/100 + 125/1000 + .... = 1
>

> That's decimal you baboon!!!

But 25 > 10 and 125 > 100, so it's wrong.

[John Gabriel]

You do not know what is a definition, never mind understand it...

> You can't just shop off a series and write 0.875... = 1/2 + 1/4 + 1/8 + ...,

That's exactly what you do when you write 0.999... you baboon!!!

> because you as the number of terms grows you will surpass 0.875 and the digits will not match.

You will also surpass the 0.999 and the digits matching play no role whatsoever.

> We use base-10, and hence 0.875... = 8/10 + 7/100 + 5/1000 + ...

Or

5/10 + 25/100 + 125/1000 + ....

They are equivalent.

>
> A series is defined as the limit of ITS PARTIAL SUMS. It is NOT defined as ITS OWN LIMIT.

You just contradicted yourself!!! What a moron. S = Lim S. A series IS defined as its own limit.

> The theorem you keep referring to only applies to finite decimal expansions.

It applies to rational numbers that can't be measured in a given base.
Incommensurable magnitudes cannot be measured.

Baboon.

> > > You "decimal" means 10, so this a base 10 digit series.
> > > On the otherhand this one here is not a decimal, base 10,
> > > representation:
> > >
> > > 1/2 + 1/4 + 1/8 + ... = 1
> >
> > 5/10 + 25/100 + 125/1000 + .... = 1
> >
> > That's decimal you baboon!!!
>
> But 25 > 10 and 125 > 100, so it's wrong.

Nope. It's correct. You are simply too stupid and do not understand how radix systems work. Go and study.

[burs...@gmail.com]

Thats the same what Markus Klyver already told you
3 trillion times, namely Q-series need not have
a limit in Q. Here see for yourself:

1 + 1/2 - 1/8 + 1/16 - 5/128 + 7/256 ... = sqrt(2)

Each partial sum is from Q, i.e. is a rational number,
their values are, all from Q, aka rational numbers:

1
1 1/2
1 3/8
1 7/16
1 51/128
1 109/256
Etc...

Nevertheless the limit is not from Q, since sqrt(2)
is an irrational number, or in Euclid terms an
incommensurable magnitude ratio.

Got it?

Question: Why do you sign your posts with "Baboon",
is this the reason you don't understand real analysis?

[burs...@gmail.com]

Measurement in base 10 is not a criteria for a limit,
some Q-series indeed have a limit in Q, for example:

0.333... = 1/3

[genm...@gmail.com]

On Tuesday, 3 October 2017 18:03:53 UTC-4, John Gabriel wrote:
> Finally the discussion is over: S = Lim S is a bad definition.
>
> https://www.youtube.com/watch?v=NBOs-Xf_UIg
>
> Comments are unwelcome and will be ignored.
>
> Posted on this newsgroup in the interests of public education and to eradicate ignorance and stupidity from mainstream mythmatics.
>
> gils...@gmail.com (MIT)
> huiz...@psu.edu (HARVARD)
> and...@mit.edu (MIT)
> david....@math.okstate.edu (David Ullrich)
> djo...@clarku.edu
> mar...@gmail.com

There must be a psychological name for this refusal by orangutans to come to their senses. Is it delusional disorder?

[Markus Klyver]

I perfectly know how decimal expansions are defined. No, you can't just shop off an arbitrarily series and write the decimals up to that point, because when you add more terms, previous decimals can change. This is not the case with 0.999... or any other decimal expansion. It's also not how decimal expansions are defined, because we require each digit to be less or equal to the base we are currently using.

5/10 + 25/100 + 125/1000 + .... will not be 8/10 + 7/100 + 5/1000 + ... as you will get tenth and hundreds altering the 8 and 7 in the decimal expansion. This will not happen for decimal expansions. No matter how many digits you add, you can't alter previous digits.

And no, Gabriel. You're dead wrong. A series is defined as the limit of ITS PARTIAL SUMS. It is NOT defined as ITS OWN LIMIT. And the theorem you are referring to really states that a rational number p/q with GCD(p, q) = 1 will have a finite decimal expansion (aka, its infinite decimal expansion will end in zeros) if the considered base contains all the prime factors of q. For example, 1/3 will not have a finite decimal expansion in base 10 since the prime factors of 10 are 2 and 5.

[burs...@gmail.com]

Bamboo is commenting his own posts? Here have a banana:

Banana Song (I'm A Banana)
https://www.youtube.com/watch?v=LH5ay10RTGY

[John Gabriel]

You mean "chop" stupid. But that is what YOU do. You take the partial sum of the first 3 terms in 0.9+0.09+0.009+... and chop the rest off. Then you add an ellipsis.

> because when you add more terms, previous decimals can change.

It doesn't matter whether "previous" decimals change or not you MORON. What matters is that the ENTIRE sum changes! This is true for 0.999... and 0.875...

> It's also not how decimal expansions are defined, because we require each digit to be less or equal to the base we are currently using.

Nonsense. We are talking about radix systems. Decimal expansions are irrelevant crap. As for definitions, you don't get to decide! I decide. You keep forgetting this moron. Let me remind you: I rejected Euler's S = Lim S definition. I don't care that you are using it. It is WRONG!!!

>
> 5/10 + 25/100 + 125/1000 + .... will not be 8/10 + 7/100 + 5/1000 + ... as you will get tenth and hundreds altering the 8 and 7 in the decimal expansion.

They are exactly equivalent you HUGE APE! You have no idea what you are talking about.

>
> And no, Gabriel. You're dead wrong. A series is defined as the limit of ITS PARTIAL SUMS.

That's always what I have said you moron!!!! That is S = Lim S.

It's ill formed and I have rejected it.

> It is NOT defined as ITS OWN LIMIT.

It is defined AS ITS OWN LIMIT. A series is NOTHING but its PARTIAL SUMS, you infinitely stupid retard. There is no such thing as an "infinite series". Everything WE do with series involves PARTIAL SUMS you MOOOOOOROOOOOOOON.

A series is a PARTIAL SUM. An "infinite series" is a PARTIAL SUM followed by an ellipsis.

Get it moron?

> And the theorem you are referring to really states that a rational number p/q with GCD(p, q) = 1 will have a finite decimal expansion (aka, its infinite decimal expansion will end in zeros) if the considered base contains all the prime factors of q. For example, 1/3 will not have a finite decimal expansion in base 10 since the prime factors of 10 are 2 and 5.

Correct. Except that GCD(p,q) does not have to equal to 1 you confused dimwit!!! Have you heard of equivalent fractions? Also you have misstated the theorem. I have stated it correctly for you. Go back and read it.

Given any p and q integers and base b, then p/q can be expressed as kp/b^n where n is a +ve integer if and only if, b contains ALL the prime factors of q.

Now the theorem is true, so this means that you cannot measure 1/3 in base 10. Do you finally get it now? This means you CANNOT say 0.333... = 1/3 because 0.333... implies 3/10 + 3/100 + 3/1000 + ... which falsely suggests that 1/3 has a measure in base 10.

[burs...@gmail.com]

As long as it only "suggests", then everything is fine.
Then its obviously only a problem of your percept.

[Markus Klyver]

Gabriel, you don't listen to reason or any explanation for why you are wrong. No, you can't chop off an abitary series and write the decimals up to that point. You can only do that if you know new terms will not alter previous terms.

How is defining a series as the limit of its partial sums ill-formed? You have yet to demonstrate this. A series is not its partial sums, and not a finite sum. A series is a limit of its partial sums. This is how we define a series, and you can't simply outright deny a definition. Adress the definition in a sensible manner.

I stated the theorem correctly, but you didn't. I required GCD(p,q) = 1 and this does not make it false. You left out the crucial part, as the theorem only says p/q does not have a finite decimal expansion in a certain base.

[John Gabriel]

It literally hurts to listen to unbearably stupid individuals like you. My work of reeducating the lot of you morons is truly a labour of love.

> No, you can't chop off an abitary series and write the decimals up to that point.

Huh? That's exactly what you do!! 0.333... , 0.999..., etc,

Do you need more examples?

> You can only do that if you know new terms will not alter previous terms.

No. As I said, altering has nothing to do with it. Look, in order to know that the previous terms are not altered, you need to know that the series converges, which means you know it has a LIMIT! Get it moron? So you need to know a limit exists before? You contradict yourself in every sentence and every word. What a moron!

>
> How is defining a series as the limit of its partial sums ill-formed?

How is defining an apple to be a Mercedes ill-formed?

> You have yet to demonstrate this.

Been done many times.

>
> I stated the theorem correctly, but you didn't.

Nah uh just proves you are an idiot.

> I required GCD(p,q) = 1 and this does not make it false.

It does make it FALSE. 6/8 is one such counterexample: GCD(6,8) <> 1. In fact any equivalent fraction is a counterexample. Were you born such an idiot or was it gradually learned?

> You left out the crucial part, as the theorem only says p/q does not have a finite decimal expansion in a certain base.

Nonsense. Nothing is missing. If it's not finite then it's garbage because it does not exist as a well-formed concept.

[7777777]

torstai 5. lokakuuta 2017 9.34.12 UTC+3 FromTheRafters kirjoitti:
> After serious thinking 7777777 wrote :

> > torstai 5. lokakuuta 2017 8.44.17 UTC+3 Zelos Malum kirjoitti:
> >> 0.999... must equal 1, there cannot be any other way for it to be.
> >
> > fail.
> >
> > in real numbers 0.(9) is not equal to 1.
>

> Yes, it is.

nope.

> If it and zero were two different real numbers, there would
> be at least one more real number sitting between them.

there is:
0.(9) < 0.(9)5 < 1

[7777777]

torstai 5. lokakuuta 2017 11.59.01 UTC+3 Zelos Malum kirjoitti:
> Den torsdag 5 oktober 2017 kl. 08:01:05 UTC+2 skrev 7777777:

> > torstai 5. lokakuuta 2017 8.44.17 UTC+3 Zelos Malum kirjoitti:
> > > 0.999... must equal 1, there cannot be any other way for it to be.
> >
> > fail.
> >
> > in real numbers 0.(9) is not equal to 1.
>

> Incorrect, as per usual. It is trivial to prove it using dedekinds, cauchy or any number of other methods.

fail.

What is trivial is to prove that you are wrong. And to prove it without using
dedekinds, cauchy or any number of other methods.

[7777777]

torstai 5. lokakuuta 2017 16.44.43 UTC+3 Markus Klyver kirjoitti:
> Den torsdag 5 oktober 2017 kl. 08:01:05 UTC+2 skrev 7777777:
> > torstai 5. lokakuuta 2017 8.44.17 UTC+3 Zelos Malum kirjoitti:
> > > 0.999... must equal 1, there cannot be any other way for it to be.
> >
> > fail.
> >
> > in real numbers 0.(9) is not equal to 1.
>
> It indeed does.

nope.

> Or how do you define 0.(9)?

Using real numbers:

0.(9) = Σ_(n=1 to ∞)_9/10^n = Σ_(n=1 to Z)_9/10^n = 0.999...999

and

Σ_(n=1 to ∞)_9/10^n = 0.9 + 0.09 + 0.009 +...+ 9/10^∞ = 0.(9)
Σ_(n=1 to Z)_9/10^n = 0.9 + 0.09 + 0.009 +...+ 9/10^Z = 0.999...999

thus

0.999...999 + 0.000...001 = 1
0.(9)(9) = 0.(9) + 0.(0)(9) = 0.999...999 + 0.000...000999... = 0.999... = 1

0.999... is equal to 1 only if infinitesimals are included into the real numbers. Since the real number definition says that there are no infinitesimals
in real numbers 0.999... can't be equal to 1 in real numbers, and then
0.999... = 0.999...999 = 0.(9) ≠ 1

You have failed to accept or understand the ambiguity of the notation 0.999...
You have tried to treat it as an absolute, always equal to 1. In your
absoluteness you have rejected the infinitesimals, and the infinitesimal
analysis, and ended up with a dead end. You can't have rejected them and
using them too, you can't eat your cake and have it too.

At the same time, you have also rejected tons of useful into that I have given,
for example "my number" Z. It has led to that at the moment, you are light years behind me in doing infinitesimal analysis, and that's just because you did not come here to learn, but to win an argument, to fight against me, to fight against the truth.

[WM]

Am Freitag, 6. Oktober 2017 21:23:46 UTC+2 schrieb Markus Klyver:
> Den fredag 6 oktober 2017 kl. 19:51:56 UTC+2 skrev John Gabriel:

> > > It is NOT defined as ITS OWN LIMIT.
> >
> > It is defined AS ITS OWN LIMIT. A series is NOTHING but its PARTIAL SUMS,
> >

> > A series is a PARTIAL SUM. An "infinite series" is a PARTIAL SUM followed by an ellipsis.
> >

> > Now the theorem is true, so this means that you cannot measure 1/3 in base 10. Do you finally get it now? This means you CANNOT say 0.333... = 1/3 because 0.333... implies 3/10 + 3/100 + 3/1000 + ... which falsely suggests that 1/3 has a measure in base 10.
>

> How is defining a series as the limit of its partial sums ill-formed? You have yet to demonstrate this. A series is not its partial sums, and not a finite sum. A series is a limit of its partial sums. This is how we define a series, and you can't simply outright deny a definition. Adress the definition in a sensible manner.

Originally a series was considered as a sequence of partial sums. Cantor even used the technical term "series" (German: Reihe) throughout his papers to denote a sequence (German: Folge).

When people were not yet able (or too sloppy) to distinguish sequences and limits they used the series to denote its limit. This happened to become standard in mathematics such that we write 0.999... = 1. This definition leads to imprecise mathematics. But it does not matter in potentially infinite mathematics because nobody expects the complete series 0.999... to exist or to have any use. But the situation changed with set theory. There people believe that aleph_0 nines in 0.999... exist. They believe in a completed string or sequence of nines. But obviously none of the nines reaches the limit. Therefore we have to distinguish the limit 1 from the complete series SUM 9/10^n (summed over all natural numbers but not taking the limit).

Cantor' theory needs to identify the infinite digit sequence with its limit. Like the ordered set or sequence of natural numbers is said to be its limit omega. Both are wrong.

Therefore set theory is based on these mistakes. Set theorists are much more sloppy an careless than they recognize and pretend and than is allowed in mathematics.

Regards, WM

[burs...@gmail.com]

Why the small word "even", is something wrong? A series always
contains a sequence, and vice versa.

https://de.wikipedia.org/wiki/Reihe_%28Mathematik%29

https://de.wikipedia.org/wiki/Folge_%28Mathematik%29

=>)
Here is how they related take the Reihe or infinite sum:

a = a1 + a2 + a3 + ...

Then this gives rise to the sequence (sn):

sn = a1 + .. + an

<=)
Now the other direction take a Folge or sequence, not the comma:

s1, s2, s3, ...

The this gives rise to the series:

a = s1 + (s2-s1) + (s3-s2) + ...

But I guess the Augsburg Crank institute was to busy
writing its hugh pile of shit, to even understand
this simple fact.

[burs...@gmail.com]

Corr.:
Now the other direction take a Folge or sequence, note the comma:

s1, s2, s3, ...

[Markus Klyver]

0.333... and 0.999.. aren't abitary series. They are very specific, and has the property that adding more terms does not alter the previous digits. Taking 1/2+1/4+1/8+1/16+... as an example, its partial sums will be 0.5, 0.75, 0.875, 0.9375, 0.96875, 0.984375, ... Note how the first digit changes from a 5 to 7, and then to an 8 and lastly to a 9. So you can't simply chop off the end and write the decimals up to that point.

In the case of 0.333..., adding no terms will not alter previous digits so there's no ambiguity in what's meant. Writing the decimal expansion requires you to *know* what a certain digit will be, no matter how many terms are added. And you can know this in the case of 0.333... because adding new terms will not alter the previous digits in the decimal expansion.

Yes, you need to know the series converges to a limit, which is does. Every real monotonic bounded sequence will have a real limit, because the real numbers are complete. Every real Cauchy sequence will have a real limit.

This goes back to the definition: We define a series as the limit of its partial sums. This is not ill-formed, or else you have to demonstrate it.

And a theorem can make restrictions. I didn't say p/q with GCD(p, q) ≠ 1 WASN'T a rational number. I required p/q to be written with GCD(p, q) = 1, because it makes the proof easier and you can always write an abitary rational number a/b on the form p/q with GCD(p, q). It also is clearer what's meant, because you assume the rational already is written in a reduced form. But regardless, you miss the point: I didn't say 6/8 wasn't a rational number. I only required 6/8 to be written in its reduced form. This doesn't make my formulation false.

And you are missing the crucial part. The theorem states something about the existence of FINITE decimal expansions for a rational in a certain base. No, 1/3 will not have a finite decimal expansion in base 10. That doesn't mean it will not have a INFINITE decimal expansion in base 10. It will, and every real number has an infinite decimal expansion in every base.

Den lördag 7 oktober 2017 kl. 10:02:38 UTC+2 skrev 7777777:
> torstai 5. lokakuuta 2017 9.34.12 UTC+3 FromTheRafters kirjoitti:
> > After serious thinking 7777777 wrote :

> > > torstai 5. lokakuuta 2017 8.44.17 UTC+3 Zelos Malum kirjoitti:
> > >> 0.999... must equal 1, there cannot be any other way for it to be.
> > >
> > > fail.
> > >
> > > in real numbers 0.(9) is not equal to 1.
> >

> > Yes, it is.
>
> nope.
>
> > If it and zero were two different real numbers, there would
> > be at least one more real number sitting between them.
>
> there is:
> 0.(9) < 0.(9)5 < 1

Then, what do you mean by 0.(9)5, because you can't have infinitely many nines and then a 5 at the end.

Den lördag 7 oktober 2017 kl. 10:39:56 UTC+2 skrev 7777777:
> torstai 5. lokakuuta 2017 16.44.43 UTC+3 Markus Klyver kirjoitti:

> > Den torsdag 5 oktober 2017 kl. 08:01:05 UTC+2 skrev 7777777:
> > > torstai 5. lokakuuta 2017 8.44.17 UTC+3 Zelos Malum kirjoitti:
> > > > 0.999... must equal 1, there cannot be any other way for it to be.
> > >
> > > fail.
> > >
> > > in real numbers 0.(9) is not equal to 1.
> >
> > It indeed does.
>

> nope.

>
> > Or how do you define 0.(9)?
>

> Using real numbers:
>
> 0.(9) = Σ_(n=1 to ∞)_9/10^n = Σ_(n=1 to Z)_9/10^n = 0.999...999
>
> and
>
> Σ_(n=1 to ∞)_9/10^n = 0.9 + 0.09 + 0.009 +...+ 9/10^∞ = 0.(9)
> Σ_(n=1 to Z)_9/10^n = 0.9 + 0.09 + 0.009 +...+ 9/10^Z = 0.999...999
>
> thus
>
> 0.999...999 + 0.000...001 = 1
> 0.(9)(9) = 0.(9) + 0.(0)(9) = 0.999...999 + 0.000...000999... = 0.999... = 1
>
> 0.999... is equal to 1 only if infinitesimals are included into the real numbers. Since the real number definition says that there are no infinitesimals
> in real numbers 0.999... can't be equal to 1 in real numbers, and then
> 0.999... = 0.999...999 = 0.(9) ≠ 1
>
> You have failed to accept or understand the ambiguity of the notation 0.999...
> You have tried to treat it as an absolute, always equal to 1. In your
> absoluteness you have rejected the infinitesimals, and the infinitesimal
> analysis, and ended up with a dead end. You can't have rejected them and
> using them too, you can't eat your cake and have it too.
>
> At the same time, you have also rejected tons of useful into that I have given,
> for example "my number" Z. It has led to that at the moment, you are light years behind me in doing infinitesimal analysis, and that's just because you did not come here to learn, but to win an argument, to fight against me, to fight against the truth.

But there's no last number to a infinite string. Writing Σ_(n=1 to ∞)_9/10^n = 0.9 + 0.09 + 0.009 +...+ 9/10^∞ makes no sense. Σ_(n=1 to ∞)_9/10^n is interpreted as a limit, and this limit is 1.

Do you understand how decimal expansions are defined? Do you understand limits?

[burs...@gmail.com]

So Cantor was correctly writing the partial sums
as a sequence in his paper where he used the
Cauchy criteria:

Ueber die Ausdehnung eines Satzes aus
der Theorie der trigonometrischen Reihen
Von G. Cantor in Halle a. S. [Math. Annalen 5, 123–132 (1872).]
http://www.maths.tcd.ie/pub/HistMath/People/Cantor/Ausdehnung/Ausdehnung.pdf

Note the comma, he writes, and says that he
considers rational numbers:

a1,a2,...an,...

dass bei beliebig angennommenem (positiven,
rationalen) ε eine ganze Zahl n1 vorhanden ist,
so dass |an+m − an| < ε, wenn n ≥ n1 und wenn
m eine beliebige positive ganze Zahl ist.

Thats a variant of Cauchy criteria:

forall n>=N(ε),m |a_(n+m)-an| < ε

Which is logically equivalent to:

forall n,m>=N(ε) |a_n-a_m| < ε

As a next step he introduces very quickly the Z
series for the 0 limit, and then addition, product
and division for Cauchy series. He does
ordering as well.

He uses lim without the extra n->oo. Later he
proves the transcendence of some series.

[John Gabriel]

On Saturday, 7 October 2017 05:15:22 UTC-4, WM wrote:
> Am Freitag, 6. Oktober 2017 21:23:46 UTC+2 schrieb Markus Klyver:
> > Den fredag 6 oktober 2017 kl. 19:51:56 UTC+2 skrev John Gabriel:
>
> > > > It is NOT defined as ITS OWN LIMIT.
> > >
> > > It is defined AS ITS OWN LIMIT. A series is NOTHING but its PARTIAL SUMS,
> > >
> > > A series is a PARTIAL SUM. An "infinite series" is a PARTIAL SUM followed by an ellipsis.
> > >
>
> > > Now the theorem is true, so this means that you cannot measure 1/3 in base 10. Do you finally get it now? This means you CANNOT say 0.333... = 1/3 because 0.333... implies 3/10 + 3/100 + 3/1000 + ... which falsely suggests that 1/3 has a measure in base 10.
> >
> > How is defining a series as the limit of its partial sums ill-formed? You have yet to demonstrate this. A series is not its partial sums, and not a finite sum. A series is a limit of its partial sums. This is how we define a series, and you can't simply outright deny a definition. Adress the definition in a sensible manner.
>
> Originally a series was considered as a sequence of partial sums. Cantor even used the technical term "series" (German: Reihe) throughout his papers to denote a sequence (German: Folge).

Well, don't go too far. Newton did not view his series as infinite even though he made the mistake of calling them "infinite series". This mistake has been costly. Not only is the idea of infinite series conceptually flawed, but it has led as you noted to more wrong ideas.

>
> When people were not yet able (or too sloppy) to distinguish sequences and limits they used the series to denote its limit.

Like pi, e, sqrt(2), etc. The series gave them the illusion that they were able to measure these incommensurable quantities.

> This happened to become standard in mathematics such that we write 0.999... = 1.

But 1 is the UNIT!! How could anyone not distinguish this from ALL other numbers? It is the chosen standard for measurement.

No WM, they chose to define 0.999... = 1 because they were ANGRY at their failure to measure sqrt(2) and other incommensurables. Chuckle. They would punish the UNIT by giving it another name. How dare the UNIT not be able to measure most "irrational" magnitudes! Yes, how dare it the orangutans chanted in unison. They fools in mainstream could not accept the fact that there are magnitudes that cannot be measured. They thought the Ancient Greeks were just using long difficult to understand words like "incommensurable".

> This definition leads to imprecise mathematics.

It led to nonsense.

> But it does not matter in potentially infinite mathematics because nobody expects the complete series 0.999... to exist or to have any use. But the situation changed with set theory. There people believe that aleph_0 nines in 0.999... exist. They believe in a completed string or sequence of nines.

It is a very dangerous thing to believe in Jewish fables which although entertaining are by no means useful in forming important opinions that relate to rational thinking.

> But obviously none of the nines reaches the limit. Therefore we have to distinguish the limit 1 from the complete series SUM 9/10^n (summed over all natural numbers but not taking the limit).

Euler decided that S = Lim S was sufficient and the orangutans chanted: Euler Oagbar! Euler Oagbar!

>
> Cantor' theory needs to identify the infinite digit sequence with its limit.

Of course. His diagonal "argument" needs this just to get started.

[burs...@gmail.com]

Corr.:
Oops, it rather looks like he proves the continuity.

[burs...@gmail.com]

Yes sure a "Jewish fables", I guess bird brain
John Gabrial does the banana dance again:

Banana Song (I'm A Banana)
https://www.youtube.com/watch?v=LH5ay10RTGY

[John Gabriel]

Deluded much? Where did I even suggest this? Idiot.

> They are very specific, and has the property that adding more terms does not alter the previous digits.

Altering the previous digits is nonsense. It does not appear in any of your bibles you moron.

> Taking 1/2+1/4+1/8+1/16+... as an example, its partial sums will be 0.5, 0.75, 0.875, 0.9375, 0.96875, 0.984375, ... Note how the first digit changes from a 5 to 7, and then to an 8 and lastly to a 9. So you can't simply chop off the end and write the decimals up to that point.

Of course you can idiot! One uses 0.875... as an identifier. The real object, that is, 1/2+1/4+1/8+1/16+... is pretty clear. The standard UNIT is very well defined as 1. It does not require additional names like 0.999... or 0.875...

>
> In the case of 0.333..., adding no terms will not alter previous digits so there's no ambiguity in what's meant. Writing the decimal expansion requires you to *know* what a certain digit will be, no matter how many terms are added. And you can know this in the case of 0.333... because adding new terms will not alter the previous digits in the decimal expansion.

Again, that is just your ignorant opinion. Assertions are worthless.
>


<incomprehensible and confused rot>

Sorry, I do not have time for all your bullshit. You are full of it!

[burs...@gmail.com]

Poor Newton, our mini-Hitler bird brain John Gabriel
wants change reality, would like to re-lable his works
called "THE METHOD OF FLUXIONS AND INFINITE SERIES"

Why not burn these books? You read anyway no books
bird brain John Gabriel, why not burn all books? They
are all beige on the outside, aren't they?

Am Samstag, 7. Oktober 2017 12:54:35 UTC+2 schrieb John Gabriel:

[Markus Klyver]

You are partially correct. 0.999... is considered to be a limit, and taking about a series as an actual sum makes no sense at all since you can't literary add infinitely many terms. And you could interpret the series 0.999... as having "ℵ_0 nines", but you'd need to be precise on what you mean. The cardinality of the set {0.9, 0.99, 0.999, ...} is ℵ_0. You also seem to misinterpreted what a limit ordinal is. In fact, it has little to do with limits at all. A limit ordinal is an ordinal which is neither zero nor a successor ordinal. ω is neither zero, nor a successor ordinal. ω is simply the name we give the order type of the natural numbers, and isn't regarded as a limit. Every set {1, 2, 3, 4, ..., n} will have a finite order type and it makes no sense to talk about limits of ordinals. ω is simply the least ordinal that isn't finite. It's not a result of any limit.

[burs...@gmail.com]

Yeah this is typical nonsense of WM, he freely jumps
from real analysis to set theory.

[Markus Klyver]

Because it only makes sense to chop off an series and write out the digits up to that point if you don't alter previous digits, otherwise we could write 0.776... = 0.23436... = 0.999245... which wouldn't be very useful at all.

And you are still missing the crucial part of the theorem you are keep referring to. It only makes a statement about the existence of a FINITE decimal expansion. You totally ignore this. Yes, 1/3 will not have a finite decimal expansion in base 10. No one ever attempted to argue against this.

[FromTheRafters]

7777777 used his keyboard to write :

That is not a real number, it is a fabrication pretending to indicate
that you can have an infinite string of nines with a five at the end.

But, there is no "end" to an infinite string for you to glue that five
onto.

[John Gabriel]

I have never met anyone as stupid and intransigent as you in my life. You are probably the biggest dimwit I have ever known. I think even the chief troll of sci.math Dan Christensen is not as stupid as you are. Dishonest, vile, evil? Yes, Christensen is all of these things, but for the life of me, you are as of today the biggest idiot I have ever known.

You will get no more responses, only ridicule and once I am tired of that, I'll just ignore you.

[Markus Klyver]

Because you keep attacking strawmans and adhere to racial slur, Gabriel? You have yet to adress the FACTUAL definitions we actually use.

[WM]

Am Samstag, 7. Oktober 2017 12:25:33 UTC+2 schrieb burs...@gmail.com:

> Why the small word "even", is something wrong? A series always
> contains a sequence, and vice versa.

But a sequence *is* not always a series.

And if a series always contains a sequence, as you correctly say, then the series is not a sum. 1 does not contain a sequence.

Regards, WM

[WM]

Am Samstag, 7. Oktober 2017 12:52:07 UTC+2 schrieb burs...@gmail.com:

> So Cantor was correctly writing the partial sums
> as a sequence in his paper where he used the
> Cauchy criteria:
>
> Ueber die Ausdehnung eines Satzes aus
> der Theorie der trigonometrischen Reihen
> Von G. Cantor in Halle a. S. [Math. Annalen 5, 123–132 (1872).]

He was not always incorrect, but here he was:

"die Mächtigkeit der positiven ganzen rationalen Zahlenreihe"
"alle Mengen, die in Form einer n-fach unendlichen Reihe mit dem allgemeinen Gliede E1,2,...,n (wo 1, 2, ...n unabhängig voneinander alle positiven ganzen Zahlenwerte zu erhalten haben)"
and there are many more such wrong applications (in the modern sense).

Regards, WM

[WM]

Am Samstag, 7. Oktober 2017 13:12:36 UTC+2 schrieb Markus Klyver:


> Yes, 1/3 will not have a finite decimal expansion in base 10.

And it will not have an infinite decimal expansion in base 10 either, because even if there were infinitely many digits 3 we can prove for each one that it fails to complete 1/3. 1/3 can only be the limit.

Regards, WM

[WM]

Am Samstag, 7. Oktober 2017 13:05:49 UTC+2 schrieb Markus Klyver:
> Den lördag 7 oktober 2017 kl. 11:15:22 UTC+2 skrev WM:


> > Therefore set theory is based on these mistakes. Set theorists are much more sloppy an careless than they recognize and pretend and than is allowed in mathematics.
> >

> You are partially correct. 0.999... is considered to be a limit, and taking about a series as an actual sum makes no sense at all since you can't literary add infinitely many terms.

Cantor could and did.

> And you could interpret the series 0.999... as having "ℵ_0 nines", but you'd need to be precise on what you mean.

Every 9 has a natural index, and every natural number appears as an index. That is sufficient to say: there are aleph_0 indexed nines.

> The cardinality of the set {0.9, 0.99, 0.999, ...} is ℵ_0.

The cardinality of the set {9_1, 9_2, 9_3, ...} is ℵ_0 too.

> You also seem to misinterpreted what a limit ordinal is. In fact, it has little to do with limits at all.

Chuckle. Meanwhile matheologians seem to have recognized that Cantor's orginal work is a load of rubbish. But they try to save their pet buy redefining the crucial notions.

> ω is simply the least ordinal that isn't finite. It's not a result of any limit.

It is provable that ω does not exist in mathematics. Its existence does not even follow from the axiom of infinity. Therefore the matheologians fetch it from the blue air - with no reason and no application except to furnish a means to distinguish matghematics and matheology.

Regards, WM

[burs...@gmail.com]

Description: The existence of omega (the
class of natural numbers). Axiom 7 of
[TakeutiZaring] p. 43. This theorem is proved
assuming the Axiom of Infinity and in fact
is equivalent to it, as shown by the reverse
derivation inf0 7317.

A finitist (someone who doesn't believe in
infinity) could, without contradiction,
replace the Axiom of Infinity by its
denial ¬ 𝜔 ∈ V; this would lead to 𝜔 = On
by omon 4665 and Fin = V (the universe of
all sets) by fineqv 7073. The finitist could
still develop natural number, integer, and
rational number arithmetic but would be denied
the real numbers (as well as much of the
rest of mathematics).

In deference to the finitist, much of our
development is done, when possible, without
invoking the Axiom of Infinity; an example is
Peano's axioms peano1 4673 through peano5 4677
(which many textbooks prove more easily assuming
Infinity). (Contributed by NM, 6-Aug-1994.)

http://us.metamath.org/mpeuni/omex.html

[burs...@gmail.com]

I guess matheologians are at least no liars,
not like WM, like 75% of his posts are lies.

[John Gabriel]

Seems to me that WM has given you a good lesson. Maybe you should try putting on some brains? Chuckle.

[John Gabriel]

On Sunday, 8 October 2017 07:41:30 UTC-4, WM wrote:
> Am Samstag, 7. Oktober 2017 13:05:49 UTC+2 schrieb Markus Klyver:
> > Den lördag 7 oktober 2017 kl. 11:15:22 UTC+2 skrev WM:
>
>
> > > Therefore set theory is based on these mistakes. Set theorists are much more sloppy an careless than they recognize and pretend and than is allowed in mathematics.
> > >
>
> > You are partially correct. 0.999... is considered to be a limit, and taking about a series as an actual sum makes no sense at all since you can't literary add infinitely many terms.
>
> Cantor could and did.
>
> > And you could interpret the series 0.999... as having "ℵ_0 nines", but you'd need to be precise on what you mean.
>
> Every 9 has a natural index, and every natural number appears as an index. That is sufficient to say: there are aleph_0 indexed nines.
>
> > The cardinality of the set {0.9, 0.99, 0.999, ...} is ℵ_0.
>
> The cardinality of the set {9_1, 9_2, 9_3, ...} is ℵ_0 too.
>
> > You also seem to misinterpreted what a limit ordinal is. In fact, it has little to do with limits at all.
>
> Chuckle. Meanwhile matheologians seem to have recognized that Cantor's orginal work is a load of rubbish. But they try to save their pet buy redefining the crucial notions.

One look at Klyver's Jan Burse and Zelos Malum's comments show very desperate mainstreamers, clutching at impossible straws to save their bogus theory. The thing about S = Lim S, is that it does not matter which way one interprets S - as a series or sequence. The result is the same.

[burs...@gmail.com]

Whats worse matheologians or crank spammers
that constantly lie? Well there is a third

category: bird brains! John Gabriel for example,
they just don't know nothing and understand nothing.

[burs...@gmail.com]

Know nothing and unerstand nothing, John
Gabriels S=Lim S confusion doesn't really

invoke the finite. Its more a category error,
like saying a giraffe is a tree.

https://en.wikipedia.org/wiki/Category_mistake

https://en.wikipedia.org/wiki/Colorless_green_ideas_sleep_furiously

[John Gabriel]

There is something you need to know about Greeks you worthless moron: we have been and always will be on the RIGHT side of history. We always win - even if it takes hundreds of years to do so.

We Greeks are the light and beauty of the world. You are nothing but vulgar and ugliness. We built Western Civilisation and ultimately we are the only ones to save it.

You can be on the wrong or right side. Currently you are on the wrong side. Chuckle.

[WM]

Am Sonntag, 8. Oktober 2017 14:00:04 UTC+2 schrieb burs...@gmail.com:

> Description: The existence of omega (the
> class of natural numbers). Axiom 7 of
> [TakeutiZaring] p. 43. This theorem is proved
> assuming the Axiom of Infinity and in fact
> is equivalent to it, as shown by the reverse
> derivation inf0 7317.

omega is either a limit ordinal larger than all natural ordinals or it is denoting the class of all natural ordinals, but not both simultaneously.

Zermelo's axiom of infinity is rather the same as Dedekind's or Peano's. In Peano arithmetic there is no limit omega.

Regards, WM



Regards, WM

[Dan Christensen]

On the contrary, we can prove that 0.333... = 0.3 + 0.03 + 0.003 + ... = 1/3

BTW, were you ever able to prove from those goofy axioms yours (without any hand waving) that 1 =/= 2, Mucke?


Dan

Download my DC Proof 2.0 software at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com

[burs...@gmail.com]

Yes omega will be a class, when the axiom
of infinity is dropped, I guess it also
appears as such in these "Peano" axioms:

http://us.metamath.org/mpeuni/peano5.html

But then the "Peano" axiom itself also
talks about another class A. In "Peano"
you can identify omega with the

predication:

omega(x) :<=> x=x

or written as a class:

omega = { x | x=x }

So it is also existent in some sense also
in "Peano" arithmetic without the axiom of
infinity.

[burs...@gmail.com]

Classes are an example of the Münchhausen trilemma
https://en.wikipedia.org/wiki/M%C3%BCnchhausen_trilemma

When you want to do "Peano", you only get superficially
rid of the axiom of infinity, when you even add the
negation of it.

On a meta level, it is still there. So why not
add it in the first place, and make the meta level
explicit, instead of trying to hide it?

[John Gabriel]

Rather than remove all doubt how stupid you are, listen to WM because he is far more intelligent than you or Klyver or dipshit Malum will ever be.

You are privileged that he even bothers responding to you. Reeducating you morons is a thankless task.

[genm...@gmail.com]

On Sunday, 8 October 2017 08:16:32 UTC-4, burs...@gmail.com wrote:

> Know nothing and unerstand nothing, John
> Gabriels S=Lim S confusion doesn't really
>
> invoke the finite. Its more a category error,
> like saying a giraffe is a tree.

Actually not at all. It does not matter how you interpret any of the S in S = Lim S. It is WRONG whichever way you interpret it - whether a series or a sequence. Let's see one last time:

S_series = 0.3+0.03+0.003+...
S_sequence = {0.3; 0.33; 0.333; ...}

1 = Lim S_series
1 = Lim S_sequence

S_series = Lim S_series=1 <---- This is what Euler meant: S = Lim S where S is interpreted as a series. Euler did not mean the partial nth sum or anything else.

S_series = Lim S_sequence=1

S_sequence = Lim S_series = 1

S_sequence = Lim S_sequence = 1

See, no difference, Limit is always one and everyone of those definitions are ILL FORMED!

It's become boring fucking you up all the time. LOL. You poor stupid, dumb, retarded, ignorant, unemployed, miserable bastard. Tsk, tsk.

Kill yourself fool! It's the best thing you can do.

<birdbrain Jan Burse rant>

[burs...@gmail.com]

You are just heavily confused, maybe your brain turmor is growing.
See here for what you got right concerning "generated", and
what you got wrong concerning "generated":

https://groups.google.com/d/msg/sci.math/bgU-4JWvHbY/u9vIap7VAQAJ

It also doesn't help that you repeat your blunder over
and over. Euler didn't use whole series notation such
as {0.3; 0.33; 0.333; ...} in his booklet taylord towards

the public, he didn't use the comman notation. And he
didn't have to since, when he would write:

0.3+0.03+0.003+... = 1/3

The last ellipsis already includes a limit operator
apply to a sequence, its the same as writing:

lim n->oo (0.3, 0.33, 0.333, ...) = 1/3

This definition persis to today, you find it explained
on wikipedia, here have a picture:
https://gist.github.com/jburse/e60242e2e02e611e4373df55bfc37953#gistcomment-2219906

Or read the wikipedia definition:
https://en.wikipedia.org/wiki/Series_%28mathematics%29

Calm your tits, and admit your mistake. Here have a
Banana, its good for the heart, it has Potassium:

Banana Song (I'm A Banana)
https://www.youtube.com/watch?v=LH5ay10RTGY

[genm...@gmail.com]

On Sunday, 8 October 2017 12:05:07 UTC-4, Jan Burse (lives in his mother's basement in Zurich) burs...@gmail.com wrote:

> You are ...

SHUT UP MORON. SHUT UP YOU VICIOUS TROLL!!!!

[burs...@gmail.com]

It would really help if you would once open
a book, you know these things with a beige cover.

The limit operator is not the only operator with
a variable in it, that is bound.

You should know this from integration in
your new calculus, if you write:

integral_0^1 x^2*y dx

This is not the same as:

integral_0^1 x^2*y dy

The results are different since the
bound variable is different:

integral_0^1 x^2 y dx = y/3

integral_0^1 x^2 y dy = x^2/2

And there is no Euler blunder "S=Lim S", you need
to know how the lim n->oo operator works, and that
it binds the variable n.

And we use the following phrase for this operator:
"Limit of S(n) when n tends to infinity". Its important
what tends to infinity, I guess this obvious, isn't it?

Calm your tits, and admit your mistake. Here have a
Banana, its good for the heart, it has Potassium:

Banana Song (I'm A Banana)
https://www.youtube.com/watch?v=LH5ay10RTGY

[burs...@gmail.com]

Thats also why your new calculus has zero credibility,
you don't understand bound variables, but they appear
in definite integrals? How do you explain this?

http://mathworld.wolfram.com/DefiniteIntegral.html

[7777777]

lauantai 7. lokakuuta 2017 13.47.09 UTC+3 Markus Klyver kirjoitti:

>
> Den lördag 7 oktober 2017 kl. 10:02:38 UTC+2 skrev 7777777:
> > torstai 5. lokakuuta 2017 9.34.12 UTC+3 FromTheRafters kirjoitti:
> > > After serious thinking 7777777 wrote :

> > > > torstai 5. lokakuuta 2017 8.44.17 UTC+3 Zelos Malum kirjoitti:
> > > >> 0.999... must equal 1, there cannot be any other way for it to be.
> > > >
> > > > fail.
> > > >
> > > > in real numbers 0.(9) is not equal to 1.
> > >

> > > Yes, it is.
> >
> > nope.
> >
> > > If it and zero were two different real numbers, there would
> > > be at least one more real number sitting between them.
> >
> > there is:
> > 0.(9) < 0.(9)5 < 1
>

> Then, what do you mean by 0.(9)5, because you can't have infinitely many nines and then a 5 at the end.

yes I can. You assume that endlessness automatically means the same as infinite, but there can be an infinite set although it is not endless:
0.999...999 <---- number of nines is infinite, yet it is not endless

0.(9)5 is a real number 0.(9) with an included infinitesimal part 0.(0)5


>
> Den lördag 7 oktober 2017 kl. 10:39:56 UTC+2 skrev 7777777:

> > torstai 5. lokakuuta 2017 16.44.43 UTC+3 Markus Klyver kirjoitti:
> > > Den torsdag 5 oktober 2017 kl. 08:01:05 UTC+2 skrev 7777777:
> > > > torstai 5. lokakuuta 2017 8.44.17 UTC+3 Zelos Malum kirjoitti:
> > > > > 0.999... must equal 1, there cannot be any other way for it to be.
> > > >
> > > > fail.
> > > >
> > > > in real numbers 0.(9) is not equal to 1.
> > >
> > > It indeed does.
> >

> > nope.

> >
> > > Or how do you define 0.(9)?
> >

> > Using real numbers:
> >
> > 0.(9) = Σ_(n=1 to ∞)_9/10^n = Σ_(n=1 to Z)_9/10^n = 0.999...999
> >
> > and
> >
> > Σ_(n=1 to ∞)_9/10^n = 0.9 + 0.09 + 0.009 +...+ 9/10^∞ = 0.(9)
> > Σ_(n=1 to Z)_9/10^n = 0.9 + 0.09 + 0.009 +...+ 9/10^Z = 0.999...999
> >
> > thus
> >
> > 0.999...999 + 0.000...001 = 1
> > 0.(9)(9) = 0.(9) + 0.(0)(9) = 0.999...999 + 0.000...000999... = 0.999... = 1
> >
> > 0.999... is equal to 1 only if infinitesimals are included into the real numbers. Since the real number definition says that there are no infinitesimals
> > in real numbers 0.999... can't be equal to 1 in real numbers, and then
> > 0.999... = 0.999...999 = 0.(9) ≠ 1
> >
> > You have failed to accept or understand the ambiguity of the notation 0.999...
> > You have tried to treat it as an absolute, always equal to 1. In your
> > absoluteness you have rejected the infinitesimals, and the infinitesimal
> > analysis, and ended up with a dead end. You can't have rejected them and
> > using them too, you can't eat your cake and have it too.
> >
> > At the same time, you have also rejected tons of useful into that I have given,
> > for example "my number" Z. It has led to that at the moment, you are light years behind me in doing infinitesimal analysis, and that's just because you did not come here to learn, but to win an argument, to fight against me, to fight against the truth.
>
> But there's no last number to a infinite string. Writing Σ_(n=1 to ∞)_9/10^n = 0.9 + 0.09 + 0.009 +...+ 9/10^∞ makes no sense. Σ_(n=1 to ∞)_9/10^n is interpreted as a limit, and this limit is 1.

S(∞) = Σ_(n=1 to ∞)_9/10^n = 0.9 + 0.09 + 0.009 +...+ 9/10^∞ = 0.(9)

You have not shown how do you get S(∞) = 1

[Zelos Malum]

what the hell is "matheologians"!?

[Zelos Malum]

>yes I can. You assume that endlessness automatically means the same as infinite, but there can be an infinite set although it is not endless:
0.999...999 <---- number of nines is infinite, yet it is not endless
>
>0.(9)5 is a real number 0.(9) with an included infinitesimal part 0.(0)5

Which makes them not inifnite, if it has an end like that it is by definition, finite.

>S(∞) = Σ_(n=1 to ∞)_9/10^n = 0.9 + 0.09 + 0.009 +...+ 9/10^∞ = 0.(9)
>
>You have not shown how do you get S(∞) = 1

FIrst of, that is pisspoor notation and extremely abused and someone as dumb as you shouldn't do it.

Secondly, we get it by the definition that the sum equals the value it can get arbitrarily close to, and that number is 1.

[WM]

Am Sonntag, 8. Oktober 2017 14:43:56 UTC+2 schrieb Dan Christensen:
> On Sunday, October 8, 2017 at 7:41:14 AM UTC-4, WM wrote:
> > Am Samstag, 7. Oktober 2017 13:12:36 UTC+2 schrieb Markus Klyver:
> >
> >
> > > Yes, 1/3 will not have a finite decimal expansion in base 10.
> >
> > And it will not have an infinite decimal expansion in base 10 either, because even if there were infinitely many digits 3 we can prove for each one that it fails to complete 1/3. 1/3 can only be the limit.
> >
>
> On the contrary, we can prove that 0.333... = 0.3 + 0.03 + 0.003 + ... = 1/3
>

Apply logic. What digit entitles you to write the second "="?
I can show that every digit fails.

Note: claiming without proving is not mathematics.

Regards, WM

[WM]

Am Sonntag, 8. Oktober 2017 14:58:49 UTC+2 schrieb burs...@gmail.com:

> When you want to do "Peano", you only get superficially
> rid of the axiom of infinity, when you even add the
> negation of it.
>
> On a meta level, it is still there. So why not
> add it in the first place, and make the meta level
> explicit, instead of trying to hide it?

On the "meta level" you first have to distinguish between potential infinity and finished infinity. Peano's axioms adhere to the former.

Regards, WM

[WM]

Am Montag, 9. Oktober 2017 09:15:15 UTC+2 schrieb Zelos Malum:


>
> what the hell is "matheologians"!?

A matheologian is a man, or, in rare cases, a woman, who believes in thoughts that nobody can think, except, perhaps, a God, or, in rare cases, a Goddess.
https://www.hs-augsburg.de/~mueckenh/Transfinity/Transfinity/pdf, p. 330.

In particular this specis believes in "real numbers" (chuckle) that cannot be defined.

Regards, WM

[burs...@gmail.com]

Augsburg Crank institute at its best. The Greek
would be ashed by such a nonsense.

[Zelos Malum]

Uh dipshit, the reals can be defined quite easily.