Sqrt(2) =/= 1.41421356237...

[bassam king karzeddin]

Even this was explained quite many times but never mind to prove it again and again:

First, the Greek construction of a number by unmarked straightedge and a compass with finite number of steps, with arbitrary shortest distance between two distinct visualized locations on the straight number line defined as a unity, was the base of construction of an existing real number, which implies its true existence, wither it can be measured by rational numbers or not, since the construction of the rational numbers is defined by those definitions also, and was based on the perfection of the ideas behind this elementary principle

So if we deny or disprove the Greek famous principle, then yes no numbers can be defined on a number line except two numbers by convention as you mentioned earlier, where then the concept of a constructing or measuring a number becomes so meaningless

So, depending on the validity of the Greek principle, Sqrt(2) is a real existing number, being abstractly and physically a diagonal of a square of defined unity side, thus it is exactly constructed with unique location on a number line that no rational number can occupy, and was originated from the unity “one”, despite being immeasurable by rational.

Doubling the square in real non zero integers is impossible, (n^2 =/= 2m^2), therefore taking the sqrt of both sides of this eqn. would yield:
Sqrt(2) =/= n/m, where (n/m) is rational number, NO matter if both (n & m) tends to be infinite integers

So, the rational representation (or the best approximation) of Sqrt(2) is always rational number, no matter if you can fill out the galaxy size of some of its endless digits
And since Sqrt(2) was proved to be irrational number which is impossible to be rational number, hence it is rational representation in any rational number system is fake number that is impossible to exist, trying always and forever to replace the unique location of Sqrt(2) but always unsuccessfully

Let us see it clearly in our decimal 10base number system representation, as a sequence of endless approximation, for Sqrt(2)

First Sqrt (2) = 1 = 1/(10)^0
Second = 1.4 = 14/10^1
Third = 1.41 = 141/10^2

…………. = …………………

Tenth = 1414213562/10^9

…….. = ……………

K’th = n/m, where (m = 10^(k - 1),
and (n) is integer with (k) number of digits

(k + 1) = n/m, where (m = 10^k), and
(n) is integer with (k + 1) number of digits

Hence, if we go after exact value, we find this task is impossible to achieve, because we require both of
(m & n) to be infinite integers with infinite sequence of digits, where this is obviously impossible, and also not permissible in mathematics, (then we better admit the truth of real best approximation), or say this is the magnitude of Sqrt(2) in rational number (which is not an exact number)- as John Gabriel continuously describes for immeasurable numbers

The proof is therefore completed

Regards
Bassam King Karzeddin
17Th,Nov., 2016

[John Gabriel]

Actually, it is very easy to show how one can attempt to measure sqrt(2).

Of course it is impossible, but to get the digits is easy.

Start with a right angled isosceles triangle. Take one of the legs and notice it fits only ONCE into the hypotenuse. So, the first digit is 1.

Now divide the legs into 10 equal parts. You will notice that you get 14 equal parts when you place a leg over the hypotenuse and a little left over. So, 1.4

Now divide the legs into 100 equal parts. You get 1.41.

And so on and on it goes. There is always a remainder which contains the incommensurable magnitude.

In fact, you don't even need to use division in this process. Simply increase the triangle by proportion so that legs are always multiples of the unit. You see, this is why it means nothing if you construct a right angle isosceles triangle because it gives you only the symptom of sqrt(2), not the measure.

[abu.ku...@gmail.com]

there is always such a remainder, but
there are always approsimants that can be divided by any power of two,
mod two

[abu.ku...@gmail.com]

but, I'm only concerned with approximants of pi -- actually,
PI, which is one/pi, or thirty-two hundredths,
and this nicely infinite set of approximants,
probably with no pattern, at all, but let's just see about it

[7777777]

torstai 17. marraskuuta 2016 15.50.08 UTC+2 bassam king karzeddin kirjoitti:
> Even this was explained quite many times but never mind to prove it again and again:
>

Sqrt(2) = 1.41421356237... only if S = Lim S


but as we have seen over and over again, the cranks deny the validity of the statement S = Lim S, although at the same time they are using it.

[John Gabriel]

On Friday, 2 December 2016 01:55:34 UTC-8, 7777777 wrote:
> torstai 17. marraskuuta 2016 15.50.08 UTC+2 bassam king karzeddin kirjoitti:
> > Even this was explained quite many times but never mind to prove it again and again:
> >
>
>
> Sqrt(2) = 1.41421356237... only if S = Lim S

Not even then, because Lim S is not a number.

It does not matter if you can construct the *symptom* of square root two because it tells you NOTHING about its measure.

If Lim S = sqrt(2), then Lim S is not a number because sqrt(2) is not a number.

https://www.youtube.com/watch?v=B3AlAil5Crc

**** A number is the measure of a magnitude. ****

[burs...@gmail.com]

Hey JG the cheese cake factory is calling you.

They said they don't want you to touch anything
structuralist. This belong to another factory,
called math, where it is the modus operandi,
except maybe for monadic second order logic.

They said equality is also a structuralist
thing in mathematics. It can be freely choosen,
according to the application or for pure studies,
and might change from theory to theory.

[7777777]

perjantai 2. joulukuuta 2016 15.54.28 UTC+2 John Gabriel kirjoitti:
>
> If Lim S = sqrt(2), then Lim S is not a number because sqrt(2) is not a number.
>

We can ask if a non-existent number is still a number. To be or not to be?
To be a number or not to be a number, that is the question.

sqrt(2) = 1.41421356237...41421356237...

is that a number? It is similar to ∞ = 1000...000
a number that does not exist. Infinity does not exist as a form of a number.

We have
Lim 1.41421356237...41421356237... = 1.41421356237...
also
Lim sqrt(2)= 1.41421356237...

the mainstream morons think that this means Lim sqrt(2)= sqrt(2) because of their Lim S = S and therefore they arrive at sqrt(2) = 1.41421356237...

[John Gabriel]

On Friday, 2 December 2016 21:53:54 UTC-8, 7777777 wrote:
> perjantai 2. joulukuuta 2016 15.54.28 UTC+2 John Gabriel kirjoitti:
> >
> > If Lim S = sqrt(2), then Lim S is not a number because sqrt(2) is not a number.
> >
>
> We can ask if a non-existent number is still a number.

No. A number either exists or it does not. There is no maybe or in between.

If a magnitude cannot be measured, then there is no number that describes it.

> To be or not to be?
> To be a number or not to be a number, that is the question.
>
> sqrt(2) = 1.41421356237...41421356237...

Nonsense.

>
> is that a number? It is similar to ∞ = 1000...000

Yes, both are nonsense.

> a number that does not exist. Infinity does not exist as a form of a number.
>
> We have
> Lim 1.41421356237...41421356237... = 1.41421356237...
> also
> Lim sqrt(2)= 1.41421356237...

Same nonsense here. Infinity is a junk concept. You can't reify it in any shape or form. It's like your mythical Z.

[Virgil]

In article <148331f4-3b14-4a5b...@googlegroups.com>,

7777777 <jus...@yahoo.com> wrote:

> perjantai 2. joulukuuta 2016 15.54.28 UTC+2 John Gabriel kirjoitti:
> >
> > If Lim S = sqrt(2), then Lim S is not a number because sqrt(2) is not a
> > number.
> >
>
> We can ask if a non-existent number is still a number. To be or not to be?
> To be a number or not to be a number, that is the question.
>
> sqrt(2) = 1.41421356237...41421356237...
>
> is that a number?

Which? Sqrt(2) is a number, and 1.41421356237...41421356237.. is also a
number, but they are not necessarily the same number.

> We have
> Lim 1.41421356237...41421356237... = 1.41421356237...

Where is your evidence of any such alleged equality?

> also
> Lim sqrt(2)= 1.41421356237...

Since sqrt(2) is already a single fixed number,
what do you mean by the ambiguous expression "Lim sqrt(2)"?

>
> the mainstream morons think that this means Lim sqrt(2)= sqrt(2)

Since sqrt(2) is not a variable expression,
"Lim sqrt(2)" is nonsense, like lim(2^2).
--
Virgil
"Mit der Dummheit kampfen Gotter selbst vergebens." (Schiller)

[in...@xlog.ch]

JG still no clue what math is?

> > We can ask if a non-existent number is still a number.
> No. A number either exists or it does not. There is no maybe or in between.

Everything depends on which math theory you
are using. You know these little things
that consists of axioms and definitions.

You used these words yourself, axiom
and definition, when you were halllucinating
that some vetting creates axioms, like nuggets.

Its not that easy. And there is a fairly large
number of number concepts in math, represented
by the various theories that hsave been explored.

What you use for counting cocunuts or
designing railways, its up to you. Anyway how
about some matroids as numbers, and doing some
combinatorial geometriy?

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

If its geometry is reifiable, right? So its
wellformed, right?

[in...@xlog.ch]

Hey Bassam,

How is your progress with a*x^n+b*x^m+c = 0.
If you don't mind, here is a probe for any method,
I suggest to use for example a=1,n=3,b=2,m=2,c=-10,
namely the equation:

f(x) = x^3 + 2*x^2 - 10 = 0

This program can potentially give us as many bits
as we want, provided I were not too lazy to deploy
some BigInteger. In the present example I could
make it up to 30 bits:

public class Irrational {

public static double fun(double x) {
return x * x * x + 2 * x * x - 10;
}

public static void main(String args[]) {
int p = 2;
int q = 1;
System.out.println("p=" + p + ",\tq=" + q);
for (int i = 0; i < 30; i++) {
int t = 2 * p;
double sign1 = Math.signum(fun((double) (t - p) / q));
for (; ; ) {
t--;
double sign2 = Math.signum(fun((double) (t - p) / q));
if (sign2 != sign1) {
t++;
break;
} else {
sign1 = sign2;
}
}
p = t;
q = 2 * q;
System.out.println("p=" + p + ",\tq=" + q);
}
}
}

A run gives:

p=2, q=1
p=4, q=2
p=8, q=4
p=15, q=8
p=29, q=16
p=56, q=32
p=109, q=64
p=215, q=128
p=427, q=256
p=851, q=512
...
p=27753703, q=16777216
p=55507399, q=33554432
p=111014790, q=67108864
p=222029572, q=134217728
p=444059136, q=268435456
p=888118264, q=536870912
p=1776236519, q=1073741824

Here is a little evaluation of the posed equation,
using double for simplicity:

a_approx = 1.654249168001115
f(a_approx) = 0.000000150406497

So we know roughly what we have to expect from
Euler/Lambert or one of your formulas in the
present case.

Bye

[7777777]

lauantai 3. joulukuuta 2016 22.31.49 UTC+2 Virgil kirjoitti:

> 7777777 wrote:

> > sqrt(2) = 1.41421356237...41421356237...
> >
> > is that a number?
>
> Which? Sqrt(2) is a number, and 1.41421356237...41421356237.. is also a
> number, but they are not necessarily the same number.
>

sqrt(2) = 1.41421356237...41421356237... is an equality, doesn't this
mean that they are the same, that they are the same number?
And that number is a non-existent number. The question is:
is a non-existent number still number? To be or not to be? To be a number

or not to be a number, that is the question.

> > We have
> > Lim 1.41421356237...41421356237... = 1.41421356237...
>
> Where is your evidence of any such alleged equality?

The evidence is: in the real numbers
0.(9) ≠ 1 because
Lim 0.(9) = 1, meaning the same as Lim 1 = 0.(9)

this leads into
0.(9)(9) = 1
Lim 0.(9)(9) = 0.(9) which is of the same form as
Lim 1.41421356237...41421356237... = 1.41421356237...

>
> > also
> > Lim sqrt(2)= 1.41421356237...
>
> Since sqrt(2) is already a single fixed number,
> what do you mean by the ambiguous expression "Lim sqrt(2)"?

Lim sqrt(2)= 1.41421356237... means the same as Lim 1.41421356237... = sqrt(2)

the proof that the logic is right:
Lim Lim sqrt(2) = Lim Lim 1.41421356237...41421356237... = Lim 1.41421356237... = sqrt(2)
and that's right, as it should be.

The mainstream logic
Lim sqrt(2) = sqrt(2) is false.

> >
> > the mainstream morons think that this means Lim sqrt(2)= sqrt(2)
>
> Since sqrt(2) is not a variable expression,
> "Lim sqrt(2)" is nonsense, like lim(2^2).

no, it is not nonsense.
If it were nonsense, then also 1 = Lim 1 would also be the same nonsense,
but it is used by the mainstream to "prove" that 0.(9) = 1

Also, if it were nonsense, then also sqrt(2) = 1.41421356237... would be nonsense, because there is used the same formula S = Lim S:

We have
Lim 1.41421356237...41421356237... = 1.41421356237...

[Virgil]

In article <e007444e-50b7-4f0d...@googlegroups.com>,

7777777 <jus...@yahoo.com> wrote:

> lauantai 3. joulukuuta 2016 22.31.49 UTC+2 Virgil kirjoitti:

> > 49 wrote:
>
> > > sqrt(2) = 1.41421356237...41421356237...
> > >
> > > is that a number?
> >
Which? Sqrt(2) is a number,

but 1.41421356237...41421356237.. is NOT a number.

>
> sqrt(2) = 1.41421356237...41421356237... is an equality

A possibly false one, since you have not proved that there are any
"..."s, for which (1.41421356237...41421356237...)^2 = 2,
and you certainly cannot prove it, so it is almost certainly false!

> doesn't this
> mean that they are the same, that they are the same number?

But "1.41421356237...41421356237..." is not a number at all
until both "..." strings have been replaced by appropriate digit strings.

> And that number is a non-existent number.

In standard math, the set of real numbers x for which x^2 < 2 has a
real number least upper bound, a y for which y^2 = 2

> The question is:
> is a non-existent number still number?

That y is a real real number which really exists in
any and every complete real number field.

> > > We have
> > > Lim 1.41421356237...41421356237... = 1.41421356237...

You may claim it but no one else is forced to accept any such clam.

>
> The evidence is: in the real numbers
> 0.(9) ≠ 1 because
> Lim 0.(9) = 1, meaning the same as

In proper math, "Lim 0.(9) = 1" is not the same as "Lim 1 = 0.(9)"

>
> >
> > > also
> > > Lim sqrt(2)= 1.41421356237...
> >
> > Since sqrt(2) is already a single fixed number,
> > what do you mean by the ambiguous expression "Lim sqrt(2)"?
>
> Lim sqrt(2)= 1.41421356237...
> means the same as Lim 1.41421356237... = sqrt(2)

Not in any sort of proper math!

> the proof that the logic is right:
> Lim Lim sqrt(2) = Lim Lim 1.41421356237...41421356237... = Lim
> 1.41421356237... = sqrt(2)

WRONG!

>
> The mainstream logic
> Lim sqrt(2) = sqrt(2) is false.

Since sqrt(2) is a fixed number, not a variable quantity
Lim sqrt(2) connot differ from sqrt(2).

>
> > >
> > > the mainstream morons think that this means Lim sqrt(2)= sqrt(2)
> >
> > Since sqrt(2) is not a variable expression,
> > "Lim sqrt(2)" is nonsense, like lim(2^2).
>
> no, it is not nonsense.

It is nonsense in proper mathematics


> Lim 1.41421356237...41421356237... = 1.41421356237...
Actually, you have no way of knowing or proving that
Lim 1.41421356237...41421356237... =\= 1.41421356238
.

It is not known whether "41421356237" appears more than once in the
infinite decimal expansion of sqrt(2) so that your
Lim 1.41421356237...41421356237... = 1.41421356237...
is a stupid nonsense assumption!
>
> the mainstream morons think that this means Lim sqrt(2)= sqrt(2)6237...

Since sqrt(2) is a fixed quantity,
how is lim sqrt(2) any different from sqrt(2) ?

[John Gabriel]

sqrt(2) is not a number. It is the name given to that magnitude that cannot be measured. It is an incommensurable magnitude.

[7777777]

sunnuntai 4. joulukuuta 2016 22.00.44 UTC+2 Virgil kirjoitti:

> but 1.41421356237...41421356237.. is NOT a number.

then sqrt(2) is also NOT a number.

[John Gabriel]

Of course it is not a number.

[John Gabriel]

On Sunday, 4 December 2016 12:36:49 UTC-8, 7777777 wrote:

Look 7s, you can only construct the 'Symptom' of sqrt(2). You can't even construct the magnitude and it only makes sense once you try to measure it, that is, unless you can measure it, you have nothing but a magnitude.

[Virgil]

In article <f3e382c7-220e-4017...@googlegroups.com>,

Until one can know whether
(1.41421356237...41421356237...)^2 = 2 or not,
1.41421356237...41421356237...is not a number

And jussir@yahoo himself can not himself KNOW that until he can
at least prove that the digit sequence "41421356237" must appear
at least TWICE in the non-terminating decimal representation of
sqrt(2).

Which he has not done and cannot do!

[burs...@gmail.com]

give me two numbers p,q such that:

p^2+1 = 2*q^2.

Note: Such numbers do exist.

Then I will compute sqrt(2) for you can
check 41421356237 is repeated or not.

Diclaimer: I might fail.

[burs...@gmail.com]

Here is an example p=1393, q=985, we can
then compute digits of it via:

sqrt(2) = (1393/985)*1/sqrt(1-1/1940450)

But I am currently looking for p^2+k = 2*q^2,
where q is a power of 10, which would give
an algorithm without any hassel of converting
between binary and decimal, here is an example:

sqrt(2) = (1414/1000)*1/sqrt(1-604/2000000)

See also:
http://stackoverflow.com/a/15434306/502187

Question: What would be the next interesting p,k,q
to give it a try and even get a better convergence
than the SO solution?

[bassam king karzeddin]

> give me two numbers p,q such that:
>
> p^2+1 = 2*q^2.
>
> Note: Such numbers do exist.
>
> Then I will compute sqrt(2) for you can
> check 41421356237 is repeated or not.
>
> Diclaimer: I might fail.

Consider (p = 7, and q = 5), then how do you make it?

Bassam King Karzeddin

[burs...@gmail.com]

Am Montag, 5. Dezember 2016 13:10:05 UTC+1 schrieb bassam king karzeddin:
> Consider (p = 7, and q = 5), then how do you make it?
>
> Bassam King Karzeddin

Like here:
> See also:
> http://stackoverflow.com/a/15434306/502187

Using sqrt(2) = (7/5)*1/sqrt(1-1/50)
But convergence will be not very interesting.
Not leaping multiple digits, taking much more
time to reach for example:

10 million digits of the square root of 2 - NASA
http://apod.nasa.gov/htmltest/gifcity/sqrt2.10mil

(Which I guess can be done by adding some
sliding window technique)

With this provisio:
> Diclaimer: I might fail.

Means for the task of 7777777 I might return with
the following two answers:
Answer a): Yes I have tried this and this number of
digits and found the pattern 41421356237 twice.
Answer b): Inconclusive, I have tried this and this
number of digits, and didn't found the pattern
41421356237 twice, and I don't know if I would
find the 41421356237 twice if I would look at
more digits.

(BTW: The pattern does not occur twice in the
NASA HTML page, but the NASA HTML page breaks the
number by newline, so this search is not representativ,
since I am too lazy to remove the newlines, I prefer
computing the digits from ground up)

[burs...@gmail.com]

Am Montag, 5. Dezember 2016 13:52:40 UTC+1 schrieb burs...@gmail.com:
> 10 million digits of the square root of 2 - NASA
> http://apod.nasa.gov/htmltest/gifcity/sqrt2.10mil

Note: Smaller patterns such as 41421
already occur twice.

Warning: Your browser might now show the
whole file, browsers sometimes clip HTML
files at 1 MByte. So we would anyway need
to download the file and massage it with
some code. But computing the digits from
ground up sounds more challenging.

[burs...@gmail.com]

> Warning: Your browser might now show the
> whole file, browsers sometimes clip HTML

Corr.:
Warning: Your browser might not show the

[bassam king karzeddin]

At any case, fast or much faster programs or algorithms, would only show up a very little part of unreal integer being as distinct infinity assumed in mind only, that would actually never be achievable or existing, since it is endless, thus you are clearly chasing an illusion in mind (phobia of numbers) only , that is (Sqrt(2)) impossible to exist in your rational number system

But mathematicians cheat the public by convincing them that what they are doing is real science that require so much funds from world Governments, just to play and enjoy the absurdity of finding more and more digits, as if they are going to discover something useful at the end

It is only a little minds game that is worthless

Bassam King Karzeddin

[burs...@gmail.com]

Don't get fooled by me. If I am fooling somebody,
than this is because I fooled myself.

JB wrote:
> give me two numbers p,q such that:
> p^2+1 = 2*q^2.
> Note: Such numbers do exist.

The Pell equation always gets me, I am
too blind to see the pattern.

Here is a recursion formula for this Pell
equation, start with the following pair:

p = 1

q = 1

Then use the following recursion equation:

p′=3p+4q

q′=2p+3q

You can use these pairs to compute p/q,
which approximates sqrt(2) very quickly:

P Q P/Q
1 1 1.000000000
7 5 1.400000000
41 29 1.413793103
239 169 1.414201183
1393 985 1.414213198
8119 5741 1.414213552
47321 33461 1.414213562

This would consist a further method to compute
the digits of sqrt(2) and maybe answering
777777 question.

See also:
http://math.stackexchange.com/q/2045083/4414

[Vinicius Claudino Ferraz]

You need a psychiatrist of your confidence.

First you write in a txt 0.9999999...
infinitely many bytes.
then you write in the txt [infinity + 1]-th digit a 9
then you write in the txt [infinity + 2]-th digit a 9
then you write in the txt [infinity + 3]-th digit a 9
then you write in the txt [infinity + 4]-th digit a 9
then you write in the txt [infinity + 5]-th digit a 9

The name of this thing is 0.(9)(9)

Second you write in a txt 1.41421356237...
infinitely many bytes.
then you write in the txt [infinity + 1]-th digit a 4
then you write in the txt [infinity + 2]-th digit a 1
then you write in the txt [infinity + 3]-th digit a 4
then you write in the txt [infinity + 4]-th digit a 2
then you write in the txt [infinity + 5]-th digit a 1

The name of this thing is 1.(41421356237...)(41421356237...)

I need your computer. : - )

Em domingo, 4 de dezembro de 2016 16:16:15 UTC-2, 7777777 escreveu:
> 0.(9)(9) = 1
> Lim 0.(9)(9) = 0.(9) which is of the same form as
> Lim 1.41421356237...41421356237... = 1.41421356237...
>

> Lim Lim sqrt(2) = Lim Lim 1.41421356237...41421356237... = Lim 1.41421356237... = sqrt(2)
>

[burs...@gmail.com]

For the likes of you I have also calculated the
error, I hope your headache goes away:

P Q P/Q (P/Q)^2-2
1 1 1 -1
7 5 1.4 -0.04
41 29 1.413793103 -0.001189061
239 169 1.414201183 -3.50128E-05
1393 985 1.414213198 -1.03069E-06
8119 5741 1.414213552 -3.03407E-08
47321 33461 1.414213562 -8.93146E-10

(Note for simplicity Excel computation,
not Prolog rationals computation)

Am Montag, 5. Dezember 2016 18:13:25 UTC+1 schrieb Vinicius Claudino Ferraz:
> The name of this thing is 1.(41421356237...)(41421356237...)

This hasnt been settled yet. JB wrote:
> Means for the task of 7777777 I might return with
> the following two answers:
> Answer a): Yes I have tried this and this number of
> digits and found the pattern 41421356237 twice.
> Answer b): Inconclusive, I have tried this and this
> number of digits, and didn't found the pattern
> 41421356237 twice, and I don't know if I would
> find the 41421356237 twice if I would look at
> more digits.

But there is a third option:
Answer c): No, we can find some argument, for
example a number theoretic one, that shows
that 41421356237 cannot appear twice.

Please be patient, we are working on it...

[Vinicius Claudino Ferraz]

x = pi - 3 = 0.1415926535897932384626433832795
y = sqrt 2 / 10 = 0.14142135623730950488016887242097
x - y = 0.0001,7129735248373358247451085853308 < 2 * 10^(-4)

0 < x - y
y < x
sqrt 2 / 10 < pi - 3
sqrt 2 < 10 pi - 30

what is the difference?

I bet somebody will say both are not numbers.
Not-numbers can't be compared. Right?

[burs...@gmail.com]

Yo man, you are asking the right questions.

Am Montag, 5. Dezember 2016 18:44:53 UTC+1 schrieb Vinicius Claudino Ferraz:
> x = pi - 3 = 0.1415926535897932384626433832795
> y = sqrt 2 / 10 = 0.14142135623730950488016887242097
> x - y = 0.0001,7129735248373358247451085853308 < 2 * 10^(-4)

> what is the difference?

One thing is a fixed difference.

And the other thing is a series
of differences that gets smaller
and smaller towards zero.

[burs...@gmail.com]

Shameless self promotion:

Computing 1 million digits of sqrt(2) in less a minute. (Prolog)
http://stackoverflow.com/questions/15362117/find-as-many-digits-of-the-square-root-of-2-as-possible/40982112#40982112

[John Gabriel]

12/5/16 12:13

[burs...@gmail.com]

> 12/5/16 12:13

Again the size of your bird brain?

[bassam king karzeddin]

Thus, the exact value of sqrt(2) would require both (P and Q) to be distinct coprime integers with infinite (endless) sequence of digits, which is first, impossible to achieve, and second not permissible in the holy grail of mathematics,

Does this so simple logic or so basic common sense that was repeated quite many times require all that (what is called too advanced mathematics or set theories to alter the truth)

The judgement through those so basic and elementary tools would immediately throw away all those fake theories as set theory and many others (even without knowing anything about them)

So, throw away their books for ever

Regards
Bassam King Karzeddin
6th, Dec., 2016

[burs...@gmail.com]

Am Dienstag, 6. Dezember 2016 09:08:52 UTC+1 schrieb bassam king karzeddin:
> Thus, the exact value of sqrt(2)
> would require both (P and Q) to be
> distinct coprime integers with infinite
> (endless) sequence of digits, which is
> first, impossible to achieve, and second
> not permissible in the holy grail of
> mathematics,

Thats nowhere said. { p/q | p*p+1 = 2*q*q } is just
a ordinary set of rationals, each rational being from
the ordinary set Q. You confusing this thread with the
thread about your unreals.

[burs...@gmail.com]

You can also use the set { p/q | p*p-1 = 2*q*q } ,
note the changed plus sign to minus sign,

which can be constructed by another recurrence
relation, and was already know to antiquity:

https://en.wikipedia.org/wiki/Square_root_of_2#Continued_fraction_representation

"The convergents formed by truncating
this representation form a sequence of
fractions that approximate the square
root of two to increasing accuracy, and
that are described by the Pell numbers
(known as side and diameter numbers to
the ancient Greeks because of their
use in approximating the ratio between
the sides and diagonal of a square)."

[FredJeffries]

No. Even if there existed "integers with infinite (endless) sequence of digits", it would still not yield "the exact value of sqrt(2)". Pythagoras will always bite you: sqrt(2) is not commensurable with integers, no matter how many digits there are.

[John Gabriel]

So, 0.333... =/= 1/3 ?

1.414... =/= sqrt(2) ?

At infinity, 1.414... becomes irrational, no? Chuckle.

> Pythagoras will always bite you: sqrt(2) is not commensurable with integers, no matter how many digits there are.

WRONG. sqrt(2) is not commensurable with ANYTHING but itself.

**** A number is the measure of a magnitude. ****

The measure of a magnitude by any other magnitude except itself. So, for example, pi is not a number because the diameter does not measure the circumference, not because the diameter is not an integer. Chuckle.

Try again? :-)

[burs...@gmail.com]

Am Dienstag, 6. Dezember 2016 14:02:49 UTC+1 schrieb FredJeffries:
> > Thus, the exact value of sqrt(2) would require both (P and Q) to be distinct coprime integers with infinite (endless) sequence of digits
>
> No. Even if there existed "integers with infinite (endless) sequence of digits", it would still not yield "the exact value of sqrt(2)". Pythagoras will always bite you: sqrt(2) is not commensurable with integers, no matter how many digits there are.

I gave one definition of add for "endless digits
integer", with the suprising result:

...999 + ...001 = ...000

Now define a multiply and a two, and show
that the following is impossible for
some "unreal" X:

X * X - 2 = 0

Here is a definition of multiplication, it
will send two "unreals" d and e to f and a
carry c:

f(i)=(sumj+k=i d(j)*e(k)+c(i)) mod 10
c(0)=0
c(i+1)=(sumj+k=i d(j)*e(k)+c(i)) div 10

Now I get:

...53124141 * ...53124141 = ...99999991

Unfortunately this multiplication is not
compatible with the strange addition above,
(probably A*(B+C)=A*B+A*C will fail
I guess, not sure)

But if we accept ...99999991 = ...002 inside "unreals"
then an infinite endless sequence of digits
is exactly what makes the equation satisfiable.

(BTW: I am working on a different addition for
*unreals", it will use some triangle:

Take ...770 + ..550 this will give

70 + 50 = 21
770 550 = 231
7770 5550 2331
... ... ...

So the result of the addition will be ...331. )

[burs...@gmail.com]

See also:
E. Specker (1949), "Nicht konstruktiv
beweisbare Sätze der Analysis" Journal
of Symbolic Logic, v. 14, pp. 145–158.

He mentions 3 different real constructions
and in passing says that some of them don't
allow multiplication and some of them don't
allow addition, to be defined constructively.

For example we have this beast:
https://en.wikipedia.org/wiki/Specker_sequence

But I don't think sqrt(2) is a beast.

[burs...@gmail.com]

Sorry, my multiplication is wrong, I mean
the formula, we also need a triangle...

The carry also walks in the different direction.
So I guess unreals a pretty dead...

[John Gabriel]

BTW Freddiekins, speaking of integers, there are no two integers p and q such that p/q = 0.999...

[FredJeffries]

On Tuesday, December 6, 2016 at 5:59:51 AM UTC-8, burs...@gmail.com wrote:
> Am Dienstag, 6. Dezember 2016 14:02:49 UTC+1 schrieb FredJeffries:
> > > Thus, the exact value of sqrt(2) would require both (P and Q) to be distinct coprime integers with infinite (endless) sequence of digits
> >
> > No. Even if there existed "integers with infinite (endless) sequence of digits", it would still not yield "the exact value of sqrt(2)". Pythagoras will always bite you: sqrt(2) is not commensurable with integers, no matter how many digits there are.
>
> I gave one definition of add for "endless digits
> integer", with the suprising result:
>
> ...999 + ...001 = ...000

Yes, The 10-adic numbers
http://www.numericana.com/answer/p-adic.htm#decimal
http://www.maths.manchester.ac.uk/~khudian/Etudes/Arithmetics/10-adic1.pdf

There is no sqrt(2) among the 10-adic integers
http://math.stackexchange.com/questions/741800/does-the-p-adic-shows-the-other-end-side-of-numbers-i-e-from-right-to-left

But that was not my point, which was that the representations don't matter. That there are no integers P and Q such that P/Q is the square root of two has nothing to do with decimal places and representations. Those are accidental properties. The incommensurability of sqrt(2) depends only on the essential natures of integers and sqrt(2)

[John Gabriel]

On Tuesday, 6 December 2016 06:54:04 UTC-8, FredJeffries wrote:

> The incommensurability of sqrt(2) depends only on the essential natures of integers and sqrt(2)

That is nonsense. The incommensurability of sqrt(2) is a fact stemming from the attempted measure of the hypotenuse of a right-angled isosceles triangle using the leg. It has ZERO to do with integers.

See, you can't even construct sqrt(2) or pie. All you do is construct the symptom. But sqrt(2) refers not to the symptom, but the ***measure***.

Please watch my video and become wise Freddie!

https://www.youtube.com/watch?v=B3AlAil5Crc

[burs...@gmail.com]

Am Dienstag, 6. Dezember 2016 15:59:18 UTC+1 schrieb John Gabriel:
> The incommensurability of sqrt(2) is a fact.

And not relevant for the real line "construction" be it
constructive or non-constructive.

Computation with real represented as sequences as rationals
is darn simple. If we have two reals a and b, as sequences
of rationals r1,r2,.. and s1,s2,..

a = (r1,r2,..)

b = (s1,s2,..)

Then we can readily define:

a+b = (r1+s1,r2+s2,..)

a*b = (r1*s1,r2*s2,..)

The only problem is when computing with decimals and not with
rationals. Since when we have a real:

a = (r1,r2,...)

And we find some digit in rk at some place we are not sure that
it flips at some time later in the sequence. And deciding whether
a digit is stable very much depends on how the sequence was constructed.

I will give an example soon.

[John Gabriel]

12/6/16 7:27am

[burs...@gmail.com]

Am Dienstag, 6. Dezember 2016 16:27:28 UTC+1 schrieb John Gabriel:
> 12/6/16 7:27am

Obviously the number of marbles you have
lost. JG, the cheese cake factory is calling you.

[Vincent Granville]

Here is a rudimentary formula that generates all the digit of SQRT(2)/2:

p(0) = 0, p(1)= 1, e(1) = 2
If 4p(n) + 1 < 2e(n) Then
p(n+1) = 2p(n) + 1
e(n+1) = 4e(n) - 8p(n) - 2
d(n+1) = 1
Else
p(n+1) = 2p(n)
e(n+1) = 4e(n)
d(n+1) = 0

d(n) is the n-th digit in base two. For details, go to http://www.analyticbridge.com/forum/topics/challenge-of-the-week-square-root-of-two

[John Gabriel]

There is no formula that generates *all* the digits of sqrt(2) or pi. Any formula can only generate n digits and that which is generated is never sqrt(2) or pi.

Thus, is truth, there is no formula that can generate the digits of either, since innumerably other numbers have the same n digits in the same places.

Pretty futile eh? :-)

[konyberg]

That is why we have the symbol sqrt(). Sqrt(2) is well defined as sqrt(2).
As pi is represented by pi.

KON

[konyberg]

tirsdag 6. desember 2016 22.26.24 UTC+1 skrev John Gabriel følgende:

Besides you say innumerably other numbers have the same n digits in the same places ? Can you prove it, or is it your faulty understanding of infinity that tells you?
Also interesting that you use the term numbers of these numbers :)

KON

[burs...@gmail.com]

Am Dienstag, 6. Dezember 2016 21:50:02 UTC+1 schrieb Vincent Granville:
> Here is a rudimentary formula that generates all the digit of SQRT(2)/2:
>
> p(0) = 0, p(1)= 1, e(1) = 2
> If 4p(n) + 1 < 2e(n) Then
> p(n+1) = 2p(n) + 1
> e(n+1) = 4e(n) - 8p(n) - 2
> d(n+1) = 1
> Else
> p(n+1) = 2p(n)
> e(n+1) = 4e(n)
> d(n+1) = 0

Cool! I hope there is no bug in it, and that
the following is satisfied:

sqrt(2)/2 = lim n->oo sum_k=0^n d(i)/2^i

BTW: Here is very simple non-constructive
proof of such a sequence.

Just stsrt with:

x(0) = sqrt(2)/2

Then set:

d(i) = floor(x(i) * 2)
x(i+1) = x(i) * 2 - d(i)

Compared to Euler-Lagrange, which worked
with continued fractions, much simpler.

[John Gabriel]

On Tuesday, 6 December 2016 13:45:10 UTC-8, konyberg wrote:

> > There is no formula that generates *all* the digits of sqrt(2) or pi. Any formula can only generate n digits and that which is generated is never sqrt(2) or pi.

> That is why we have the symbol sqrt(). Sqrt(2) is well defined as sqrt(2).
> As pi is represented by pi.

The symbol sqrt(2) tells us NOTHING about the measure of sqrt(2) just as the symbol pi tells us nothing about the measure of pi.

> >
> > Thus, is truth, there is no formula that can generate the digits of either, since innumerably other numbers have the same n digits in the same places.
> >
> > Pretty futile eh? :-)
>
> Besides you say innumerably other numbers have the same n digits in the same places ?

The proof is so simple that a 5 year old can get it. Okay, let's say you calculate 2 million digits, then there are infinitely many other numbers with these same 2 million digits in the first 2 million places and different digits in the rest. This is very easy.

> Can you prove it, or is it your faulty understanding of infinity that tells you?

Just showed you.

> Also interesting that you use the term numbers of these numbers :)

Never used such a phrase. I said there are "innumerably many". That means so many that you can never count them all.

>
> KON

[burs...@gmail.com]

JG, the cheese cake factory is calling you.

They sad they see to many square cakes not
yet delivered, and they want you to first

take the root. But you should take care not
to get lost in the infinite labyrinth of
minotauros, since you seem easily disturbed.

[Virgil]

In article <bac0b490-ad54-4314...@googlegroups.com>,

bassam king karzeddin <sophy...@gmail.com> wrote:

> So, throw away their books for ever
>
> Regards
> Bassam King Karzeddin
> 6th, Dec., 2016

Let badass throw out all his math books and remain mathematically
ignorant forever!

[John Gabriel]

On Thursday, 17 November 2016 05:50:08 UTC-8, bassam king karzeddin wrote:
> Even this was explained quite many times but never mind to prove it again and again:
>
> First, the Greek construction of a number

It was never a construction of a number, only the symptom of a magnitude. The number comes in later to described the measure of the magnitude.

> by unmarked straightedge and a compass with finite number of steps, with arbitrary shortest distance between two distinct visualized locations on the straight number line defined as a unity, was the base of construction of an existing real number, which implies its true existence, wither it can be measured by rational numbers or not, since the construction of the rational numbers is defined by those definitions also, and was based on the perfection of the ideas behind this elementary principle
>
> So if we deny or disprove the Greek famous principle, then yes no numbers can be defined on a number line except two numbers by convention as you mentioned earlier, where then the concept of a constructing or measuring a number becomes so meaningless

You can reify numbers as invisible markers on a number line:

https://www.youtube.com/watch?v=2ENN47E_j_4

>
> So, depending on the validity of the Greek principle, Sqrt(2) is a real existing number,

It is never a number, only a magnitude that cannot be measured.

> being abstractly and physically a diagonal of a square of defined unity side, thus it is exactly constructed with unique location on a number line that no rational number can occupy, and was originated from the unity “one”, despite being immeasurable by rational.
>
> Doubling the square in real non zero integers is impossible, (n^2 =/= 2m^2), therefore taking the sqrt of both sides of this eqn. would yield:
> Sqrt(2) =/= n/m, where (n/m) is rational number, NO matter if both (n & m) tends to be infinite integers
>
> So, the rational representation (or the best approximation) of Sqrt(2) is always rational number, no matter if you can fill out the galaxy size of some of its endless digits
> And since Sqrt(2) was proved to be irrational number which is impossible to be rational number, hence it is rational representation in any rational number system is fake number that is impossible to exist, trying always and forever to replace the unique location of Sqrt(2) but always unsuccessfully
>
> Let us see it clearly in our decimal 10base number system representation, as a sequence of endless approximation, for Sqrt(2)
>
> First Sqrt (2) = 1 = 1/(10)^0
> Second = 1.4 = 14/10^1
> Third = 1.41 = 141/10^2
>
> …………. = …………………
>
> Tenth = 1414213562/10^9
>
> …….. = ……………
>
> K’th = n/m, where (m = 10^(k - 1),
> and (n) is integer with (k) number of digits
>
> (k + 1) = n/m, where (m = 10^k), and
> (n) is integer with (k + 1) number of digits
>
> Hence, if we go after exact value, we find this task is impossible to achieve, because we require both of
> (m & n) to be infinite integers with infinite sequence of digits, where this is obviously impossible, and also not permissible in mathematics, (then we better admit the truth of real best approximation), or say this is the magnitude of Sqrt(2) in rational number (which is not an exact number)- as John Gabriel continuously describes for immeasurable numbers
>
> The proof is therefore completed
>
> Regards
> Bassam King Karzeddin
> 17Th,Nov., 2016

[burs...@gmail.com]

Bla bla JG, you don't know shit what you
are talking. If we have:

sqrt(2)/2 = 0.v1 v2 ....

Which can be easily constructed geometrically.
Just take the diagonal of the 1/2 square.

Than move it down on the real line, and then
do the following geometric algorithm:

Loop:
Check whether the measure is less than 1 unit.
Answer Yes: Write a zero (0) on a paper,
and double the measure
Answer No: Write a one (1) on a paper,
and double the measure and the substract 1 unit

The above can be all done with rule and compass,
and gives exactly 0.v1 v2 ...

[abu.ku...@gmail.com]

we can generate i.e the unit octonion
st ;east as far as two halves,
just as with the secondr00t of a negative half

> sqrt(2)/2 = 0.v1 v2 ....

[bassam king karzeddin]

On Wednesday, December 7, 2016 at 2:54:49 AM UTC+3, John Gabriel wrote:
> On Thursday, 17 November 2016 05:50:08 UTC-8, bassam king karzeddin wrote:
> > Even this was explained quite many times but never mind to prove it again and again:
> >
> > First, the Greek construction of a number
>

John Gabriel wrote:

> It was never a construction of a number, only the symptom of a magnitude. The number comes in later to described the measure of the magnitude.
>

Do you mean that rational numbers are continuous?

If this is proved, then yes what you claim beyond any doubt

Where I think, it is impossible for rational numbers to be continuous, but they are isolated by those defined as constructible numbers (excluding the rational numbers from them), thus together, the constructible numbers including the rational numbers must form a continuous state on the real number line, where then no any location is left for any other type of numbers such as real algebraic number or transcendental number,

So, yes real number is only constructible number

Note that here I'm stating this in terms of existence of numbers on the real number line, since existence is more fundamental state of measurement,

And why the real number line is the criteria?, well, and yes because mathematics must describe the physical existing world in our sense, and if physics is governed by gravity for example then maths must be governed by a number line at least which is ultimately physics, otherwise nothing would actually govern the mathematicians to make it as a mind endless games that are useless

So they simply imagined and intuitively concluded that there is an exact number for cube root of two on the real number line, then they expanded this game for ever, of course without any rigorous proof as the case of sqrt(2), but by infinite approximation which is a carpenter can make without all their shit or set theories even before thousands of years if you asked him to make a cube that can contain two unit cube measure (approximately)

Regards
Bassam King Karzeddin
7th, Dec., 2016

[burs...@gmail.com]

Ok then, lets call this the busy
carpenter algorithm:

> Loop:
> Check whether the measure is less than 1 unit.
> Answer Yes: Write a zero (0) on a paper,
> and double the measure
> Answer No: Write a one (1) on a paper,
> and double the measure and the substract 1 unit
>

> The above can be all done with rule and compass,
> and gives exactly 0.v1 v2 ...

Nobody saw the error, well it should say:
> Check whether the measure is less than 1/2 unit.

Now we have seen by using Francois Vietes ideas of
symbolic logistics, an algorithm can be verified where
we trade the ruler and compass for integer arithmetic.

d(n) is the n-th digit in base two.
For details, go to
http://www.analyticbridge.com/forum/topics/challenge-of-the-week-square-root-of-two

This algorithm has a state (s1, .., sn) represented
as integer, this state is advanced in each iteration
where a bit is spit out to a new state (s1',..,sn').

Proof the following:

1) If the state is bounded, i.e. if the integers s1,..,sn
are not allowed to grow arbitrarily large, i.e. if there

is an upper bound k, such that |s1|<k, .. |sn|<k
then the algorithm will no be able to generate

the bits of an irrational number, it will only
generate the bits of a rational number

2) There is also an algorithm that does
the same job for pi, show it.

3) There is also an algorithm that does
the same job for e, show it.

4) The ideal carpetener can do his work for every real
line number r, in that we can ask him for 0.v1 v2 ...
as many bits of it as we want.

Show that there is an inverse carpenter, that from
a sequence 0.v1 v2 ... he can construct an approximation
r' of an r, arbitary close.

5) Show that not every real line number r, has a finite
corresponding algorithm with some integer initial state (s1,..,sn),

assume algorithm will be a "while"-program, hint you can
use Cantor diagonalization, but 1) is not needed.

So yes, not all real line numbers can be communuicated
in the form of a finite algorithm with integer initial
state (s1,..,sn), thats what Cantor can be used to show.

Bye

[burs...@gmail.com]

Bonus question about some anomaly:

7) Show that the carpenter might sometimes be stupid,
maybe he has some problems with his eyesight and
needs some new glasses.

The ideal carpenter sure works fine for the interval
[0,1), but if we give him 1 unit, he will produce
0.111... like crazy, right?

Will the inverse carpenter return 1 unit?

[John Gabriel]

On Tuesday, 6 December 2016 23:35:48 UTC-8, bassam king karzeddin wrote:
> On Wednesday, December 7, 2016 at 2:54:49 AM UTC+3, John Gabriel wrote:
> > On Thursday, 17 November 2016 05:50:08 UTC-8, bassam king karzeddin wrote:
> > > Even this was explained quite many times but never mind to prove it again and again:
> > >
> > > First, the Greek construction of a number
> >
> John Gabriel wrote:
>
> > It was never a construction of a number, only the symptom of a magnitude. The number comes in later to described the measure of the magnitude.
> >
>
> Do you mean that rational numbers are continuous?

No. They are most definitely not continuous.

>
> If this is proved, then yes what you claim beyond any doubt

Nope. No proof of anything is required in addition to what I already stated.

>
> Where I think, it is impossible for rational numbers to be continuous,

You do not "construct numbers". You can construct the SYMPTOM of a number. In fact, you construct magnitudes which when measured, result in a rational number or don't result in a rational number. If you can't measure a magnitude, then there IS NO number associated with it.

> but they are isolated by those defined as constructible numbers (excluding the rational numbers from them), thus together, the constructible numbers including the rational numbers must form a continuous state on the real number line, where then no any location is left for any other type of numbers such as real algebraic number or transcendental number,
>
> So, yes real number is only constructible number
>
> Note that here I'm stating this in terms of existence of numbers on the real number line, since existence is more fundamental state of measurement,

Numbers have nothing to do with the number line. A number line is CALIBRATED with numbers that describe distances on it. Using invisible markers. Did you watch the video I recommended?

https://www.youtube.com/watch?v=2ENN47E_j_4

[burs...@gmail.com]

We wonder more about the symptom of craze here,
has it to with BIG. Some things not working anymore?

[konyberg]

A five year old can do the proof? That may be your problem!
If the number in question is irrational, that is not made by some repeating decimal expansion, then no repeating will occur! You are using lay man logic and not thinking of mathematics here.
If your reasoning is correct, then any irrational number will at som level include all numbers, rationals as also irrationals. This is easily disproved.

KON

[John Gabriel]

On Wednesday, 7 December 2016 12:06:15 UTC-8, konyberg wrote:
> onsdag 7. desember 2016 00.35.36 UTC+1 skrev John Gabriel følgende:
> > On Tuesday, 6 December 2016 13:45:10 UTC-8, konyberg wrote:
> >
> > > > There is no formula that generates *all* the digits of sqrt(2) or pi. Any formula can only generate n digits and that which is generated is never sqrt(2) or pi.
> >
> > > That is why we have the symbol sqrt(). Sqrt(2) is well defined as sqrt(2).
> > > As pi is represented by pi.
> >
> > The symbol sqrt(2) tells us NOTHING about the measure of sqrt(2) just as the symbol pi tells us nothing about the measure of pi.
> >
> > > >
> > > > Thus, is truth, there is no formula that can generate the digits of either, since innumerably other numbers have the same n digits in the same places.
> > > >
> > > > Pretty futile eh? :-)
> > >
> > > Besides you say innumerably other numbers have the same n digits in the same places ?
> >
> > The proof is so simple that a 5 year old can get it. Okay, let's say you calculate 2 million digits, then there are infinitely many other numbers with these same 2 million digits in the first 2 million places and different digits in the rest. This is very easy.
> >
> > > Can you prove it, or is it your faulty understanding of infinity that tells you?
> >
> > Just showed you.
> >
> > > Also interesting that you use the term numbers of these numbers :)
> >
> > Never used such a phrase. I said there are "innumerably many". That means so many that you can never count them all.
> >
> > >
> > > KON
>
> A five year old can do the proof? That may be your problem!

Actually you are the one with the problem. Seeing it is futile trying to convince you with common sense, I'll convince you this way:

Give me a number for pi which you think does not have the same n places as any other number.

Go on, if you can, this is called a counterexample and you have won. If not, you are still the same dimwit as always. Deal? chuckle.

[burs...@gmail.com]

Hey JG again loosing your marbles, and not knowing
shit, tell us about the arrow notation and the difference
and commonality of functions and series.

[konyberg]

That is your problem, common sense. It does not always work that way in math. Your common sense tells you that since a decimal expansion is infinite, it has to include all numbers we now of. It is not just so! Use your mathematical brain and do some probabilistic reasoning.

KON

[John Gabriel]

Er, no. My common sense tells me that there is no such thing as an infinite decimal expansion. It's a myth. And that is your problem! You need to study my 4 steps that determine what it means for a concept to be well defined:

https://www.linkedin.com/pulse/what-does-mean-concept-well-defined-john-gabriel?trk=prof-post

[burs...@gmail.com]

Hey JG again loosing your marbles, and not knowing

shit, even not the arrow notation and the difference
and commonality of functions and series,

He He looser. BTW the cheese cake factory is
calling you, they want you to make a series
of cakes, but they are not sure whether

the wip cream machine functions.

[konyberg]

I can give you the number pi
Isn't that good enough?
If you want me to give a series that give the decimal expansion of pi, that guarantees that f.inst. sqrt(2) wont pop up, I cannot do that, but I can prove that it wont happen!

KON

[konyberg]

Then why are you discussing this topic?

KON

[burs...@gmail.com]

JG wrote:
> no such thing as an infinite decimal expansion

Can we boil this down to:

Functions exist (for example from reals to reals):
f : R -> R

But series don't exist (for example of rationals):
s : N -> Q

Aha, Ok. Great!

[John Gabriel]

Liar. You can't give me the number pi. The symbol is not the number.

> If you want me to give a series that give the decimal expansion of pi, that guarantees that f.inst. sqrt(2) wont pop up, I cannot do that, but I can prove that it wont happen!

Irrelevant. I can give you innumerably many numbers that have exactly the first n digits as pi, no matter how many n digits you determine.

So what is your counterexample? Chuckle.

>
> KON

[John Gabriel]

I never discuss anything with my inferiors, but I do sometimes educate them as I am doing with you now.

So, how about a counterexample? chuckle.

>
> KON

[burs...@gmail.com]

And know what JG, nobody is discussing with you
on LinkedIn. In particular:

Instead of "How we got numbers" I
was reading in the voice of JG

"How I got dumber".

Instead of "Whatever I imagine is real,
because whatever I imagine is well defined."
I was reading in the voice of JG

"Whatever I shit is gold, because whatever
I shit has the form of nuggets."

[abu.ku...@gmail.com]

thir1y-one tenths, or twenty-two sevenths are g00d approximants, but
you have to take their reciprocals, to see any c00l property; hey,
long division

[wpih...@gmail.com]

Standard methods

Existence of sqrt(2):

Let S be the set of all rational numbers, r, such that r*r<2.
S is a set of real numbers bounded above and thus has a supremum, call it a.
It is easy to show a*a = 2 (Note that this proof of existence of sqrt(2) is
valid whether or not sqrt(2) has a decimal representation. )

Decimal representation of sqrt(2):

let m_n be the largest integer such that (m_n/10^n)^2<2
It is easy to show that for any e>0 there exists an m such that if
k>m then |a - m_k/10^k|<e. Thus lim_{n->oo} m_n/10^n = a
(note there is no mention of n=oo)

[abu.ku...@gmail.com]

and, it has nothing to do with the regular tetragon per se,
even though it does apply to that shape, of course;
how can any one be tuck in such ancient prejudice,
merely because he may be proficient in a language?

[John Gabriel]

On Thursday, 8 December 2016 20:26:37 UTC-8, wpih...@gmail.com wrote:
> Standard methods
>
> Existence of sqrt(2):

No one is denying the existence of the magnitude sqrt(2). But there is no number that describes it.

Bwaaa haaaa haaaaa. Nope. That is not correct or a proof that you have a number which describes sqrt(2). It's just a proof that you can find n places of accuracy for sqrt(2).

[burs...@gmail.com]

JG wrote:
> No one is denying the existence of the
> magnitude sqrt(2). But there is no number
> that describes it.

In case you didn't notice, and since you
are going to continue stating the obvious,
nobody cares that there is no rational number
numeral for sqrt(2).

[genm...@gmail.com]

12/9/16

[Harry Stoteles]

Am Freitag, 9. Dezember 2016 14:53:58 UTC+1 schrieb genm...@gmail.com:
> 12/9/16

The size of your bird brain.

[abu.ku...@gmail.com]

On Thursday, December 8, 2016 at 9:07:53 PM UTC-8, abu.ku...@gmail.com wrote:
> and, it has nothing to do with the regular tetragon per se,
> even though it does apply to that shape, of course;

you see that I use a p-adic notation, actually ten-adics insofar as usefully;
what is the continued fraction for the secondr00t of 00,
not infinitude, oo?... and, three dots means, not summorial,
3? :=: 3!, even if one isn't primal

> how can any one be ticklish in such ancient prejudice,

> merely because he may be proficient in a language?
>
> > valid whether or not sqrt(2) has a decimal representation. )

[abu.ku...@gmail.com]

that is base_one accounting, of course, or
preinventing the zed. now,
one could reconstruct my definition of summorial,
in terms of factorial, from 3! :=: 3?

[abu.ku...@gmail.com]

of course, 1.4 is sufficient for most apps, and
that is seven fifths;
1.414 is 707/500, which only yields interest
upon reciprocation, 500/707;
31/10 is pi, and
32/100 is one over pi, but in only one base

[bassam king karzeddin]

On Friday, December 2, 2016 at 12:55:34 PM UTC+3, 7777777 wrote:

> torstai 17. marraskuuta 2016 15.50.08 UTC+2 bassam king karzeddin kirjoitti:
> > Even this was explained quite many times but never mind to prove it again and again:
> >
>
>

> Sqrt(2) = 1.41421356237... only if S = Lim S
>
>
> but as we have seen over and over again, the cranks deny the validity of the statement S = Lim S, although at the same time they are using it.

Get out of all those ill definitions as (limits, infinity, famous cuts, convergence, intermediate theorem, Newton's approximations,..., etc)

All those definitions are impossible to substitute the exact meaning of equality, with it is ignored notation "="

Where did I use the limit Lier?, or where did even I equates them absolutely?

I proved clearly (and beyond any doubt) that:

Sqrt(2) =/= 1.41421356237...

Why the mathematicians realize the non solvability of some Diophantine equations, then later deny them completely?

This Diophantine eqn. does not have any solution in the whole non zero integers
(2n^2 = m^2), it is the impossibility of doubling the square problem (in integers
And was proved rigorously by the Greek thousands of years back, no need to repeat this well known so easy proof

Then what modern maths does, is finding a near solution that actually does not exist, but me be near solution for practical problem as for carpentry works

they simply divided both side of the eqn by (m^2) and pretended that

(m/n)^2 = 2, whereas actually it is (m/n)^2 =/= 2

then they took the square root of both sides to and pretending illegal equality just by showing long enough digits of accuracy (trying and convincing the so innocent (as you) that was a perfect solution)

And the infinity concept was ideal to make a complete brain wash for you for this purpose, then they got addicted to the ill concept where they had fill the universe with their infinitely many fake numbers, especially the sheep never understands the slaughtering purpose of their silly existence)

sqrt(2) = m/n, whereas it is indeed (asrt(2) =/= m/n)

Then they started approximation (say in decimal 10base number system) by letting (n = 10^k), and (m) is a positive integer with (k+1) digits and showing you one day "at infinity" they would find it in rational, poor mythematics and silly game beyond any doubt

But the fact must be well exposed by now,had they confessed this only an approximation or magnitude from the beginning, then everything would be gladly accepted, but unfortunately, it was a matter of business for them.

So, can you understand the fiction story of the endless number now?

I guess very few well

Regards
Bassam King Karzeddin
15th, Dec., 2016


On Friday, December 2, 2016 at 12:55:34 PM UTC+3, 7777777 wrote:

> torstai 17. marraskuuta 2016 15.50.08 UTC+2 bassam king karzeddin kirjoitti:
> > Even this was explained quite many times but never mind to prove it again and again:
> >
>
>

> Sqrt(2) = 1.41421356237... only if S = Lim S
>
>
> but as we have seen over and over again, the cranks deny the validity of the statement S = Lim S, although at the same time they are using it.

[burs...@gmail.com]

> So, can you understand the fiction story of the endless number now?

Yes, why, whats prollololoblem?

[bassam king karzeddin]

On Thursday, December 15, 2016 at 4:17:58 PM UTC+3, burs...@gmail.com wrote:
> > So, can you understand the fiction story of the endless number now?
>
> Yes, why, whats prollololoblem?

Great that you started understanding fiction stories in mathematics now,(I HOPE), hurry up to Wikipedia, or your secretive research, just before somebody else make it officially before you, make a decent discovery, it is too good chance for your alikes, is not it?

We need urgently our ideas to be stolen by the professionals, at least they would certainly upraise the truth

Bursegan, there are many other fiction stories that are more thrilling, just wait

But I do not understand why the cat had eaten your tongue, (prollololoblem)

Also educate that troll, still (Virgin) about the meaning of "nonexistence" of a solution, he might accept it from you

Tell him also, that no protection would be available from the well established definitions in current mythematics


Regards
Bassam King Karzeddin

[bassam king karzeddin]

On Friday, December 2, 2016 at 12:55:34 PM UTC+3, 7777777 wrote:
> torstai 17. marraskuuta 2016 15.50.08 UTC+2 bassam king karzeddin kirjoitti:
> > Even this was explained quite many times but never mind to prove it again and again:
> >
>

7777777 wrote:
>
> Sqrt(2) = 1.41421356237... only if S = Lim S
>
>
> but as we have seen over and over again, the cranks deny the validity of the statement S = Lim S, although at the same time they are using it.

Bassam King Karzeddin wrote:

Get out of all those ill definitions as (limits, infinity, famous cuts, convergence, intermediate theorem, Newton's approximations,..., etc)

All those definitions are impossible to substitute the exact meaning of equality, with it is ignored notation "="

Where did I use the limit Lier?, or where did even I equates them absolutely?

I proved clearly (and beyond any doubt) that:

Sqrt(2) =/= 1.41421356237...

Why the mathematicians realize the non solvability of some Diophantine equations, then later deny them completely?

This Diophantine equation does not have any solution in the whole non zero integers
(2n^2 = m^2), it is the impossibility of doubling the square problem (in integers)

And was proved rigorously by the Greek thousands of years back, no need to repeat this well known so easy proof

Then what modern maths does, is finding a near solution that actually does not exist, but may be near solution for practical problem as for carpentry works

They simply divided both side of the eqn. by (n^2) and pretended that

(m/n)^2 = 2, whereas actually it is (m/n)^2 =/= 2

then they took the square root of both sides and pretending illegal equality just by showing long enough digits of accuracy (trying and convincing the so innocent (as you) that was a perfect solution)

And the infinity concept was ideal to make a complete brain wash for you for this purpose, then they got addicted to that ill concept where they had fill the universe with their infinitely many fake and non existing numbers, especially the sheep never understand the slaughtering purpose of their silly existence)

sqrt(2) = m/n, whereas it is indeed (asrt(2) =/= m/n)

Then they started approximation (say in decimal 10base number system) by letting (n = 10^k), where (k) is positive integer and (m) is a positive integer with (k+1) digits and showing you that one day "at infinity" they would find it in rational, poor mythematics and silly game beyond any doubt

So, they require (m and k) to be integers with infinite sequence of digits, in order to get it exactly, where this obviously impossible and also not permissible in the holy grail principles of mathematics, hence "non existing"

But the fact must be well exposed by now, had there been a clear confession that was only an approximation or magnitude from the beginning, then everything would be gladly accepted, but unfortunately, it was a matter of business for them, or may be innocent stupidity

So, can you understand the fiction story of the endless number now?

[burs...@gmail.com]

> So, can you understand the fiction story of the endless number now?

Yes again, can you enlighten us what the prolololoblem is?

[bassam king karzeddin]

On Thursday, December 15, 2016 at 7:42:32 PM UTC+3, burs...@gmail.com wrote:
> > So, can you understand the fiction story of the endless number now?
>

Bursegan wrote:
> Yes again, can you enlighten us what the prolololoblem is?

Actually you discovered that yourself, and said it in other reply

"It is (mathematics) for entertainment" right?

And nothing actually had been added after Pythagoras (real constructible numbers only) to the concept of real numbers except fiction stories that is too good for entertainment

And this is a fact, then it is necessary that the world Governments must investigate the issue and take actions, at least they would save so many billions from being brainwashed and many billions of currencies to the world economy

They (world Governments) also can manage those many brain masters and rescue them to make something more useful to the societies they belong to, instead of entertaining and spoiling the population minds and other sciences especially physics, and wasting the human resources unnecessarily

Regards
Bassam King Karzeddin

[Harry Stoteles]

> They (world Governments)

You don't understand, do you see a
government somewhere that entertains me?

It is you!

[abu.ku...@gmail.com]

that is to say that one over pi is eight twenty-fifths, or
2^3/5^2, the volumetric double over the areal mid-triple-prime,
which is g00d to go in base_200

[Virgil]

In article <78de3ba6-ecd0-46dd...@googlegroups.com>,

bassam king karzeddin <sophy...@gmail.com> wrote:

> I proved clearly (and beyond any doubt) that:
>
> Sqrt(2) =/= 1.41421356237..

No you haven't!

To do so, you must name a positive epsilon provably less than
|Sqrt(2) - 1.41421356237..|
which you have not done and cannot do!
--
Virgil
"Mit der Dummheit kampfen Gotter selbst vergebens." (Schiller)

[Virgil]

In article <bb9b2dbd-b8bd-4fa8...@googlegroups.com>,

bassam king karzeddin <sophy...@gmail.com> wrote:

> Tell him also, that no protection would be available from the well
> established definitions in current mythematics
>
>
> Regards
> Bassam King Karzeddin

Established mathematics, with its current definitions, is still
sufficient to protect us from the delusions of Badass Queen Karzeddin.

[Virgil]

I> Badass Queen Karzeddin wrote:

> I proved clearly (and beyond any doubt) that:
>
> Sqrt(2) =/= 1.41421356237...

Until BQK has found a positive epsilon such that
|Sqrt(2)- 1.41421356237..| > epsilon
or
|2- (1.41421356237..)^2| > epsilon
she has done no such thing!

[Vinicius Claudino Ferraz]

somebody thinks the straight-line is ℚ.
so 2^0.5 is a hole.
But ℝ - ℚ has more holes than ℚ-points.
ℵ_1 holes
ℵ_0 points

What's the cardinality of JG's holes?

[Virgil]

In article <d11a108f-7d60-4e97...@googlegroups.com>,

bassam king karzeddin <sophy...@gmail.com> wrote:

> And nothing actually had been added after Pythagoras (real
> constructible numbers only) to the concept of real numbers except
> fiction stories that is too good for entertainment

Stories (plural) should be "ARE", not "IS"!

You should learn proper English before trying to teach math to your
betters!

[konyberg]

torsdag 8. desember 2016 00.10.30 UTC+1 skrev John Gabriel følgende:

> > I can give you the number pi
> > Isn't that good enough?
>
> Liar. You can't give me the number pi. The symbol is not the number.
>
> > If you want me to give a series that give the decimal expansion of pi, that guarantees that f.inst. sqrt(2) wont pop up, I cannot do that, but I can prove that it wont happen!
>
> Irrelevant. I can give you innumerably many numbers that have exactly the first n digits as pi, no matter how many n digits you determine.
>
> So what is your counterexample? Chuckle.
>
> >
> > KON

We have a lot of symbols. F.inst. 0. 1. 2. and so on. And even A, B, C and so on.
These are as you hopefully knows symbols?
Pi is a symbol. What is the difference?
And if you have a series for pi, give me one that also contains f.inst. sqrt(2)! You cannot.

The evidence is on you, not me!

KON