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It is a very bad idea and nothing less than stupid to define 1/3 = 0.333...

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John Gabriel

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Feb 12, 2017, 8:14:11 AM2/12/17
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S = Lim S in this case, contradicts the fact that 1/3 has no representation in base 10.

However, it also leads to even more absurd definitions, that is, pi=3.14159... when in fact it is known that pi has NO measure.


https://www.youtube.com/watch?v=5hulvl3GgGk

https://www.youtube.com/watch?v=w8s_8fNePEE


Your comments are unwelcome shit and will be ignored.

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

shio...@googlemail.com

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Feb 12, 2017, 9:30:17 AM2/12/17
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1/3 has a representation as g-adic.
Similarly, pi is a clearly defined value and also, as any real number, has a g adic represantation.

John Gabriel

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Feb 12, 2017, 10:28:20 AM2/12/17
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It has a representation in many other radix systems too you imbecile. Your point? I see. None.

John Gabriel

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Feb 12, 2017, 10:29:36 AM2/12/17
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On Sunday, 12 February 2017 08:30:17 UTC-6, shio...@googlemail.com wrote:
Pi is a clearly defined value? What is you moron? Don't tell me circumference length divided by diameter.

Pi only has a number associated with it, if such a number describes its MEASURE you infinite FUCKING MORON!

shio...@googlemail.com

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Feb 12, 2017, 11:38:24 AM2/12/17
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Pi is clearly defined as value by many different expressions, for example as a certain integral.
Since that value is unique, it defines pi.

And my point is that the radix system in actual math IS the 10-adic system, and that 1/3 has an expression in it.
It is infinitely long, but that is no problem. It can be infinitely long, that's not against the law.

abu.ku...@gmail.com

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Feb 12, 2017, 12:11:11 PM2/12/17
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what is g-adic?... anyway,
PI is the ratio of diameter to the area of the sphere,
which requires some thought, but it is about 32 hundredths;
the ratio of circmference to the diameter is 31 tenths; see?

> Pi only has a number associated with it, if such a number describes its MEASURE

<deletia excretia>

Dan Christensen

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Feb 12, 2017, 1:17:43 PM2/12/17
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On Sunday, February 12, 2017 at 8:14:11 AM UTC-5, John Gabriel wrote:
> S = Lim S in this case, contradicts the fact that 1/3 has no representation in base 10.
>

JG also doesn't believe in the number pi, the square root of 2, negative numbers or even zero. JG is a full-on crank and a troll. He claims to be greatest mathematician ever, but cannot even prove that 2+2=4 in his goofy system! (See the thread, "The spamming troll John Gabriel in his own words.")


Dan

John Gabriel

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Feb 12, 2017, 3:27:20 PM2/12/17
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On Sunday, 12 February 2017 10:38:24 UTC-6, shio...@googlemail.com wrote:
> On Sunday, 12 February 2017 16:29:36 UTC+1, John Gabriel wrote:
> > On Sunday, 12 February 2017 08:30:17 UTC-6, shio...@googlemail.com wrote:
> > > On Sunday, 12 February 2017 14:14:11 UTC+1, John Gabriel wrote:
> > > > S = Lim S in this case, contradicts the fact that 1/3 has no representation in base 10.
> > > >
> > > > However, it also leads to even more absurd definitions, that is, pi=3.14159... when in fact it is known that pi has NO measure.
> > > >
> > > >
> > > > https://www.youtube.com/watch?v=5hulvl3GgGk
> > > >
> > > > https://www.youtube.com/watch?v=w8s_8fNePEE
> > > >
> > > >
> > > > Your comments are unwelcome shit and will be ignored.
> > > >
> > > > This is posted on this newsgroup in the interests of public education and to eradicate ignorance and stupidity from mainstream mythmatics.
> > >
> > > 1/3 has a representation as g-adic.
> > > Similarly, pi is a clearly defined value and also, as any real number, has a g adic represantation.
> >
> > Pi is a clearly defined value? What is you moron? Don't tell me circumference length divided by diameter.
> >
> > Pi only has a number associated with it, if such a number describes its MEASURE you infinite FUCKING MORON!
>
> Pi is clearly defined as value by many different expressions, for example as a certain integral.

No fool. It's not clearly defined as an integral. It's only definition is circumference / diameter. Any integral you claim represents pi does not, because it is a "limit" that the integral returns, not the value of pi. In this case, no one knows what the fuck is the limit because pi has no measure.

> Since that value is unique, it defines pi.

Asshole. That it is unique means shit. Moooorrrrroooooon. 1/3 is also unique.

>
> And my point is that the radix system in actual math IS the 10-adic system, and that 1/3 has an expression in it.

By saying this, you are claiming that it is possible to represent 1/3 in base 10. A number theorem contradicts your claim. You are an idiot. Period.

> It is infinitely long, but that is no problem. It can be infinitely long, that's not against the law.

Bwaaa haaaaa haaaaa.

The only thing that is infinitely long is your STUPIDITY.

Chuckle. Fuck off you idiot. I piss and shit on you!

burs...@gmail.com

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Feb 12, 2017, 4:14:16 PM2/12/17
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Last time I looked at pi it was 6*atan(sqrt(1/3)) and
somebody made a nice streaming algorithm from it.

Computing the Digits in π
Carl D. Offner - October 15, 2015
http://www.cs.umb.edu/~offner/files/pi.pdf

Am Sonntag, 12. Februar 2017 21:27:20 UTC+1 schrieb John Gabriel:

burs...@gmail.com

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Feb 12, 2017, 4:19:23 PM2/12/17
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Street math:
“I knew this kid. He found the exact value of pi. He went nuts.”

JG went nuts without finding anything.

empt...@hotmail.com

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Feb 12, 2017, 4:43:49 PM2/12/17
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[3 divided into 1] scaled to [3 divided into 10]:

10 - 3 = 7, sum of counts of 1
7 - 3 = 4, sum of counts of 2
4 - 3 = 1, sum of counts of 3
1 - 3 < 0, remainder of 1

Result of 3 + 1/3

Then [3 divided into 10] scaled to [3 divided into 1]:

Result of 3/10 + (1/3 /10) = 3/10 + 1/30
.
.


empt...@hotmail.com

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Feb 12, 2017, 4:54:25 PM2/12/17
to

[3 divided into 1] scaled to [3 divided into 10]:

10 - 3 = 7, sum of counts of 1
7 - 3 = 4, sum of counts of 2
4 - 3 = 1, sum of counts of 3
1 - 3 < 0, remainder of 1

Result of 3 + 1/3

Then [3 divided into 10] scaled to [3 divided into 1]:

Result of 3 + 1/3 divided by 10 = 3/10 + 1/30
.

shio...@googlemail.com

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Feb 12, 2017, 5:01:36 PM2/12/17
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""
> > Pi is clearly defined as value by many different expressions, for example as a certain integral.
>
> No fool. It's not clearly defined as an integral. It's only definition is circumference / diameter. Any integral you claim represents pi does not, because it is a "limit" that the integral returns, not the value of pi. In this case, no one knows what the fuck is the limit because pi has no measure.""

No. Simply and flat out no.
The integral well defines a value (and so can a limit by the way).
There is no other value that integral could have than pi, so it defines it.

Also, as i said, defining something as the limit of a sequence bears no problem at all, since the only important thing in a definition is that it uniquely defines something.

For example, 1/3 can easily be defined as limit of the sequences 0,3, 0,33 and so on because that limit is unique and no other limit of any such sequence (the sequences which define g-adics) can have it as limit.


""
> > Since that value is unique, it defines pi.
>
> Asshole. That it is unique means shit. Moooorrrrroooooon. 1/3 is also unique.
> ""

That it is unique is the only important thing here, and yes, the same applies for 1/3 and its limit definition.



""
> >
> > And my point is that the radix system in actual math IS the 10-adic system, and that 1/3 has an expression in it.
>
> By saying this, you are claiming that it is possible to represent 1/3 in base 10. A number theorem contradicts your claim. You are an idiot. Period.
> ""

No i am not. I am saying that 1/3 has a representation as 10-adic, which may aswell be infinite.
You might want to rehash your knowledge of g-adics.
They are always infinite, even if infinitely many digits are 0.
Even 1 is defined by an infinitely long sequence as g-adic.


""
> The only thing that is infinitely long is your STUPIDITY.
>
> Chuckle. Fuck off you idiot. I piss and shit on you!
""

But how you a little man like you be able to do that?

abu.ku...@gmail.com

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Feb 12, 2017, 5:29:50 PM2/12/17
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ah 6(atan(secondr00t(1/3))), nice

Efftard K. Donglemeier

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Feb 12, 2017, 8:46:34 PM2/12/17
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Choke on ball-sack, you boring idiot.


John Gabriel

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Feb 12, 2017, 10:22:46 PM2/12/17
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On Sunday, 12 February 2017 16:01:36 UTC-6, shio...@googlemail.com wrote:

> > No fool. It's not clearly defined as an integral. It's only definition is circumference / diameter. Any integral you claim represents pi does not, because it is a "limit" that the integral returns, not the value of pi. In this case, no one knows what the fuck is the limit because pi has no measure.""
>
> No. Simply and flat out no.

Yes, you idiot. Yes.


> The integral well defines a value (and so can a limit by the way).

No and NO and NO again. An improper integral is a limit and limits require the existence of "irrational numbers" which DO NOT exist. Therefore, there is no
measure and hence no number.


> There is no other value that integral could have than pi, so it defines it.

Idiot. If a limit is not a rational number, then it is NOT a number. The only numbers are RATIONAL numbers. There are NO other numbers. Deal with it moron.

In mathematics, we talk about things being well defined. A number is well defined as the measure of a magnitude.


You are not a mathematician and have ZERO qualifications in mathematics. Plainly, you are an idiot.

>

<excrement>

abu.ku...@gmail.com

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Feb 12, 2017, 10:54:40 PM2/12/17
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it was said that a limit cannot be irrational,
such as the secondr00t of a half, or
the secondr00t(...9999.o)

> <deletia excretia>

shio...@googlemail.com

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Feb 12, 2017, 11:24:00 PM2/12/17
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""
> > The integral well defines a value (and so can a limit by the way).
>
> No and NO and NO again. An improper integral is a limit and limits require the existence of "irrational numbers" which DO NOT exist. Therefore, there is no
> measure and hence no number.""

What you call measure is completely irrelevant for the definition of a mathematical element.
And obviously irrational numbers exist.
To deny their existance means basically to deny the existance of infinite sequences and there is no basis for that.



>""
> > There is no other value that integral could have than pi, so it defines it.
>
> Idiot. If a limit is not a rational number, then it is NOT a number. The only numbers are RATIONAL numbers. There are NO other numbers. Deal with it moron.
>
> In mathematics, we talk about things being well defined. A number is well defined as the measure of a magnitude.
> ""

What you call number is irrelevant for mathematics.
Pi is a proper and well defined element of the ring of real numbers.

In mathematics, your definition of measure and number both have absolutely no place, because they are bad and lead to nothing.

If you want, yes, say that after your definition, pi is not a number.
It is not like anyone cares what you think is a number because pi as a ring element is absolutely well defined and useful.

""
> You are not a mathematician and have ZERO qualifications in mathematics. Plainly, you are an idiot.
> ""

I got a degree unlike you, which qualifies me to teach you.

John Gabriel

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Feb 13, 2017, 9:50:23 AM2/13/17
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Yes, if you keep on telling yourself that enough times, you will believe it. Chuckle.

last...@gmail.com

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Feb 13, 2017, 10:12:22 AM2/13/17
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Get new material. No one cares about how badly you don't understand anything.

thugst...@gmail.com

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Feb 13, 2017, 10:59:49 AM2/13/17
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yeah, get some new material. like,
if the area of the sphere is the unit,
what is a)
the circumference, and b)
the diameter

abu.ku...@gmail.com

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Feb 13, 2017, 2:52:11 PM2/13/17
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well, I can't think if a sum to approach the r00t of a half,
although 2 is just 1/1 +1/2 +1/4 + some dots

Jan

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Feb 13, 2017, 5:47:43 PM2/13/17
to
On Sunday, February 12, 2017 at 8:24:00 PM UTC-8, shio...@googlemail.com wrote:
> ""
> > > The integral well defines a value (and so can a limit by the way).
> >
> > No and NO and NO again. An improper integral is a limit and limits require the existence of "irrational numbers" which DO NOT exist. Therefore, there is no
> > measure and hence no number.""
>
> What you call measure is completely irrelevant for the definition of a mathematical element.
> And obviously irrational numbers exist.
> To deny their existance means basically to deny the existance of infinite sequences and there is no basis for that.

I think John suffers from some mental condition. Nothing serious AFAICT but
just enough to make him produce those nonsensical posts here.

--
Jan

shio...@googlemail.com

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Feb 13, 2017, 6:22:28 PM2/13/17
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Don't need to tell it to myself, got it signed by my uni.

shio...@googlemail.com

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Feb 13, 2017, 6:22:55 PM2/13/17
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ya, most probably.

John Gabriel

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Sep 30, 2017, 12:50:58 AM9/30/17
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The problem lies not with me but those who are too stupid to understand.

Euler blundered seriously by defining S = Lim S.

https://www.linkedin.com/pulse/eulers-worst-definition-lim-john-gabriel/

>
> --
> Jan

Quadibloc

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Sep 30, 2017, 2:32:28 AM9/30/17
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On Sunday, February 12, 2017 at 8:22:46 PM UTC-7, John Gabriel wrote:

> Idiot. If a limit is not a rational number, then it is NOT a number. The
> only numbers are RATIONAL numbers. There are NO other numbers. Deal with
> it moron.

We all have to deal with facts. Why we have to deal with the things you
say, however, is not apparent: you may claim that you know better than
the majority of the people who call themselves mathematicians, but except
for making loud and annoying claims, you really present no reason why we
should believe any of this stuff.

Now, it _is_ true that we don't need any irrational numbers to measure
distances in the real world, because we can't measure them accurately
enough to even need more than a tiny fraction of the rational numbers.

Maybe you have figured out a way to still do calculus while using a
number system that has holes in it like the rational number system does,
instead of one where stuff like Dedekind cuts are used to plug all the
wholes. Why it's worth taking the extra trouble to care about that kind
of stuff is more than merely unclear.

John Savard

Quadibloc

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Sep 30, 2017, 2:35:45 AM9/30/17
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On Sunday, February 12, 2017 at 8:22:46 PM UTC-7, John Gabriel wrote:

> You are not a mathematician and have ZERO qualifications in mathematics.
> Plainly, you are an idiot.

If it's plain, why is the whole world under the sway of mythmatics instead
of what you call mathematics?

John Savard

John Gabriel

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Sep 30, 2017, 9:01:04 AM9/30/17
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On Saturday, 30 September 2017 01:32:28 UTC-5, Quadibloc wrote:
> On Sunday, February 12, 2017 at 8:22:46 PM UTC-7, John Gabriel wrote:
>
> > Idiot. If a limit is not a rational number, then it is NOT a number. The
> > only numbers are RATIONAL numbers. There are NO other numbers. Deal with
> > it moron.
>
> We all have to deal with facts. Why we have to deal with the things you
> say, however, is not apparent: you may claim that you know better than
> the majority of the people who call themselves mathematicians, but except
> for making loud and annoying claims, you really present no reason why we
> should believe any of this stuff.

Actually I do and there are mainstream academics who agree with me.

Dr. Ahmad Zainy Al-Yasry (PhD mathematics) stated on LinkedIn that my article

https://www.linkedin.com/pulse/how-we-got-numbers-john-gabriel-1

is the most accurate account of how we got numbers. He has never read anything with more clarity, accuracy and rigour.

Your statement is just an assertion.

>
> Now, it _is_ true that we don't need any irrational numbers to measure
> distances in the real world, because we can't measure them accurately
> enough to even need more than a tiny fraction of the rational numbers.

We can't measure incommensurable magnitudes. If we had irrational numbers, there would be no need to measure them because a number is the measure of a magnitude.

>
> Maybe you have figured out a way to still do calculus while using a
> number system that has holes in it like the rational number system does,

The expression "number system" is meaningless nonsense and those who use it clearly do not understand what is a number. There are no holes because there is no such thing as a "real" number line - it is a myth.

> instead of one where stuff like Dedekind cuts are used to plug all the
> wholes.

By the ridiculous and illogical notion that every distance is related to some indistinguishable point? Absurd. A distance is not a number. The measure of a distance/magnitude is a number. Unless you can reify points on a number line, what you have is nonsense. You can construct a rational number line, but nothing more.

Moreover, calculus works because of the arithmetic mean given from an interval of ordinates for a function that is both continuous and smooth. There are NO holes to plug as you say. This seemingly impossible mean is determinable by virtue of the fact that the sum telescopes. I was the first to prove this constructively using your bogus calculus and the new calculus:

Flawed mainstream calculus with a patch I created called a positional derivative:

https://drive.google.com/open?id=0B-mOEooW03iLZG1pNlVIX2RTR0E

The positional derivative:

https://drive.google.com/open?id=0B-mOEooW03iLVVg3QWtOdkxUbVk

New Calculus:

https://drive.google.com/open?id=0B-mOEooW03iLblJNLWJUeGxqV0E

> Why it's worth taking the extra trouble to care about that kind
> of stuff is more than merely unclear.

Well, for starters, education of calculus is in a dire mess. Students never understand calculus. Even their professors never understand. They simply learn to use. Knisley has written several articles on the state of calculus and the education.

http://faculty.etsu.edu/knisleyj/calculus/Crisis.htm

But Knisley does not have the answers. I on the other hand know the answers. A couple of articles showing that Knisley does not understand calculus:

https://drive.google.com/open?id=0B-mOEooW03iLaU5PUGNyaXhaajg

https://drive.google.com/open?id=0B-mOEooW03iLUkJTZE9FLUtZUEk

Secondly, the current formulation is flawed even though its results are generally correct.

Thirdly, the mainstream calculus has reached a dead end many years ago. The New Calculus contains many new features and theorems not possible using the flawed Newtonian formulation. The New Calculus is the first and only rigorous formulation of calculus in human history. Although I have made significant progress in establishing the New Calculus, there is still much more to be discovered.

Finally, your conclusion/assertions that I don't know better are simply false. I do know better than all other academics.

>
> John Savard

John Gabriel

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Sep 30, 2017, 9:06:48 AM9/30/17
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Most students have no influence or sway what their curricula entail.
The world is under the sway of the academic trash heap composed of ignorant, arrogant and incompetent academics who refuse to see the light.

In due time, the ideas of the New Calculus will replace the rot of mainstream calculus. As with everything, people are very slow to catch on to the truth. Already, there are thousands who have learned the New Calculus and have applied it. That group is growing daily.

Understanding and progress only comes through well-formed concepts, not anti-mathematical nonsense such as infinity, infinitesimals and limit theory that is based on the assumption that real numbers are constructible. Real analysis is that bogus subject about an object that does not exist: "real" number.

Points have no extent or dimension and mainstreamers do not have a clue what is a number or how it is perfectly derived from nothing:

https://www.linkedin.com/pulse/how-we-got-numbers-john-gabriel-1

It's ironic because numbers are the foundation of mathematics.

>
> John Savard

Zelos Malum

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Sep 30, 2017, 9:14:55 AM9/30/17
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Den söndag 12 februari 2017 kl. 14:14:11 UTC+1 skrev John Gabriel:
> S = Lim S in this case, contradicts the fact that 1/3 has no representation in base 10.
>
> However, it also leads to even more absurd definitions, that is, pi=3.14159... when in fact it is known that pi has NO measure.
>
>
> https://www.youtube.com/watch?v=5hulvl3GgGk
>
> https://www.youtube.com/watch?v=w8s_8fNePEE
>
>
> Your comments are unwelcome shit and will be ignored.
>
> This is posted on this newsgroup in the interests of public education and to eradicate ignorance and stupidity from mainstream mythmatics.

ANd so you continue your shit about focusing only on your own delusions, common, grow up.

Dan Christensen

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Sep 30, 2017, 9:39:14 AM9/30/17
to
On Sunday, February 12, 2017 at 8:14:11 AM UTC-5, John Gabriel wrote:
> S = Lim S in this case, contradicts the fact that 1/3 has no representation in base 10.
>

S = Lim S is nonsense to begin with -- one of your biggest blunders ever, Troll Boy. And that's saying a LOT!


> However, it also leads to even more absurd definitions, that is, pi=3.14159... when in fact it is known that pi has NO measure.
>

Like it or not, Troll Boy, pi is a real number. So is root 2, negative numbers, and 0. Your hero would have had you gassed and incinerated as a mental defective and for attempting to sabotage the education system with your kooky ideas.


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

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Sep 30, 2017, 12:05:28 PM9/30/17
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Your days are numbered moron. You will be ashamed of everything that you have accused me of - well, that's if you live long enough.

Please, whatever you do, do not produce any offspring. There are enough stupid people in academia and we don't need more.

burs...@gmail.com

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Sep 30, 2017, 5:04:36 PM9/30/17
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I don't know what is more stupid, to make "Euler S =
Lim S" a case, or to think Newton series work
without convergence.

Here is an example of a Newton rule, that doesn't work
when diverging series are invokved, we quickly get the
contradiction:

0 = 1

I am using Newtons schema from Page 158/159: in his
THE METHOD OF FLUXIONS AND INFINITE SERIES. For
a picture of this schema see here:
https://gist.github.com/jburse/e60242e2e02e611e4373df55bfc37953#gistcomment-2211516

So I apply the schema:

1 + 1 + 1 + 1 + 1 + 1 ...

- 1 - 1 - 1 - 1 - 1 ...

==================================
0 + 0 + 0 + 0 + 0 + 0 ... = 1

mitchr...@gmail.com

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Sep 30, 2017, 5:14:36 PM9/30/17
to
.9 repeating and One share a sameness. They are quantities
that are different by the infinitely small.
.9 repeating is a transcendental One; the First quantity
below one. The infinitely small difference means a shared
sameness that is still not absolutely same.

Mitchell Raemsch

netzweltler

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Sep 30, 2017, 5:42:46 PM9/30/17
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Am Samstag, 30. September 2017 23:14:36 UTC+2 schrieb mitchr...@gmail.com:
>
> .9 repeating and One share a sameness. They are quantities
> that are different by the infinitely small.
> .9 repeating is a transcendental One; the First quantity
> below one. The infinitely small difference means a shared
> sameness that is still not absolutely same.
>
> Mitchell Raemsch

If there is a quantity between 0.999... and 1 and, therefore, these are two different points on the number line then you should define the distance between these two points. If you don't, then your first quantity is simply undefined.

'infinitely small' is not a definition. There are no two distinct points on the number line 'infinite(simal)ly' far away from each other.

John Gabriel

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Sep 30, 2017, 5:57:30 PM9/30/17
to
On Saturday, 30 September 2017 16:04:36 UTC-5, burs...@gmail.com wrote:
> I don't know what is more stupid, to make "Euler S =
> Lim S" a case, or to think Newton series work
> without convergence.

Huh? You need to slow down with all that pot because your offspring will be affected. As it is I am worried about what kind of morons you will produce.

Who said Newton series works without convergence?

Jan, the rest of your comment is just too absurd.

In future, be "brief". No, I am not talking about your sex life man. I mean your comments just go on and on. If you want to hold a discussion, keep your comments short and focused. You are a scatterbrain. Hope this helps.

FromTheRafters

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Sep 30, 2017, 6:25:16 PM9/30/17
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netzweltler explained on 9/30/2017 :
They do not differ
by infinite small.
They differ only
by none at all.

John Gabriel

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Sep 30, 2017, 6:58:40 PM9/30/17
to
Well, if you define 0.999... to be equal to a brick, then a brick and 0.999... differ by none at all.

There is not a single support for this bullshit equality aside from S = Lim S and this is an ill-formed definition - the Eulerian Blunder.

burs...@gmail.com

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Sep 30, 2017, 8:23:32 PM9/30/17
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Well you wrote here Newton didn't consider infinity,
and you say he can define partial sums without infinity.

Well this might be true, but you then go on and say
he used limits. But how do you get limits, without

https://groups.google.com/d/msg/sci.math/HIzzJSLsw60/vSOH7WnhAwAJ

knowing whether a series converges or not? For convergence
you need to make statement about infinitely many elements,

for example the Cauchy condition, is for infinitely many
pairs n,m, namely you need to know (or assume you know):

forall n,m >= N(e) |an - am| =< e

The above looks like a pi-sentence, and is not verifiable
if we do not know much about {ak}. So you are in the waters of:

It is also familiar in the philosophy of science that most
hypotheses are neither verifiable nor refutable. Thus, Kant’s
antinomies of pure reason include such statements as that space
is infinite, matter is infinitely divisible, and the series of
efficient causes is infinite. These hypotheses all have the form

forall x exists y P(x, y).

For example, infinite divisibility amounts to “for every
product of fission, there is a time by which attempts to cut
it succeed” and the infinity of space amounts to “for each
distance you travel, you can travel farther.”

https://www.andrew.cmu.edu/user/kk3n/complearn/chapter11.pdf

John Gabriel

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Sep 30, 2017, 8:31:14 PM9/30/17
to
On Saturday, 30 September 2017 19:23:32 UTC-5, burs...@gmail.com wrote:
> Well you wrote here Newton didn't consider infinity,
> and you say he can define partial sums without infinity.
>
> Well this might be true, but you then go on and say
> he used limits. But how do you get limits, without
>
> https://groups.google.com/d/msg/sci.math/HIzzJSLsw60/vSOH7WnhAwAJ

Very easy: Limits don't care if the terms are all there or even there at all.

> For convergence you need to make statement about infinitely many elements,

Wrong. You arrive at the conclusion about convergence from only the general partial sum.

>
> for example the Cauchy condition, is for infinitely many
> pairs n,m, namely you need to know (or assume you know):

That is false. We use inference and the general term to arrive at the conclusion. Nothing about infinity anywhere.

>
> forall n,m >= N(e) |an - am| =< e

The forall is true because of the conclusion. Nothing about infinity here also.

burs...@gmail.com

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Sep 30, 2017, 8:32:08 PM9/30/17
to
So the product, its terms sn*tn might be observable,
but that the product is Cauchy is not observable directly.

That a series is Cauchy is neither effectively refutable
nor effectively verifiable. If you find e, n, m with:

|an-am| > e

You still don't know whether there is N, where the series
behaves Cauchy. The full Cauchy condition is:

forall e exists N forall n,m>=N |an-am|=<e

So it has the shape VEV.

burs...@gmail.com

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Sep 30, 2017, 8:35:38 PM9/30/17
to
This doesn't mean that math or Newton cannot identify
some series as Cauchy, but if we had a black box:

+------+
| a_n |---> You
+------+

And you could take a ticket one by one with the
numbers of the sequence, you will never know whether

the series is Cauchy or not.

burs...@gmail.com

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Sep 30, 2017, 8:41:05 PM9/30/17
to
Math can even reason, that if these two boxes
are Cauchy, i.e. the series {an} and {bn}:

+------+
| a_n |---> You
+------+

+------+
| b_n |---> You
+------+

That then the following series will be Cauchy
as well, namely the product series {an*bn}:

+----------+
| a_n*b_n |---> You
+----------+

You can construct the product series, this is
observable, you can just combine the two black boxes
and create a new black box. If each black box,

gives a rationl number, you can build a new
black box, for the product, but still being Cauchy
is not effectively refutable or effectively verifiable.

We only proved a formal implication:

{an}, {bn} Cauchy ==> {an*bn} Cauchy

That {an*bn} is observable is rather trivial, and
that Newton could also do it is to expect. But if
you can construct {an*bn} doesn't mean you have solved
the limit problem for unknown series.

mitchr...@gmail.com

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Sep 30, 2017, 8:52:29 PM9/30/17
to
On Saturday, September 30, 2017 at 2:42:46 PM UTC-7, netzweltler wrote:
> Am Samstag, 30. September 2017 23:14:36 UTC+2 schrieb mitchr...@gmail.com:
> >
> > .9 repeating and One share a sameness. They are quantities
> > that are different by the infinitely small.
> > .9 repeating is a transcendental One; the First quantity
> > below one. The infinitely small difference means a shared
> > sameness that is still not absolutely same.
> >
> > Mitchell Raemsch
>
> If there is a quantity between 0.999... and 1

At some point there needs to be next quantities with
nothing in between.

and, therefore, these are two different points on the number line then you should define the distance between these two points. If you don't, then your first quantity is simply undefined.
>
> 'infinitely small' is not a definition.

It has a definition of being one divided by infinity
It can't be divided any further. It is The Infinitely divided One.
Their quantity difference is by the infinitely small.
This means there are no quantities in between them.

>There are no two distinct points on the number line 'infinite(simal)ly' far away from each other.


Mitchell Raemsch

netzweltler

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Oct 1, 2017, 3:22:43 AM10/1/17
to
Am Sonntag, 1. Oktober 2017 02:52:29 UTC+2 schrieb mitchr...@gmail.com:
> On Saturday, September 30, 2017 at 2:42:46 PM UTC-7, netzweltler wrote:
> > Am Samstag, 30. September 2017 23:14:36 UTC+2 schrieb mitchr...@gmail.com:
> > >
> > > .9 repeating and One share a sameness. They are quantities
> > > that are different by the infinitely small.
> > > .9 repeating is a transcendental One; the First quantity
> > > below one. The infinitely small difference means a shared
> > > sameness that is still not absolutely same.
> > >
> > > Mitchell Raemsch
> >
> > If there is a quantity between 0.999... and 1
>
> At some point there needs to be next quantities with
> nothing in between.
Here you say there is a quantity in between.

>
> and, therefore, these are two different points on the number line then you should define the distance between these two points. If you don't, then your first quantity is simply undefined.
> >
> > 'infinitely small' is not a definition.
>
> It has a definition of being one divided by infinity
> It can't be divided any further. It is The Infinitely divided One.
> Their quantity difference is by the infinitely small.
> This means there are no quantities in between them.
Here you say there is no quantity in between.

>
> >There are no two distinct points on the number line 'infinite(simal)ly' far away from each other.
>
>
> Mitchell Raemsch

Doesn't sound like a definition to me.

Do you agree that 0.999... means infinitely many commands
Add 0.9 + 0.09
Add 0.99 + 0.009
Add 0.999 + 0.0009
…?
Then following all of these infinitely many commands won’t get you to point 1. If you reached point 1 you have disobeyed those commands, because every single of those infinitely many commands tells you to get closer to 1 but NOT reach 1.
Therefore, if you want to define the position of a “point” 0.999… on the number line, it cannot be at position 1 – and for the same reason (“disobeying those commands”) it cannot be short of 1 nor can it be past 1.
So, if you want to measure the distance |1 – 0.999…| you know where to start the measurement (at point 1) but you don’t know where to stop the measurement, because the position of a “point” 0.999… is not defined on the number line.

FromTheRafters

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Oct 1, 2017, 7:56:01 AM10/1/17
to
mitchr...@gmail.com has brought this to us :
> On Saturday, September 30, 2017 at 2:42:46 PM UTC-7, netzweltler wrote:
>> Am Samstag, 30. September 2017 23:14:36 UTC+2 schrieb mitchr...@gmail.com:
>>>
>>> .9 repeating and One share a sameness. They are quantities
>>> that are different by the infinitely small.
>>> .9 repeating is a transcendental One; the First quantity
>>> below one. The infinitely small difference means a shared
>>> sameness that is still not absolutely same.
>>>
>>> Mitchell Raemsch
>>
>> If there is a quantity between 0.999... and 1
>
> At some point there needs to be next quantities with
> nothing in between.

Not really, in fact in the reals if there are two different (nearly?)
adjacent real numbers then there is always a place between them for
another real number to occupy.

Even worse would be the case of two nearly adjacent rationals. If 0.999
repeating (a rational number) were to be taken as one of those numbers
and 1.000 repeating (another rational number) as the other then it is
easy to see that in the reals, many numbers (irrationals) would have to
exist between these two. The fact remains that these two numbers are
actually only two representations of the same exact number.

It seems counterintuitive when a number is viewed (or represented) as
an infinite unending 'process' of achieving better and better
approximations, and that we can never actually reach the destination
number. In my view, this sequence and/or infinite sum is a
representation of the destination number "as if" we could have gotten
there by that process. IOW "*After* infinitely many 'better'
approximations" we reach the destination number *exactly* even if we
cannot 'pinpoint' that number on the number line. A 'limit' is not an
approximation, it is the destination number (if there is one in that
field) implied by the sequence or series in question.

> and, therefore, these are two different points on the number line then you
> should define the distance between these two points. If you don't, then your
> first quantity is simply undefined.

I know that you are against the idea that a number can have multiple
representations (like 0.999... and 1.000...) but it happens all the
time. 1/1 2/2 3/3 etcetera all represent the number one.

>> 'infinitely small' is not a definition.
>
> It has a definition of being one divided by infinity
> It can't be divided any further. It is The Infinitely divided One.
> Their quantity difference is by the infinitely small.
> This means there are no quantities in between them.
>
>> There are no two distinct points on the number line 'infinite(simal)ly' far
>> away from each other.
>
>
> Mitchell Raemsch

Thank you for defending your view rather than just restating your view.
It makes for a much better discussion.

netzweltler

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Oct 1, 2017, 8:28:13 AM10/1/17
to
Am Sonntag, 1. Oktober 2017 13:56:01 UTC+2 schrieb FromTheRafters:
>
> It seems counterintuitive when a number is viewed (or represented) as
> an infinite unending 'process' of achieving better and better
> approximations, and that we can never actually reach the destination
> number. In my view, this sequence and/or infinite sum is a
> representation of the destination number "as if" we could have gotten
> there by that process.
If the process doesn't get us there then we don't get there. Where do you get your "as if" from?

> IOW "*After* infinitely many 'better'
> approximations" we reach the destination number *exactly* even if we
> cannot 'pinpoint' that number on the number line.
Please define "*After* infinitely many 'better' approximations". All we've got is infinitely many approximations - each approximation telling us that we get closer to 1 but don't reach 1. There is no *after* specified in this process.

John Gabriel

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Oct 1, 2017, 9:17:49 AM10/1/17
to
On Saturday, 30 September 2017 19:32:08 UTC-5, burs...@gmail.com wrote:
> So the product, its terms sn*tn might be observable,
> but that the product is Cauchy is not observable directly.
>
> That a series is Cauchy is neither effectively refutable
> nor effectively verifiable. If you find e, n, m with:
>
> |an-am| > e
>
> You still don't know whether there is N, where the series
> behaves Cauchy. The full Cauchy condition is:
>
> forall e exists N forall n,m>=N |an-am|=<e
>
> So it has the shape VEV.
>
> Am Sonntag, 1. Oktober 2017 02:23:32 UTC+2 schrieb burs...@gmail.com:
> > Well you wrote here Newton didn't consider infinity,
> > and you say he can define partial sums without infinity.
> >
> > Well this might be true, but you then go on and say
> > he used limits. But how do you get limits, without
> >
> > https://groups.google.com/d/msg/sci.math/HIzzJSLsw60/vSOH7WnhAwAJ
> >
> > knowing whether a series converges or not? For convergence
> > you need to make statement about infinitely many elements,
> >
> > for example the Cauchy condition, is for infinitely many
> > pairs n,m, namely you need to know (or assume you know):
> >
> > forall n,m >= N(e) |an - am| =< e

Each time I think you can't say anything more stupid, you surprise me.
Listen stupid, the forall you have there is based on induction. There is no forall. A Cauchy sequence does not require "forall". The "forall" is a result of inference.

FromTheRafters

unread,
Oct 1, 2017, 9:20:16 AM10/1/17
to
After serious thinking netzweltler wrote :
> Am Sonntag, 1. Oktober 2017 13:56:01 UTC+2 schrieb FromTheRafters:
>>
>> It seems counterintuitive when a number is viewed (or represented) as
>> an infinite unending 'process' of achieving better and better
>> approximations, and that we can never actually reach the destination
>> number. In my view, this sequence and/or infinite sum is a
>> representation of the destination number "as if" we could have gotten
>> there by that process.
> If the process doesn't get us there then we don't get there. Where do you get
> your "as if" from?

If you had sufficient time, then you would get there.

>> IOW "*After* infinitely many 'better'
>> approximations" we reach the destination number *exactly* even if we
>> cannot 'pinpoint' that number on the number line.
> Please define "*After* infinitely many 'better' approximations". All we've
> got is infinitely many approximations - each approximation telling us that we
> get closer to 1 but don't reach 1. There is no *after* specified in this
> process.

There is also no "time" mentioned, so why is there an assumption of a
process which takes time to complete? It is already completed (pi
exists as a number despite our inability to pinpoint it on the number
line by using an infinite alternating sum or any of the other infinite
processes) we just can't pinpoint it because we exist in a time
constrained universe with processes which take time to complete.
>
>> A 'limit' is not an
>> approximation, it is the destination number (if there is one in that
>> field) implied by the sequence or series in question.

You could define a sequence or series by progressing from zero, to zero
plus one, to zero plus one plus one half, to zero plus one plus one
half plus one quarter, etcetera. This looks like it goes on forever
getting closer and closer to some number without actually ever getting
there.

You could also define the same sequence or series by starting from two
and pulling something from one toward you by half the remaining
distance each time. In this second case, you already know the
destination even though the other representation of the same sequence
looks like it never gets there. Using the concept of infinity as
in,"infinitly many steps" you relieve yourself of the neccessity of
calculating the infinite sum approximations since you already know the
destination number (known as a limit). Despite the fact that the
process itself is neverending, these two 'things' are both
representations of the same number - namely two.

netzweltler

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Oct 1, 2017, 10:53:26 AM10/1/17
to
Am Sonntag, 1. Oktober 2017 15:20:16 UTC+2 schrieb FromTheRafters:
> After serious thinking netzweltler wrote :
> > Am Sonntag, 1. Oktober 2017 13:56:01 UTC+2 schrieb FromTheRafters:
> >>
> >> It seems counterintuitive when a number is viewed (or represented) as
> >> an infinite unending 'process' of achieving better and better
> >> approximations, and that we can never actually reach the destination
> >> number. In my view, this sequence and/or infinite sum is a
> >> representation of the destination number "as if" we could have gotten
> >> there by that process.
> > If the process doesn't get us there then we don't get there. Where do you get
> > your "as if" from?
>
> If you had sufficient time, then you would get there.
Show how time is involved in our process.

>
> >> IOW "*After* infinitely many 'better'
> >> approximations" we reach the destination number *exactly* even if we
> >> cannot 'pinpoint' that number on the number line.
> > Please define "*After* infinitely many 'better' approximations". All we've
> > got is infinitely many approximations - each approximation telling us that we
> > get closer to 1 but don't reach 1. There is no *after* specified in this
> > process.
>
> There is also no "time" mentioned, so why is there an assumption of a
> process which takes time to complete? It is already completed (pi
> exists as a number despite our inability to pinpoint it on the number
> line by using an infinite alternating sum or any of the other infinite
> processes) we just can't pinpoint it because we exist in a time
> constrained universe with processes which take time to complete.
If you insist on introducing time to our process, try this:

t = 0: write 0.9
t = 0.9: append another 9
t = 0.99: append another 9
...

By time t = 1 we have completed infinitely many steps and we know all we need to know about our process:
Since time is continuous we reach time t = 1 and after.
By t = 1 we have completed writing 0.999...
Since the steps of addition are discrete, we can tell that we don't reach point 1 - neither during the process nor *after* the process by t = 1.

If your claim is, that we reach point 1, you need to show which step on this _complete_ list of infinitely many steps accomplishes that.

burs...@gmail.com

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Oct 1, 2017, 11:12:21 AM10/1/17
to
Not every forall is induction. Induction works
only for natural numbers.

But the epsilon is a forall over rational numbers
(or real number), what induction do you have in mind.

And why do you call Peano crapaxioms, when nevertheless
you say induction is needed here.

Ever incurred to you that Peano axioms capture
natural numbers and their induction?

burs...@gmail.com

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Oct 1, 2017, 11:30:48 AM10/1/17
to
The problem with bird brain John Gabriel is a kind
of simplicistic view of math. Things he can sometimes
do by himself are summed as

"You arrive at the conclusion about convergence from
only the general partial sum.".
This is like saying nothing.

Then the nonsense goes on:

"We use inference and the general term to arrive at the
conclusion. Nothing about infinity anywhere."
This is like saying nothing again.

It only focuses on the starting point, the series give
in a form {a_n}, which JG termed general partial sum,
and next JG termed it general term.

It completely neglects what the outcome is, what shape
it is, namely the convergence statement. And it also
completely neglects what "meas" there are to get from
A to B, i.e. form {a_n} for example to {a_n} Cauchy.

Now there came "induction", which is a nice guess,
but unfortunately it is probably only half an answer,
because "induction" is N, what do we need for Q?

The statement {a_n} Cauchy is:

forall e exists N forall n,m>=N |an - am| =< e

The |an - am| =< e is still something in Q, and not
in N. How do you get rid of Q? Why should Peano be
crapaxiom? Why shouldn't there be any axioms?

The later also a favorite topic of bird brain John
Gabriel, shouting all the time, there are no axioms.
LoL, laughing my ass off.

FromTheRafters

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Oct 1, 2017, 11:45:39 AM10/1/17
to
netzweltler formulated the question :
> Am Sonntag, 1. Oktober 2017 15:20:16 UTC+2 schrieb FromTheRafters:
>> After serious thinking netzweltler wrote :
>>> Am Sonntag, 1. Oktober 2017 13:56:01 UTC+2 schrieb FromTheRafters:
>>>>
>>>> It seems counterintuitive when a number is viewed (or represented) as
>>>> an infinite unending 'process' of achieving better and better
>>>> approximations, and that we can never actually reach the destination
>>>> number. In my view, this sequence and/or infinite sum is a
>>>> representation of the destination number "as if" we could have gotten
>>>> there by that process.
>>> If the process doesn't get us there then we don't get there. Where do you
>>> get your "as if" from?
>>
>> If you had sufficient time, then you would get there.
> Show how time is involved in our process.

If you have to add a next number (like one quarter) to a previous
result of adding such previous numbers (like one plus one half) then
you have introduced time. Thee is a 'previous' calculation needed as
input to the next calculation. The idea that you 'never' get there (to
two) introduces time also. I'm with you, I don't think time has any
place in this.

>>>> IOW "*After* infinitely many 'better'
>>>> approximations" we reach the destination number *exactly* even if we
>>>> cannot 'pinpoint' that number on the number line.
>>> Please define "*After* infinitely many 'better' approximations". All we've
>>> got is infinitely many approximations - each approximation telling us that
>>> we get closer to 1 but don't reach 1. There is no *after* specified in
>>> this process.
>>
>> There is also no "time" mentioned, so why is there an assumption of a
>> process which takes time to complete? It is already completed (pi
>> exists as a number despite our inability to pinpoint it on the number
>> line by using an infinite alternating sum or any of the other infinite
>> processes) we just can't pinpoint it because we exist in a time
>> constrained universe with processes which take time to complete.
> If you insist on introducing time to our process, try this:

You misunderstand me. I'm not insisting that, in fact I insist the
opposite. I take the infinite sequence or series representation to be
just that, a represenation of a number -- not a process at all. This
avoids the idea that time is a constraint against a number being exact.

When it come to application, then you may have to consider the
indicated process and get as close an approximation as you desire. The
representations 0.999... and the infinite series or the sequences
related to it, are all just different representations of the number
one, just as our current representation are all representations of the
number two. Time has nothing at all to do with it, hence there is no
'almost, but not quite there' to worry about.

mitchr...@gmail.com

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Oct 1, 2017, 1:01:18 PM10/1/17
to
On Sunday, October 1, 2017 at 12:22:43 AM UTC-7, netzweltler wrote:
> Am Sonntag, 1. Oktober 2017 02:52:29 UTC+2 schrieb mitchr...@gmail.com:
> > On Saturday, September 30, 2017 at 2:42:46 PM UTC-7, netzweltler wrote:
> > > Am Samstag, 30. September 2017 23:14:36 UTC+2 schrieb mitchr...@gmail.com:
> > > >
> > > > .9 repeating and One share a sameness. They are quantities
> > > > that are different by the infinitely small.
> > > > .9 repeating is a transcendental One; the First quantity
> > > > below one. The infinitely small difference means a shared
> > > > sameness that is still not absolutely same.
> > > >
> > > > Mitchell Raemsch
> > >
> > > If there is a quantity between 0.999... and 1
> >
> > At some point there needs to be next quantities with
> > nothing in between.
> Here you say there is a quantity in between.

It goes both ways. There are the in-betweens
until they reach to smallest or infinitely
small difference

Mitchell Raemsch
>
> >
> > and, therefore, these are two different points on the number line then you should define the distance between these two points. If you don't, then your first quantity is simply undefined.
> > >
> > > 'infinitely small' is not a definition.
> >
> > It has a definition of being one divided by infinity
> > It can't be divided any further. It is The Infinitely divided One.
> > Their quantity difference is by the infinitely small.
> > This means there are no quantities in between them.
> Here you say there is no quantity in between.
>
> >
> > >There are no two distinct points on the number line 'infinite(simal)ly' far away from each other.

You mean together with each other... with no in between.
When not closest together there are in between.

> >
> >
> > Mitchell Raemsch
>
> Doesn't sound like a definition to me.

The usable definition is one divided by infinity...
First quantity to exist in mathematics.

John Gabriel

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Oct 1, 2017, 3:32:32 PM10/1/17
to
Hello my little stupid.

Peano's Crapaxiom 5 is the induction axiom:

If a set S of numbers contains zero and also the successor of every number in S, then every number is in S.

Did you even ever bother to study Peano's crapaxioms? Or did you just memorise them by heart? Stupid boy you are.

Me

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Oct 1, 2017, 3:38:14 PM10/1/17
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On Sunday, October 1, 2017 at 9:32:32 PM UTC+2, John Gabriel wrote:

"It is a very bad idea and nothing less than stupid to define 1/3 = 0.333..."

Why?

"0.333..." is just short for

lim SUM_{k=1..n} (3/10^n)
n->oo

and the latter *is* (provable) 1/3.

Btw. Hence 1/3 = 0.333... is a THEOREM not a DEFINITION, idiot.

John Gabriel

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Oct 1, 2017, 3:48:24 PM10/1/17
to
On Sunday, 1 October 2017 14:38:14 UTC-5, Me wrote:
> On Sunday, October 1, 2017 at 9:32:32 PM UTC+2, John Gabriel wrote:
>
> "It is a very bad idea and nothing less than stupid to define 1/3 = 0.333..."
>
> Why?
>
> "0.333..." is just short for
>
> lim SUM_{k=1..n} (3/10^n)
> n->oo

Wrong. It is short for

SUM_{k=1...oo} (3/10^n)

That is what ensures you have the correct representation and the only justification for you using 0.333... for otherwise you could @.#*!...
Ever asked yourself why you use the former? Yes idiot, because it signifies a mythical "infinite" sum.

It is most definitely not the same as 1/3 because 1/3 is well defined. It is not shorter than 1/3 because any idiot can see that 0.333... has more literals. Chuckle.

>
> and the latter *is* (provable) 1/3.
>
> Btw. Hence 1/3 = 0.333... is a THEOREM not a DEFINITION, idiot.

No dipshit. It is a ***DEFINITION***. There is ZERO to prove. The fact that the limit of the series 0.3+0.03+... is 1/3 proves NOTHING about 0.333...

The limit which is 1/3 doesn't give a fuck if all the terms in the series 0.333... (NOT a limit BUT a series which is DEFINED equal to the limit) are there or even if they are there at all! Moron!!!! You don't seem able to grasp this because your IQ is evidently too low.

Now let's hear your retort idiot!

It will go something like this:

Idiot "Me" response:

But 0.333... is the limit. John shakes his head...

But "skfalfd..." is the limit you moron. What is your justification for using 0.333... Yes idiot. The fact that it represents an "infinite sum".

Sigh....

Me

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Oct 1, 2017, 3:54:51 PM10/1/17
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On Sunday, October 1, 2017 at 9:48:24 PM UTC+2, John Gabriel wrote:
> On Sunday, 1 October 2017 14:38:14 UTC-5, Me wrote:
> > On Sunday, October 1, 2017 at 9:32:32 PM UTC+2, John Gabriel wrote:
> >
> > "It is a very bad idea and nothing less than stupid to define 1/3 = 0.333..."
> >
> > Why?
> >
> > "0.333..." is just short for
> >
> > lim SUM_{k=1..n} (3/10^n)
> > n->oo
>
> Wrong. It is short for
>
> SUM_{k=1...oo} (3/10^n)

John, you really should seek some help.

I guess, you once KNEW that

SUM_{k=1...oo}

is just short for

lim SUM_{k=1..n} .
n->oo

Hint: We CAN'T actually "sum up" infinitely many terms.

John Gabriel

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Oct 1, 2017, 3:55:07 PM10/1/17
to
And again, let's not forget the most damning fact: 1/3 CANNOT be represented in base 10. Not even if the series 0.333... could hypothetically be taken to infinity.

You will never again claim that 0.333... is a limit in an attempt to obscure and hide your ignorance, incompetence and stupidity. You WILL admit you are wrong and stop being obstinate asses.

John Gabriel

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Oct 1, 2017, 3:59:14 PM10/1/17
to
No idiot. It is DEFINED that way by Euler. It is short for your IGNORANCE and STUPIDITY.

>
> Hint: We CAN'T actually "sum up" infinitely many terms.

Of course you can't. So why use 0.333... as the representation and not asadaff... instead? Because you are a stupid imbecile who has never learned to think independently.

You use 0.333... because it is supported by the idea of an infinite sum. By the same token you retard, you would never write 3.14159... for pi if it did not have the support of the mythical infinite sum. Ironically, if it could be taken to completion (impossible), then it would always be a RATIONAL number. But it can easily be proved that pi is not a rational number. It is not a number at all!

Get a brain you baboon!
Message has been deleted

John Gabriel

unread,
Oct 1, 2017, 4:02:07 PM10/1/17
to
On Sunday, 12 February 2017 07:14:11 UTC-6, John Gabriel wrote:
> S = Lim S in this case, contradicts the fact that 1/3 has no representation in base 10.
>
> However, it also leads to even more absurd definitions, that is, pi=3.14159... when in fact it is known that pi has NO measure.
>
>
> https://www.youtube.com/watch?v=5hulvl3GgGk
>
> https://www.youtube.com/watch?v=w8s_8fNePEE
>
>
> Your comments are unwelcome shit and will be ignored.
>
> This is posted on this newsgroup in the interests of public education and to eradicate ignorance and stupidity from mainstream mythmatics.

S = Lim S

STOPS RIGHT HERE AND NOW. It is the Eulerian Blunder and has no place in rational thought, never mind mathematics.

John Gabriel

unread,
Oct 1, 2017, 4:05:23 PM10/1/17
to
On Sunday, 1 October 2017 15:01:36 UTC-5, Me wrote:
> Additional comment:
>
> > > SUM_{k=1...oo} (3/10^n)
> > >
> > [...] It is most definitely not the same as 1/3
>
> Well, actually it is. There's a simple prove for the theorem
>
> lim SUM_{k=1..n} = 1/3 .
> n->oo
>
> Hence
>
> oo
> SUM (3/10^n) = 1/3 .
> k=1

No idiot. You define

oo
SUM (3/10^n) = 1/3 [A]
k=1

as being equal to

lim SUM_{k=1..n} = 1/3 [B]
n->oo

Get it moron? You DEFINE [A] = [B] aka S = Lim S.

There is NO PROOF of anything. Definitions do not require proof.

Me

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Oct 1, 2017, 4:06:56 PM10/1/17
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On Sunday, October 1, 2017 at 9:59:14 PM UTC+2, John Gabriel wrote:

> why use "0.333..." as the representation and not "asadaff..."

Because it gives a hint which number I might mean in this case.

Same with

0.111...
0.222...
0.333...
:
0.999...

> You use 0.333... because it is supported by the idea of an infinite sum.

Guess so.

> By the same token [...] you would never write 3.14159... for pi if it
> did not have the support of the [...] infinite sum.

Guess so, yes. :-)

It's called /decimal representation/.

See: https://en.wikipedia.org/wiki/Decimal_representation

Me

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Oct 1, 2017, 4:08:11 PM10/1/17
to

John Gabriel

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Oct 1, 2017, 4:08:13 PM10/1/17
to
[A] is an infinite series.
[B] is the limit of an infinite series.

They are two different things which you are DEFINING to be the same. Get it moron?

John Gabriel

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Oct 1, 2017, 4:12:27 PM10/1/17
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On Sunday, 1 October 2017 15:06:56 UTC-5, Me wrote:
> On Sunday, October 1, 2017 at 9:59:14 PM UTC+2, John Gabriel wrote:
>
> > why use "0.333..." as the representation and not "asadaff..."
>
> Because it gives a hint which number I might mean in this case.

A hint???!!! Chuckle. asadaff... is just as good if it is defined in the same way. What hint do you get from this 3489833.2947293849879333311120000101000... ??? Go on moron. Tell me what hint you get! Chuckle.

>
> Same with
>
> 0.111...
> 0.222...
> 0.333...
> :
> 0.999...

Nonsense. 1/9, 2/9, etc are very well defined and require nothing in the form of a hint. Only idiots like you need hints.

>
> > You use 0.333... because it is supported by the idea of an infinite sum.
>
> Guess so.

Finally you admit that is a DEFINITION! Good boy! Good boy! That is the first step. Chuckle.

>
> > By the same token [...] you would never write 3.14159... for pi if it
> > did not have the support of the [...] infinite sum.
>
> Guess so, yes. :-)
>
> It's called /decimal representation/.

You can call it decimal wankation. It is still the same shit.

Message has been deleted

Me

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Oct 1, 2017, 4:19:14 PM10/1/17
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On Sunday, October 1, 2017 at 10:05:23 PM UTC+2, John Gabriel wrote:

John, you are confused. Sorry.

> You define
>
> oo
> SUM (3/10^n) = 1/3 [A]
> n=1
>
> as being equal to
>
> lim SUM_{k=1..n} (3/10^k) = 1/3 [B]
> n->oo

Nope. You are talking nonsense, man. :-)

oo
SUM a_n
n=1

is defined as

lim SUM_{k=1..n} a_k
n->oo

(where a_n is "unspecified"; just a/any function from IN in IR).

So all we know (in this case) BY DEFINITION is

oo
SUM (3/10^n) =
n=1

lim SUM_{k=1..n} (3/10^k) .
n->oo

We don't know (at this point) if

oo
SUM (3/10^n) = 1/3 .
n=1

Hence this has to be proved.

Me

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Oct 1, 2017, 4:21:58 PM10/1/17
to
On Sunday, October 1, 2017 at 9:48:24 PM UTC+2, John Gabriel wrote:

> SUM_{k=1...oo} (3/10^n)
>
> It is most definitely not the same as 1/3

Well, actually it is. There's a simple prove for the theorem

lim SUM_{k=1..n} (3/10^k) = 1/3 .
n->oo

Hence

John Gabriel

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Oct 1, 2017, 4:26:46 PM10/1/17
to
On Sunday, 1 October 2017 15:19:14 UTC-5, Me wrote:
> On Sunday, October 1, 2017 at 10:05:23 PM UTC+2, John Gabriel wrote:
>
> John, you are confused. Sorry.
>
> > You define
> >
> > oo
> > SUM (3/10^n) = 1/3 [A]
> > n=1
> >
> > as being equal to
> >
> > lim SUM_{k=1..n} (3/10^k) = 1/3 [B]
> > n->oo
>
> Nope. You are talking nonsense, man. :-)

You are writing nonsense.

>
> oo
> SUM a_n
> n=1
>
> is defined as
>
> lim SUM_{k=1..n} a_k
> n->oo
>
> (where a_n is "unspecified"; just a/any function from IN in IR).

Makes no difference idiot. You are introducing irrelevant matters.

>
> So all we know (in this case) BY DEFINITION is
>
> oo
> SUM (3/10^n) =
> n=1
>
> lim SUM_{k=1..n} (3/10^k) .
> n->oo

YES. It is defining the SERIES to be its LIMIT. Simply and plainly stupid.
>
> We don't know (at this point) if
>
> oo
> SUM (3/10^n) = 1/3 .
> n=1
>

Of course we know stupid!! There is nothing to prove. The fact that 1/3 is a limit has ZERO to do with infinity. It is an inference concluded from the nth partial sum you moron!!!

> Hence this has to be proved.

Nonsense. Nothing to prove. S = Lim S is a DEFINITION, not a theorem and requires NO proof.

Dan Christensen

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Oct 1, 2017, 4:45:46 PM10/1/17
to
On Sunday, October 1, 2017 at 4:02:07 PM UTC-4, John Gabriel wrote:
> On Sunday, 12 February 2017 07:14:11 UTC-6, John Gabriel wrote:
> > S = Lim S in this case, contradicts the fact that 1/3 has no representation in base 10.
> >
> > However, it also leads to even more absurd definitions, that is, pi=3.14159... when in fact it is known that pi has NO measure.
> >
> >
> >
> > Your comments are unwelcome shit and will be ignored.
> >
> > This is posted on this newsgroup in the interests of public education and to eradicate ignorance and stupidity from mainstream mythmatics.
>
> S = Lim S
>
> STOPS RIGHT HERE AND NOW. It is the Eulerian Blunder and has no place in rational thought, never mind mathematics.

You mean that was YOUR blunder, Troll Boy. As even you were recently forced to concede when confronted with the evidence, "Of course he [Euler] did not write 'Lim S'... He did not talk about S." (May 27, 2017)

With any sane person, that would be the end of it, but not with a psycho troll like you!


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

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Oct 1, 2017, 6:26:38 PM10/1/17
to
Nope, you both are wrong: if at all, then the k
goes to the exponent of 10 and not n:


lim SUM_{k=1..n} (3/10^k)
n->oo

Which is synonymous (by the usual convention what
oo should mean in this context, because k is integer) to:

lim SUM_{k=1..oo} (3/10^k)

So much to the dislexia of bird brain John Grabriel.
We might expect that he is neither able to read math,
nor able to write math,

and that he is completely confused.

burs...@gmail.com

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Oct 1, 2017, 6:28:50 PM10/1/17
to
Corr.:

Which is synonymous (by the usual convention what
oo should mean in this context, because k is integer) to:

SUM_{k=1..oo} (3/10^k)

Me

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Oct 1, 2017, 6:48:44 PM10/1/17
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On Sunday, October 1, 2017 at 9:38:14 PM UTC+2, Me wrote:
> On Sunday, October 1, 2017 at 9:32:32 PM UTC+2, John Gabriel wrote:
>
> "It is a very bad idea and nothing less than stupid to define 1/3 = 0.333..."
>
> Why?
>
> "0.333..." is just short for
>
> lim SUM_{k=1..n} (3/10^n)
> n->oo

Should read:

lim SUM_{k=1..n} (3/10^k)

Me

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Oct 1, 2017, 6:56:48 PM10/1/17
to
On Monday, October 2, 2017 at 12:26:38 AM UTC+2, burs...@gmail.com wrote:
> Nope, you both are wrong: if at all, then the k
> goes to the exponent of 10 and not n:
>
>
> lim SUM_{k=1..n} (3/10^k)
> n->oo
>
> Which is synonymous (by the usual convention what
> oo should mean in this context, because k is integer) to:
>
> lim SUM_{k=1..oo} (3/10^k)

Huh?! Nope. No "lim".

oo
SUM (3/10^n)
n=1

is short for

lim SUM_{k=1..n} (3/10^k)
n->oo

See: https://en.wikipedia.org/wiki/Series_(mathematics)

genm...@gmail.com

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Oct 1, 2017, 7:08:23 PM10/1/17
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On Sunday, 1 October 2017 17:56:48 UTC-5, Me wrote:
> On Monday, October 2, 2017 at 12:26:38 AM UTC+2, burs...@gmail.com wrote:
> > Nope, you both are wrong: if at all, then the k
> > goes to the exponent of 10 and not n:
> >
> >
> > lim SUM_{k=1..n} (3/10^k)
> > n->oo
> >
> > Which is synonymous (by the usual convention what
> > oo should mean in this context, because k is integer) to:
> >
> > lim SUM_{k=1..oo} (3/10^k)
>
> Huh?! Nope. No "lim".

See? Even your fellow birdbrain is confused. It doesn't matter whether you write lim in front or not stupid. You are DEFINING

>
> oo
> SUM (3/10^n)
> n=1
>
> is short for

As the LIMIT:

>
> lim SUM_{k=1..n} (3/10^k)
> n->oo
>

And these are two different objects. One is a series and the other is a limit.

S = Lim S

You are extremely dense!

burs...@gmail.com

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Oct 1, 2017, 9:30:06 PM10/1/17
to
We didn't write:

SUM_{k=1..n} (3/10^k) = lim n->oo SUM_{k=1..n} (3/10^k)

I guess you need very quickly to see a doctor, bird
brain John Gabriel. You seem to have hallucinations
in the form of "S=Lim S" or something similar.

BTW: Here is a recommendation, since Latex is used
very often in math:

Use _ for subscript: foo_bar will put bar subscript to foo

Use ^ for superscript: foo^bar will put bar superscript to foo

Now you can write the two dimensional sum in one dimensio¨n
as following text, lets begin with the partial sum:

s(n) = sum_k=1^n 3/10^k

Guess what you can directly input the RHS into Wolfram Alpha:

https://www.wolframalpha.com/input/?i=sum_k%3D1^n+3%2F10^k

And it will give you the closed form:

s(n) = 1/3(1-10^(-n))

Next step, you can use underscore, subscript also for limes,
but there are more typographic tricks:

Use -> for tends to: foo->bar will be read as foo arrow bar

Use oo for infinity: oo will be read as infinity

So lets try the limes now, we have:

a = lim_n->oo sum_k=1^n 3/10^k

= lim_n->oo 1/3(1-10^(-n))

Guess what you can again directly input the RHS
into Wolfram Alpha:

https://www.wolframalpha.com/input/?i=lim_n-%3Eoo+1%2F3%281-10^%28-n%29%29

And the result will be:

a = 1/3

So we have:

0.333... = 1/3

burs...@gmail.com

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Oct 1, 2017, 9:39:34 PM10/1/17
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Now compare when you input SUM_{k=1..n} (3/10^k) into
Wolfram Alpha. It will give up, it does not recognize it:

https://www.wolframalpha.com/input/?i=SUM_{k%3D1..n}+%283%2F10^k%29

Wolfram Alpha is close to how the sum is written:

to
Sigma summand
var=from

The flat linear representation (using underscore _ for
subscript and ^ for superscript) is (Sigma is
replaced by sum):

sum_var=from^to summand

Interestingly the greek letter sigma works also
in Wolfram Alpha, here is a test:

Σ_k=1^n 3/10^k

https://www.wolframalpha.com/input/?i=%CE%A3_k%3D1^n+3%2F10^k

Wolfram Alpha even writes:

Assuming "Σ" is a sum

P.S.: My Windows machine says:
Σ = U+03A3
http://www.fileformat.info/info/unicode/char/03a3/index.htm

Am Montag, 2. Oktober 2017 03:30:06 UTC+2 schrieb burs...@gmail.com:
> Now you can write the two dimensional sum in one dimension

Quadibloc

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Oct 1, 2017, 11:01:38 PM10/1/17
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On Saturday, September 30, 2017 at 7:01:04 AM UTC-6, John Gabriel wrote:

> Well, for starters, education of calculus is in a dire mess. Students
> never understand calculus. Even their professors never understand.
> They simply learn to use.

Well, even if I don't agree with much of what you've said, I can
certainly grant you this point...

since the ancient Greeks had so much trouble with what we call
"irrational numbers", why couldn't it be the case that today's math
students might have the same problem...

and thus benefit from a calculus that can work without them?

You are correct that 1/4 = 0.25 is the same as 1/4 = 25/100, too.

It may be wrong, in some sense, to say that 1/3 = 0.3333... but it is
correct that 1/3 is greater than 3333/10000 and less than 3334/10000.
Similar things can be said about pi - even if pi is not really a
number, sometimes, like when figuring out how much adhesive tape will
fit on a roll, we might want to do arithmetic with it.

However, I don't think I could get you to consider that perhaps you and
conventional mathematicians are simply using different words to talk
about the same thing.

John Savard

Quadibloc

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Oct 1, 2017, 11:08:52 PM10/1/17
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On Sunday, October 1, 2017 at 1:32:32 PM UTC-6, John Gabriel wrote:

> Peano's Crapaxiom 5 is the induction axiom:

> If a set S of numbers contains zero and also the successor of every
> number in S, then every number is in S.

Well, that's clearly wrong. 1/2 would not be in S, and we're all agreed
that 1/2 is a number.

However, I think this is really what Peano was saying:

If S contains zero,
and if it is also true that
if S contains x then it contains the successor of x

(where the successor of x is what we would normally call x+1, but Peano hadn't gotten around to defining addition yet)

then S will contain 0, 1, 2, 3, 4, 5... and indeed any non-negative integer.

For example, it contains 5 because

S contained zero
and because if it contains x, it contains x+1,
it contains 1 because it contains 0
it contains 2 because it contains 1
it contains 3 because it contains 2
it contains 4 because it contains 3
it contains 5 because it contains 4

Clearly, this will work for any non-negative integer, however large,
even if one doesn't bother to type that much.

John Savard

Quadibloc

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Oct 1, 2017, 11:15:43 PM10/1/17
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On Sunday, October 1, 2017 at 2:08:13 PM UTC-6, John Gabriel wrote:

> [A] is an infinite series.
> [B] is the limit of an infinite series.

> They are two different things which you are DEFINING to be the
> same.

[A] might not be real. It might not really be something that
makes sense.

[B], on the other hand, definitely does make sense, because
each of the finite series in the sequence that approaches
the limit certainly can be added up.

So what mathematicians are doing is saying, since [A] is
bad, but we either would like to have [A], or we would like
to refer to [B] by the name of [A] because it is shorter to
skip mentioning that we're "really" talking about a limit,
we will now say that whenever [A] is written, we will
understand that [B] is what is really meant whenever it is
necessary to concern oneself with that distinction.

This is not really such an awful thing for them to be doing.

John Savard

Quadibloc

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Oct 1, 2017, 11:22:32 PM10/1/17
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On Sunday, October 1, 2017 at 1:22:43 AM UTC-6, netzweltler wrote:

> Do you agree that 0.999... means infinitely many commands
> Add 0.9 + 0.09
> Add 0.99 + 0.009
> Add 0.999 + 0.0009
> …?
> Then following all of these infinitely many commands won’t get you to point
> 1. If you reached point 1 you have disobeyed those commands, because every
> single of those infinitely many commands tells you to get closer to 1 but
> NOT reach 1.

You would be correct if Zeno's paradoxes were correct. But they're not.
Achilles can and does overtake the tortoise every day.

0.9999... does *NOT* mean actually doing those infinitely many steps. There
is never time to do that many commands. Instead, it means the place that
doing them would take you, if you _could_ do them.

Yes, doing any _finite_ number of those commands would not get you to 1. You
would have to disobey them to get that far.

But you *can't* do an infinite number of commands. Period.

So that isn't the criterion you use to figure out what 0.9999... actually
is.

Is 0.9999... not equal to 1? In order for it _not_ to be equal to 1, it
would have to be less than 1 by some finite number. But pick any such
number, and by doing a sufficiently large finite number of commands, you can
get closer to 1 than that.

So 1 is indeed the only thing it can be equal to, even though that looks
funny. But that's just a problem with the decimal system of writing numbers
- it doesn't perfectly match the real numbers it refers to - not with the
numbers themselves. It doesn't mean infinitesimals have to be added to the
real number line.

John Savard

Quadibloc

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Oct 1, 2017, 11:29:18 PM10/1/17
to
On Sunday, October 1, 2017 at 2:02:07 PM UTC-6, John Gabriel wrote:

> S = Lim S

> STOPS RIGHT HERE AND NOW. It is the Eulerian Blunder and has no place in
> rational thought, never mind mathematics.

S = Lim S isn't a statement of fact. It's a definition. It means that (in
certain appropriate cases) when we write an S that doesn't really have a
legitimate meaning, but Lim S does have a value, we are simply using S as a
shorter way of writing Lim S.

So we use this not as a way of saying that the bad, invalid, S is now a good
thing, but as a way of *getting rid* of S (and stuff like infinitesimals) and
_only_ using real things which do have values - such as Lim S.

You have just misunderstood what Euler was trying to do. He wasn't trying to
introduce bad messy thinking into mathematics; instead, he found some there, and
he was using this method to get _rid_ of all the messy stuff quickly without
having to make mathematicians do a lot of extra work.

Euler was not your enemy. He wasn't saying the false thing that S is just as
good as Lim S. He knew that S was bad, but Lim S was good, and he was therefore
doing just what you are trying to do: fix mathematics so that it rests on the
good stuff and doesn't try to use the bad stuff.

John Savard

mitchr...@gmail.com

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Oct 1, 2017, 11:35:43 PM10/1/17
to
On Sunday, October 1, 2017 at 8:22:32 PM UTC-7, Quadibloc wrote:
> On Sunday, October 1, 2017 at 1:22:43 AM UTC-6, netzweltler wrote:
>
> > Do you agree that 0.999... means infinitely many commands
> > Add 0.9 + 0.09
> > Add 0.99 + 0.009
> > Add 0.999 + 0.0009
> > …?
> > Then following all of these infinitely many commands won’t get you to point
> > 1. If you reached point 1 you have disobeyed those commands, because every
> > single of those infinitely many commands tells you to get closer to 1 but
> > NOT reach 1.
>
> You would be correct if Zeno's paradoxes were correct. But they're not.
> Achilles can and does overtake the tortoise every day.
>
> 0.9999... does *NOT* mean actually doing those infinitely many steps. There
> is never time to do that many commands. Instead, it means the place that
> doing them would take you, if you _could_ do them.
>
> Yes, doing any _finite_ number of those commands would not get you to 1. You
> would have to disobey them to get that far.
>
> But you *can't* do an infinite number of commands. Period.
>
> So that isn't the criterion you use to figure out what 0.9999... actually
> is.
>
> Is 0.9999... not equal to 1? In order for it _not_ to be equal to 1, it
> would have to be less than 1 by some finite number.

That finite quantity is the infinitely small or the very first finite
quantity that is first after zero. Defined as One divided by infinity.
.9 repeating is less than one by the infinitely small.
Therefor they share a sameness to one another.

Mitchell Raemsch

7777777

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Oct 2, 2017, 1:29:13 AM10/2/17
to
are you trying to insist that 0.(3) is equal to
lim{n \to infinity} s(n) = lim{n --> infinity} 0.3 + 0.03 + 0.003 + ... + 3*10^(-n) = 1/3 ?

Using the real numbers 0.(3) is not equal to 1/3.

But it seems you have chosen to prefer eating the cake and having it too,
meaning you have rejected the infinitesimals but using them too.
That's why you end up with a falsehood 0.(3) = 1/3 in real numbers.

You should be able to check a simple arithmetic
0.(3)3 + 0.(3)3 + 0.(3)4 = 0.(3)(3)+0.(3)(3)+0.(3)(3) = 1
and therefore 0.(3)(3) = 1/3





Zelos Malum

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Oct 2, 2017, 1:43:37 AM10/2/17
to
Den söndag 1 oktober 2017 kl. 15:17:49 UTC+2 skrev John Gabriel:
> On Saturday, 30 September 2017 19:32:08 UTC-5, burs...@gmail.com wrote:
> > So the product, its terms sn*tn might be observable,
> > but that the product is Cauchy is not observable directly.
> >
> > That a series is Cauchy is neither effectively refutable
> > nor effectively verifiable. If you find e, n, m with:
> >
> > |an-am| > e
> >
> > You still don't know whether there is N, where the series
> > behaves Cauchy. The full Cauchy condition is:
> >
> > forall e exists N forall n,m>=N |an-am|=<e
> >
> > So it has the shape VEV.
> >
> > Am Sonntag, 1. Oktober 2017 02:23:32 UTC+2 schrieb burs...@gmail.com:
> > > Well you wrote here Newton didn't consider infinity,
> > > and you say he can define partial sums without infinity.
> > >
> > > Well this might be true, but you then go on and say
> > > he used limits. But how do you get limits, without
> > >
> > > https://groups.google.com/d/msg/sci.math/HIzzJSLsw60/vSOH7WnhAwAJ
> > >
> > > knowing whether a series converges or not? For convergence
> > > you need to make statement about infinitely many elements,
> > >
> > > for example the Cauchy condition, is for infinitely many
> > > pairs n,m, namely you need to know (or assume you know):
> > >
> > > forall n,m >= N(e) |an - am| =< e
>
> Each time I think you can't say anything more stupid, you surprise me.
> Listen stupid, the forall you have there is based on induction. There is no forall. A Cauchy sequence does not require "forall". The "forall" is a result of inference.
>
> > >
> > > The above looks like a pi-sentence, and is not verifiable
> > > if we do not know much about {ak}. So you are in the waters of:
> > >
> > > It is also familiar in the philosophy of science that most
> > > hypotheses are neither verifiable nor refutable. Thus, Kant’s
> > > antinomies of pure reason include such statements as that space
> > > is infinite, matter is infinitely divisible, and the series of
> > > efficient causes is infinite. These hypotheses all have the form
> > >
> > > forall x exists y P(x, y).
> > >
> > > For example, infinite divisibility amounts to “for every
> > > product of fission, there is a time by which attempts to cut
> > > it succeed” and the infinity of space amounts to “for each
> > > distance you travel, you can travel farther.”
> > >
> > > https://www.andrew.cmu.edu/user/kk3n/complearn/chapter11.pdf
> > >
> > > Am Sonntag, 1. Oktober 2017 00:58:40 UTC+2 schrieb John Gabriel:
> > > > On Saturday, 30 September 2017 17:25:16 UTC-5, FromTheRafters wrote:
> > > > > netzweltler explained on 9/30/2017 :
> > > > > > Am Samstag, 30. September 2017 23:14:36 UTC+2 schrieb mitchr...@gmail.com:
> > > > > >>
> > > > > >> .9 repeating and One share a sameness. They are quantities
> > > > > >> that are different by the infinitely small.
> > > > > >> .9 repeating is a transcendental One; the First quantity
> > > > > >> below one. The infinitely small difference means a shared
> > > > > >> sameness that is still not absolutely same.
> > > > > >>
> > > > > >> Mitchell Raemsch
> > > > > >
> > > > > > If there is a quantity between 0.999... and 1 and, therefore, these are two
> > > > > > different points on the number line then you should define the distance
> > > > > > between these two points. If you don't, then your first quantity is simply
> > > > > > undefined.
> > > > > >
> > > > > > 'infinitely small' is not a definition. There are no two distinct points on
> > > > > > the number line 'infinite(simal)ly' far away from each other.
> > > > >
> > > > > They do not differ
> > > > > by infinite small.
> > > > > They differ only
> > > > > by none at all.
> > > >
> > > > Well, if you define 0.999... to be equal to a brick, then a brick and 0.999... differ by none at all.
> > > >
> > > > There is not a single support for this bullshit equality aside from S = Lim S and this is an ill-formed definition - the Eulerian Blunder.

Sure is, for all statement made by John Gabriel, none of them is correct.

Zelos Malum

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Oct 2, 2017, 1:45:49 AM10/2/17
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Hey moron! Nice to see you :) I still see you are using horseshit notation that you cannot even define coherently!

!/3=0.(3) is trivial to prove for real numbers.

7777777

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Oct 2, 2017, 2:01:58 AM10/2/17
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let me see if I remember you.....hmmm, you must be the one who got
everything wrong at statu, right? And never admit your mistakes.

You must feel lonely here at the big world with no support from your fellow
fools. Still the same bullshit and ridicule going on every day....must be great
never to achieve anything and live with delusions.


netzweltler

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Oct 2, 2017, 2:45:50 AM10/2/17
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Am Sonntag, 1. Oktober 2017 17:45:39 UTC+2 schrieb FromTheRafters:
> netzweltler formulated the question :
> > Am Sonntag, 1. Oktober 2017 15:20:16 UTC+2 schrieb FromTheRafters:
> >> After serious thinking netzweltler wrote :
> >>> Am Sonntag, 1. Oktober 2017 13:56:01 UTC+2 schrieb FromTheRafters:
> >>>>
> >>>> It seems counterintuitive when a number is viewed (or represented) as
> >>>> an infinite unending 'process' of achieving better and better
> >>>> approximations, and that we can never actually reach the destination
> >>>> number. In my view, this sequence and/or infinite sum is a
> >>>> representation of the destination number "as if" we could have gotten
> >>>> there by that process.
> >>> If the process doesn't get us there then we don't get there. Where do you
> >>> get your "as if" from?
> >>
> >> If you had sufficient time, then you would get there.
> > Show how time is involved in our process.
>
> If you have to add a next number (like one quarter) to a previous
> result of adding such previous numbers (like one plus one half) then
> you have introduced time. Thee is a 'previous' calculation needed as
> input to the next calculation. The idea that you 'never' get there (to
> two) introduces time also. I'm with you, I don't think time has any
> place in this.
>
> >>>> IOW "*After* infinitely many 'better'
> >>>> approximations" we reach the destination number *exactly* even if we
> >>>> cannot 'pinpoint' that number on the number line.
> >>> Please define "*After* infinitely many 'better' approximations". All we've
> >>> got is infinitely many approximations - each approximation telling us that
> >>> we get closer to 1 but don't reach 1. There is no *after* specified in
> >>> this process.
> >>
> >> There is also no "time" mentioned, so why is there an assumption of a
> >> process which takes time to complete? It is already completed (pi
> >> exists as a number despite our inability to pinpoint it on the number
> >> line by using an infinite alternating sum or any of the other infinite
> >> processes) we just can't pinpoint it because we exist in a time
> >> constrained universe with processes which take time to complete.
> > If you insist on introducing time to our process, try this:
>
> You misunderstand me. I'm not insisting that, in fact I insist the
> opposite. I take the infinite sequence or series representation to be
> just that, a represenation of a number -- not a process at all. This
> avoids the idea that time is a constraint against a number being exact.
>
> When it come to application, then you may have to consider the
> indicated process and get as close an approximation as you desire. The
> representations 0.999... and the infinite series or the sequences
> related to it, are all just different representations of the number
> one, just as our current representation are all representations of the
> number two. Time has nothing at all to do with it, hence there is no
> 'almost, but not quite there' to worry about.

Correct. Time is of no concern. So, let me modify the list:

t = 0: write 0.9
t = 0.9: append another 9
t = 0.99: append another 9
...

to

1. write 0.9
2. append another 9
3. append another 9
...

Do you still agree that this is a _complete_ list of all the actions needed to write 0.999... (already present - in no time)? It is a list of additions as well. All the additions it takes to sum up to 0.999...
Again the question:
If your claim is, that we reach point 1, you need to show which step on this list of infinitely many steps accomplishes that.

John Gabriel

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Oct 2, 2017, 2:46:00 AM10/2/17
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On Sunday, 1 October 2017 22:29:18 UTC-5, Quadibloc wrote:
> On Sunday, October 1, 2017 at 2:02:07 PM UTC-6, John Gabriel wrote:
>
> > S = Lim S
>
> > STOPS RIGHT HERE AND NOW. It is the Eulerian Blunder and has no place in
> > rational thought, never mind mathematics.
>
> S = Lim S isn't a statement of fact. It's a definition. It means that (in
> certain appropriate cases) when we write an S that doesn't really have a
> legitimate meaning, but Lim S does have a value, we are simply using S as a
> shorter way of writing Lim S.

How ridiculous is that statement. You think 0.333... is a shorter way of writing the well-defined number 1/3 ? That's absurd. It's even more absurd when you consider that there is no way to write 1/3 in base 10.

>
> So we use this not as a way of saying that the bad, invalid, S is now a good
> thing, but as a way of *getting rid* of S (and stuff like infinitesimals) and
> _only_ using real things which do have values - such as Lim S.
>
> You have just misunderstood what Euler was trying to do. He wasn't trying to
> introduce bad messy thinking into mathematics; instead, he found some there, and
> he was using this method to get _rid_ of all the messy stuff quickly without
> having to make mathematicians do a lot of extra work.
>
> Euler was not your enemy. He wasn't saying the false thing that S is just as
> good as Lim S. He knew that S was bad, but Lim S was good, and he was therefore
> doing just what you are trying to do: fix mathematics so that it rests on the
> good stuff and doesn't try to use the bad stuff.

Chuckle. You are one very confused man John Savard.
>
> John Savard

John Gabriel

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Oct 2, 2017, 2:48:32 AM10/2/17
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Yes. He is the dipshit whose arse I kicked so bad over and over again on STATU.

>
> You must feel lonely here at the big world with no support from your fellow
> fools. Still the same bullshit and ridicule going on every day....must be great
> never to achieve anything and live with delusions.

You can't reason with a monkey and Zelos is a religious monkey. Stupid beyond belief is a euphemism. The tosser can't understand the simplest concepts.

John Gabriel

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Oct 2, 2017, 2:51:04 AM10/2/17
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On Sunday, 1 October 2017 20:30:06 UTC-5, burs...@gmail.com wrote:
> We didn't write:
>
> SUM_{k=1..n} (3/10^k) = lim n->oo SUM_{k=1..n} (3/10^k)

You wrote and you believe that:

n->oo SUM_{k=1..n} (3/10^k) = 0.333... = lim n->oo SUM_{k=1..n} (3/10^k) = 1/3

In other words, S = Lim S

S = n->oo SUM_{k=1..n} (3/10^k)
Lim S = lim n->oo SUM_{k=1..n} (3/10^k)

netzweltler

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Oct 2, 2017, 3:12:29 AM10/2/17
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Am Montag, 2. Oktober 2017 05:22:32 UTC+2 schrieb Quadibloc:
> On Sunday, October 1, 2017 at 1:22:43 AM UTC-6, netzweltler wrote:
>
> > Do you agree that 0.999... means infinitely many commands
> > Add 0.9 + 0.09
> > Add 0.99 + 0.009
> > Add 0.999 + 0.0009
> > …?
> > Then following all of these infinitely many commands won’t get you to point
> > 1. If you reached point 1 you have disobeyed those commands, because every
> > single of those infinitely many commands tells you to get closer to 1 but
> > NOT reach 1.
>
> You would be correct if Zeno's paradoxes were correct. But they're not.
> Achilles can and does overtake the tortoise every day.
>
> 0.9999... does *NOT* mean actually doing those infinitely many steps. There
> is never time to do that many commands. Instead, it means the place that
> doing them would take you, if you _could_ do them.
>
> Yes, doing any _finite_ number of those commands would not get you to 1. You
> would have to disobey them to get that far.

Even doing an _infinite_ number of those commands wouldn't get you to 1.

1. 0.99 + 0
2. 0.99 + 0
3. 0.99 + 0
...

Neither a finite number of the steps on the list above will get you to 1 nor an infinite number of the steps on the list above will get you to 1. We can tell that - no matter if we can do all the steps or not. For each particular line is true that we don't reach 1. And this is true for this list also:

1. 0.9 + 0.09
2. 0.99 + 0.009
3. 0.999 + 0.0009
...

> But you *can't* do an infinite number of commands. Period.
>
> So that isn't the criterion you use to figure out what 0.9999... actually
> is.
>
> Is 0.9999... not equal to 1? In order for it _not_ to be equal to 1, it
> would have to be less than 1 by some finite number.

Why that? 0.999... cannot be located at point 1 of the number line. Why do you think that means that it must be short of 1 then? It cannot be located at a point < 1 either.

Zelos Malum

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Oct 2, 2017, 6:05:07 AM10/2/17
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I think you are conflating yourself with me :) You are the one that never got anything right. You couldn't even get your shit internally consistent!

Yeah you are definately talking about yourself. You are the one accomplishing nothing, I am working on my PhD so guess what? I am doing real research, what are you doing? :)

burs...@gmail.com

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Oct 2, 2017, 6:07:20 AM10/2/17
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And they might be less dislexis, especially
concerning the ellipses and nonsense like Euler
did a blunder in the form of "S=Lim S".

Here is a nice other notation convention, lets
start with unterval description, its very common
in math to use for example:

[3...] : An open interval, the set {3,4,5,...}
the ellipses stands for a infinite continuation
of the series

[3...11] : A closed interval, the set {3,4,5,..,9,10,11}
the ellipses stands for a finite continuation
of the series.

We can use the same in decimal representation an will
get in very short notation that the partial sums are
different from the limit:

0.333... = 1/3

0.333...333 <> 1/3

Or in expanded math:

lim n->oo sum_k=1^n 3/10^k = 1/3

forall n sum_k=1^n 3/10^k <> 1/3

Or as bird brain John Gabriel puts it "You think
0.333... is a shorter way of writing the well-defined
number 1/3 ? That's absurd."

Its not absurd if you interpret the ... in 0.333...
correctly. It means two things:
- Infinite continuation of the series, we must
read off some partial sums s(n)
- Taking the limit of this series, we must then
take the limit, otherwise we would compare apple
and oranges.

Am Montag, 2. Oktober 2017 05:01:38 UTC+2 schrieb Quadibloc:
> On Saturday, September 30, 2017 at 7:01:04 AM UTC-6, John Gabriel wrote:
>
> > Well, for starters, education of calculus is in a dire mess. Students
> > never understand calculus. Even their professors never understand.
> > They simply learn to use.

burs...@gmail.com

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Oct 2, 2017, 6:10:48 AM10/2/17
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Nope, I only believe:

0.333... = 1/3

0.333...333 <> 1/3

I never ever wrote somewhere:

0.333...333 = 1/3

For an explanation see here:
https://groups.google.com/d/msg/sci.math/bgU-4JWvHbY/I3FJuzByBgAJ

Zelos Malum

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Oct 2, 2017, 6:38:18 AM10/2/17
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You never did it there and never here nro anywhere, you cannot beat me cause you are too ignorant on everything related to mathematics.

FromTheRafters

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Oct 2, 2017, 7:12:21 AM10/2/17
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netzweltler explained on 10/2/2017 :
Why would I need to do that?

e raised to the pi times i equals -1 exactly without my needing to
explain what the ellipses means in the 3.1415... or 2.71828... decimal
representations. Those representations are of numbers not strictly
procedures for approximations of numbers.

Were they only meant to be procedures then I could substitute division
by zero with division by 'e to the pi times i plus one' and avoid ever
dividing by zero again since pi and e could *only* be approximated. You
see then that everything in calculus would be an approximation under
this scenario.

Of course, some people think that this is already the case.
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