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John? Why do you keep calling yourself a genius?

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mitchr...@gmail.com

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Apr 15, 2021, 2:33:11 PM4/15/21
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Isn't that a little pathetic?

Mitchell Raemsch

Michael Moroney

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Apr 15, 2021, 3:50:37 PM4/15/21
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On 4/15/2021 2:32 PM, mitchr...@gmail.com wrote:
> Isn't that a little pathetic?

Yes, it is pathetic. Just as pathetic as you insisting that 0.999... is
not equal to 1, there are no negative numbers etc.

It's called an idee fixe.

mitchr...@gmail.com

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Apr 15, 2021, 5:39:08 PM4/15/21
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On Thursday, April 15, 2021 at 12:50:37 PM UTC-7, Michael Moroney wrote:
> On 4/15/2021 2:32 PM, mitchr...@gmail.com wrote:
> > Isn't that a little pathetic?
> Yes, it is pathetic. Just as pathetic as you insisting that 0.999... is
> not equal to 1, there are no negative numbers etc.

Then prove me wrong.
.999 repeating is different by the unlimited small you moron...
Negatives are only one thing... in math they are only subtractions
and at the no quantity math they reach their limit.

Mitchell Raemsch

Michael Moroney

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Apr 15, 2021, 5:46:17 PM4/15/21
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On 4/15/2021 5:39 PM, mitchr...@gmail.com wrote:
> On Thursday, April 15, 2021 at 12:50:37 PM UTC-7, Michael Moroney wrote:
>> On 4/15/2021 2:32 PM, mitchr...@gmail.com wrote:
>>> Isn't that a little pathetic?
>> Yes, it is pathetic. Just as pathetic as you insisting that 0.999... is
>> not equal to 1, there are no negative numbers etc.
>
> Then prove me wrong.

I already did. As did several others.

You ignored these proofs and just repeated your false babbling nonsense,
always without proof, just as you do yet again below:

Eram semper recta

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Apr 15, 2021, 6:59:30 PM4/15/21
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On Thursday, 15 April 2021 at 17:46:17 UTC-4, Michael Moroney wrote:
> On 4/15/2021 5:39 PM, mitchr...@gmail.com wrote:
> > On Thursday, April 15, 2021 at 12:50:37 PM UTC-7, Michael Moroney wrote:
> >> On 4/15/2021 2:32 PM, mitchr...@gmail.com wrote:
> >>> Isn't that a little pathetic?
> >> Yes, it is pathetic. Just as pathetic as you insisting that 0.999... is
> >> not equal to 1, there are no negative numbers etc.
> >
> > Then prove me wrong.
> I already did. As did several others.

You and others did no such thing MORONey.
0.999... is a series and 1 is a well-formed number. Placing any of <,>,= is not appropriate.

There is no proof that 0.999... and 1 are the same thing, unless you assume beforehand that 0.999... is 1. This mental decay was introduced by the crank Leonhard Euler with his decree S = Lim S.

https://drive.google.com/file/d/0B-mOEooW03iLdmRRbFByd0M0QTA

>
> You ignored these proofs and just repeated your false babbling nonsense,

He ignored your bullshit because he is uneducated, but in many ways he is better than you who claims to be educated and knows absolutely shit about mathematics.

Michael Moroney

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Apr 15, 2021, 8:04:47 PM4/15/21
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On 4/15/2021 6:59 PM, Eram semper recta wrote:
[]

Go away, Rectum Breath. You aren't smart enough to participate in this
discussion.

mitchr...@gmail.com

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Apr 15, 2021, 10:55:55 PM4/15/21
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On Thursday, April 15, 2021 at 2:46:17 PM UTC-7, Michael Moroney wrote:
> On 4/15/2021 5:39 PM, mitchr...@gmail.com wrote:
> > On Thursday, April 15, 2021 at 12:50:37 PM UTC-7, Michael Moroney wrote:
> >> On 4/15/2021 2:32 PM, mitchr...@gmail.com wrote:
> >>> Isn't that a little pathetic?
> >> Yes, it is pathetic. Just as pathetic as you insisting that 0.999... is
> >> not equal to 1, there are no negative numbers etc.
> >
> > Then prove me wrong.
> I already did. As did several others.

That is just your excuse.
Show me where I am wrong...

Mitchell Raemsch

mitchr...@gmail.com

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Apr 15, 2021, 10:59:11 PM4/15/21
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On Thursday, April 15, 2021 at 3:59:30 PM UTC-7, Eram semper recta wrote:
> On Thursday, 15 April 2021 at 17:46:17 UTC-4, Michael Moroney wrote:
> > On 4/15/2021 5:39 PM, mitchr...@gmail.com wrote:
> > > On Thursday, April 15, 2021 at 12:50:37 PM UTC-7, Michael Moroney wrote:
> > >> On 4/15/2021 2:32 PM, mitchr...@gmail.com wrote:
> > >>> Isn't that a little pathetic?
> > >> Yes, it is pathetic. Just as pathetic as you insisting that 0.999... is
> > >> not equal to 1, there are no negative numbers etc.
> > >
> > > Then prove me wrong.
> > I already did. As did several others.
> You and others did no such thing MORONey.
> 0.999... is a series and 1 is a well-formed number. Placing any of <,>,= is not appropriate.
>
> There is no proof that 0.999... and 1 are the same thing, unless you assume beforehand that 0.999... is 1. This mental decay was introduced by the crank Leonhard Euler with his decree S = Lim S.
>
> https://drive.google.com/file/d/0B-mOEooW03iLdmRRbFByd0M0QTA
> >
> > You ignored these proofs and just repeated your false babbling nonsense,
> He ignored your bullshit because he is uneducated, but in many ways he is better than you who claims to be educated and knows absolutely shit about mathematics.

I can talk for myself John Gabriel...
There is more than one kind of equality.
Math know the absolute zero difference equality.
But there is another where the infinitely small difference
behave the same...

Mitchell Raemsch

Michael Moroney

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Apr 15, 2021, 11:38:10 PM4/15/21
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zelos...@gmail.com

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Apr 16, 2021, 1:19:26 AM4/16/21
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torsdag 15 april 2021 kl. 20:33:11 UTC+2 skrev mitchr...@gmail.com:
> Isn't that a little pathetic?
>
> Mitchell Raemsch

Because like you, he is a crank that doesn't understand mathematics

zelos...@gmail.com

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Apr 16, 2021, 1:20:40 AM4/16/21
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> Then prove me wrong.

I haave a thousand times.

>.999 repeating is different by the unlimited small you moron..

This is false cause real numbers are archimedian.

>Negatives are only one thing... in math they are only subtractions

False statement by definition.

Again, all wrong/false.

zelos...@gmail.com

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Apr 16, 2021, 1:21:23 AM4/16/21
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I have several times, REAL NUMBERS ARE ARCHIMEDIAN! So you cannot say it differs by an infinitesimal because THERE ARE NO INFINITESIMALS IN REAL NUMBERS!

WM

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Apr 16, 2021, 6:59:59 AM4/16/21
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zelos...@gmail.com schrieb am Freitag, 16. April 2021 um 07:20:40 UTC+2:
> > Then prove me wrong.
>
> I haave a thousand times.
> >.999 repeating is different by the unlimited small you moron..
> This is false cause real numbers are archimedian.

0.999...is not anumber but an infinite sequence/series.

0.999... = (...(((0.9)9)9)...) but nothing else.Therefore 0.999... =/= 1.

For a detailled explanation see: "Sequences and Limits", Advances in Pure Mathematics 5, 2015, pp. 59 - 61
http://www.scirp.org/journal/Articles.aspx?searchCode=Mueckenheim&searchField=All&page=1&SKID=57296550

Regards, WM

Eram semper recta

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Apr 16, 2021, 7:04:40 AM4/16/21
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On Friday, 16 April 2021 at 01:21:23 UTC-4, zelos...@gmail.com wrote:
> fredag 16 april 2021 kl. 04:55:55 UTC+2 skrev mitchr...@gmail.com:
> > On Thursday, April 15, 2021 at 2:46:17 PM UTC-7, Michael Moroney wrote:
> > > On 4/15/2021 5:39 PM, mitchr...@gmail.com wrote:
> > > > On Thursday, April 15, 2021 at 12:50:37 PM UTC-7, Michael Moroney wrote:
> > > >> On 4/15/2021 2:32 PM, mitchr...@gmail.com wrote:
> > > >>> Isn't that a little pathetic?
> > > >> Yes, it is pathetic. Just as pathetic as you insisting that 0.999... is
> > > >> not equal to 1, there are no negative numbers etc.
> > > >
> > > > Then prove me wrong.
> > > I already did. As did several others.
> > That is just your excuse.
> > Show me where I am wrong...
> >
> > Mitchell Raemsch
> > .999 repeating is different by the unlimited small you moron...
> > Negatives are only one thing... in math they are only subtractions
> > and at the no quantity math they reach their limit.
> I have several times, REAL NUMBERS ARE ARCHIMEDIAN!

LMAO. That phrase has been repeated by morons for many decades, but it's untrue. Archimedes did not acknowledge any other numbers besides the RATIONAL NUMBERS. There are ONLY rational numbers in Classical Greece.

Another widely misunderstood mainstream doctrine concerns the Archimedean Property which correctly stated says:

Given any magnitude x (whether commensurable or incommensurable), there exist commensurable magnitudes (ie RATIONAL NUMBERS) m and n such that m < x < n.

> So you cannot say it differs by an infinitesimal because THERE ARE NO INFINITESIMALS IN REAL NUMBERS!

Fef. There is no such thing as an infinitesimal. LMAO.

Eram semper recta

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Apr 16, 2021, 7:05:41 AM4/16/21
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On Friday, 16 April 2021 at 06:59:59 UTC-4, WM wrote:
> zelos...@gmail.com schrieb am Freitag, 16. April 2021 um 07:20:40 UTC+2:
> > > Then prove me wrong.
> >
> > I haave a thousand times.
> > >.999 repeating is different by the unlimited small you moron..
> > This is false cause real numbers are archimedian.
> 0.999...is not anumber but an infinite sequence/series.

Of course.

FromTheRafters

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Apr 16, 2021, 8:15:24 AM4/16/21
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WM has brought this to us :
> zelos...@gmail.com schrieb am Freitag, 16. April 2021 um 07:20:40 UTC+2:
>>> Then prove me wrong.
>>
>> I haave a thousand times.
>>> .999 repeating is different by the unlimited small you moron..
>> This is false cause real numbers are archimedian.
>
> 0.999...is not anumber but an infinite sequence/series.

Because it is convergent it can be summed to one by using the limit of
the sequence of its partial sums. The symbol *represents* the thing.

WM

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Apr 16, 2021, 11:20:04 AM4/16/21
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FromTheRafters schrieb am Freitag, 16. April 2021 um 14:15:24 UTC+2:
> WM has brought this to us :

> > 0.999...is not anumber but an infinite sequence/series.
> Because it is convergent it can be summed to one by using the limit of
> the sequence of its partial sums. The symbol *represents* the thing.

That is known by advanced mathematicians only. As you can see here around most would-be mathematicians don't know it. And if Cantor's finished infinity exists, then there is a difference between all natnumbers, i.e., all terms of the sequence, and its limit omega. Further beginners usually don't learn these things. Therefore I plead to emphasize it always.

Regards, WM

Sergio

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Apr 16, 2021, 5:41:30 PM4/16/21
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On 4/16/2021 5:59 AM, WM wrote:
> zelos...@gmail.com schrieb am Freitag, 16. April 2021 um 07:20:40 UTC+2:
>>> Then prove me wrong.
>>
>> I haave a thousand times.
>>> .999 repeating is different by the unlimited small you moron..
>> This is false cause real numbers are archimedian.
>
> 0.999...is not anumber but an infinite sequence/series.

no.

If so, then 0.991... is not a number.

in fact all numbers with decimial representations and expansions would
not be numbers.

contradiction. Fail

<snip floundering>

Sergio

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Apr 16, 2021, 5:44:01 PM4/16/21
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On 4/15/2021 9:59 PM, mitchr...@gmail.com wrote:
> On Thursday, April 15, 2021 at 3:59:30 PM UTC-7, Eram semper recta wrote:
>> On Thursday, 15 April 2021 at 17:46:17 UTC-4, Michael Moroney wrote:
>>> On 4/15/2021 5:39 PM, mitchr...@gmail.com wrote:
>>>> On Thursday, April 15, 2021 at 12:50:37 PM UTC-7, Michael Moroney wrote:
>>>>> On 4/15/2021 2:32 PM, mitchr...@gmail.com wrote:
>>>>>> Isn't that a little pathetic?
>>>>> Yes, it is pathetic. Just as pathetic as you insisting that 0.999... is
>>>>> not equal to 1, there are no negative numbers etc.
>>>>
>>>> Then prove me wrong.
>>> I already did. As did several others.
>> You and others did no such thing MORONey.
>> 0.999... is a series and 1 is a well-formed number. Placing any of <,>,= is not appropriate.
>>
>> There is no proof that 0.999... and 1 are the same thing, unless you assume beforehand that 0.999... is 1. This mental decay was introduced by the crank Leonhard Euler with his decree S = Lim S.
>>

do not click on link, bad link

>> https://porn.drive.google.com/file/d/0B-mOEopornoW03iLdmRRbFByd0M0QTA

Eram semper recta

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Apr 16, 2021, 7:26:42 PM4/16/21
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On Friday, 16 April 2021 at 17:44:01 UTC-4, Sergio wrote:

Sci.math has many conmen and scammers pretending to be authorities in mathematics.

> do not click on link, bad link

The above is taken out of Prof. Gilbert Strang's playbook before I caught the bastard some years ago. Strang used to comment using the alias Port563. Of course there is no such link, but this is indicative of the low-IQ trolls who comment here.

>
> >> https://porn.drive.google.com/file/d/0B-mOEopornoW03iLdmRRbFByd0M0QTA

Tsk, tsk. You hate that article so much eh? LMAO. I wonder why.... Chuckle.

When the cranks in mainstream academia cannot refute you, they'll try anything to make you look bad.

Euler's S = Lim S explained:

https://drive.google.com/file/d/0B-mOEooW03iLdmRRbFByd0M0QTA

Chris M. Thomasson

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Apr 16, 2021, 8:09:20 PM4/16/21
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There are two ways to look at it. .999... is equal to 1 when you take
limits into account. However, if you use a step-by-step process, then it
will never equal 1. It will keep getting closer and closer to it, but
never equal it.

Here is a simple step-by-step process using recursion.

The main recursive formula:

i[0] = 0
i[n + 1] = i[n] + 9 / 10^(n + 1)


Here is an expansion of the recursion for several iterations:

i[0] = 0
i[1] = 0 + 9 / 10^1 = .9
i[2] = .9 + 9 / 10^2 = .99
i[3] = .99 + 9 / 10^3 = .999
i[4] = .999 + 9 / 10^4 = .9999
i[5] = .9999 + 9 / 10^5 = .99999
...

The limit is 1 when taken to infinity. However, wrt the step-by-step
process it will always be less than 1.

Mostowski Collapse

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Apr 16, 2021, 8:37:17 PM4/16/21
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"The limit is 1 when taken to infinity.", nope.
You cannot take an iteration to infinity.

All you can observe is that 1-1/10^n is
always below 1, and there is nothing inbetween

so 1 is the L.U.B., similar reasoning for limit.

Chris M. Thomasson

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Apr 16, 2021, 8:49:27 PM4/16/21
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On 4/16/2021 5:37 PM, Mostowski Collapse wrote:
> "The limit is 1 when taken to infinity.", nope.
> You cannot take an iteration to infinity.
>
> All you can observe is that 1-1/10^n is
> always below 1, and there is nothing inbetween
>
> so 1 is the L.U.B., similar reasoning for limit.

For some reason I was thinking about the limit being 1 when the
recursion is taken to infinity. Sorry about that.

FromTheRafters

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Apr 17, 2021, 3:42:22 AM4/17/21
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Chris M. Thomasson formulated on Friday :
> On 4/15/2021 2:39 PM, mitchr...@gmail.com wrote:
>> On Thursday, April 15, 2021 at 12:50:37 PM UTC-7, Michael Moroney wrote:
>>> On 4/15/2021 2:32 PM, mitchr...@gmail.com wrote:
>>>> Isn't that a little pathetic?
>>> Yes, it is pathetic. Just as pathetic as you insisting that 0.999... is
>>> not equal to 1, there are no negative numbers etc.
>>
>> Then prove me wrong.
>> .999 repeating is different by the unlimited small you moron...
>> Negatives are only one thing... in math they are only subtractions
>> and at the no quantity math they reach their limit.
>
> There are two ways to look at it. .999... is equal to 1

And the other one is wrong. :)

Zero point all nines and one point all zeroes are both representations
of real (rational) numbers which if they were 'different' real
(rational) numbers being represented would necessitate there being
other reals (rational and not) in between them. All reals have at least
one CDE representation yet there is no way for another CDE
representation to exist in between these two supposedly different
numbers' representations. The fact that the limit gives the same
obvious answer lends even more creedence to the limit idea for less
obvious Cauchy sequences.

Timothy Golden

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Apr 17, 2021, 10:03:43 AM4/17/21
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It is a shame that mathematicians have divorced themselves from philosophy.
It is clear that some of mathematics has to do with interpretation.
The words that we all write here are not mathematics.
We each have our own interpretation.
If your words exactly matched those of, say, Euler, or any other great, then you would be accused of plagiarism.
To admit that we each must have our own philosophy; our own interpretation; our own internal representation; would be mature.
Otherwise we would be bound mimics with no further freedom to explore.
That we ought here on this medium to cover the ground more fully by filling out these interpretations is a valid pursuit I believe.
Even in no human ever reads them some AI will one day digest the entirety of USENET and come to understand the human race that much better by it.
Sadly that AI's conclusions on the human race will be rather desolate relative to some of the assumptions that past philosophers have made
such as humans built in God's image, fully conscious beings with free will, the ultimate intelligence...
These assumptions are clearly wrong. We are limited and we are inhibited.
Simply partake of some alcohol and witness the reaction.
We are tamed animals; tamed by our society.
We are programmable humans.
Far more programmable and operable than our machines that we have created.
Sadly the programs that we run are dubious and such programs as
Christianity, Islam, Judaism
are simply shards of what was an exclusive branch to whom all the land and all the women were presumed by the local power known as Abraham who exteded his grasp to foreign lands and destroyed local cultures and imposed a book of law onto all.
That one book is now under the process of accumulation and variation rather many versions of exclusionary principles.
The ambiguity of this situation especially with their insistence on propagation is problematic to the human race.
That communists have formalized atheism into their system of thought (or at least did back in time) would explain quite a lot of the anti-communist and anti-socialist rhetoric here in the U.$.A. where capitalism is eating us alive and we waste more than we can even consume because it is good for the economy.
While we lay waste to the planet one might wonder...
W T F I G O H ?

We can return from blaming nations (though this does appear to be relevant in that the relative performance and behavior of nations to their people and to other nations and to other nations' people; a place where my nation has provably done great wrong) to tribes and witness the source of conflict from a very early time in history before even a word was uttered. Simply consider one bad year when the berry crop was poor in all the hills but for one fertile valley where the water runs clean. As all the tribes arrive there for berries what will we do?

As mathematics forms an escape chute from such human considerations ought we really to further split mathematics from philosophy? From reality?
This is I am afraid where academia has landed the mathematician. It is a lie.

WM

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Apr 17, 2021, 10:11:09 AM4/17/21
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Sergio schrieb am Freitag, 16. April 2021 um 23:41:30 UTC+2:
> On 4/16/2021 5:59 AM, WM wrote:
> > zelos...@gmail.com schrieb am Freitag, 16. April 2021 um 07:20:40 UTC+2:
> >>> Then prove me wrong.
> >>
> >> I haave a thousand times.
> >>> .999 repeating is different by the unlimited small you moron..
> >> This is false cause real numbers are archimedian.
> >
> > 0.999...is not anumber but an infinite sequence/series.
> no.
>
> If so, then 0.991... is not a number.

What number should it be? Of course it is no a number.
>
> in fact all numbers with decimial representations and expansions would
> not be numbers.

Wrong. Every decimal representation is an infinite sequence, but those ending with only zeros have reached their limit because they are not strictly increasing. Therefore thieir limit can directly be read. All infinite decimal representations are sequences, but common use assumes that the the limit is meant. That is not reprehensible. Unfortunately, caused by this habit many zealous mathematicians think the limit is not required but 0.999... = 1. That is wrong.

Regards, WM


WM

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Apr 17, 2021, 10:19:03 AM4/17/21
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Chris M. Thomasson schrieb am Samstag, 17. April 2021 um 02:09:20 UTC+2:

> There are two ways to look at it. .999... is equal to 1 when you take
> limits into account. However, if you use a step-by-step process, then it
> will never equal 1. It will keep getting closer and closer to it, but
> never equal it.

Very good. Once you have understood this, you shoudl be able to understand the consequence.

An infinite sequence without defining formula will never represent a number, because the limit cannot exist: Upon every digit that you can read there are infinitely many further digits following. They are unknown and remain unknown. That's why the folklore Cantor-list does neither contain real numbers nor defines a real diagonal number. It is not a proof of transcendental numbers but a proof of the devastating result caused by confusing 0.999... and 1.

Regards, WM

WM

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Apr 17, 2021, 10:25:29 AM4/17/21
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Mostowski Collapse schrieb am Samstag, 17. April 2021 um 02:37:17 UTC+2:
> "The limit is 1 when taken to infinity.", nope.
> You cannot take an iteration to infinity.

Therefore the diagonal of the folklore Cantor-list is not a real number.
>
> All you can observe is that 1-1/10^n is
> always below 1, and there is nothing inbetween

Like the sequence 1/10^n has the GLB 0.
>
> so 1 is the L.U.B., similar reasoning for limit.

And why do so many zealous mathematician believe that the digit sequence is its limit? Why do they try to avoid sequence of digits 9 in Cantor lists? Since 0.0999... is not 0.1000... there is no reason to avoid it!

When Felix Klein made this precaution in 1895 [Felix Klein: "Vorträge über ausgewählte Fragen der Elementargeometrie", Teubner, Leipzig (1895) p. 42] he showed that he did not understand this basic fact.

Regards, WM

WM

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Apr 17, 2021, 10:31:56 AM4/17/21
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FromTheRafters schrieb am Samstag, 17. April 2021 um 09:42:22 UTC+2:
> Chris M. Thomasson formulated on Friday :

> > There are two ways to look at it. .999... is equal to 1
> And the other one is wrong. :)
>
> Zero point all nines and one point all zeroes are both representations
> of real (rational) numbers which if they were 'different' real
> (rational) numbers being represented would necessitate there being
> other reals (rational and not) in between them.

The usual mistaken argument. Try to think:

There is no number between every unit fraction 1/n and zero. Nevertheless no unit fraction is the same number as zero.

> The fact that the limit gives the same
> obvious answer lends even more creedence to the limit idea for less
> obvious Cauchy sequences.

An infinite digit sequence without defining formula has no limit. There are always infinitely many unknown digits, because nobody bothered to define them, - unknown even to Gods. Not existing because no digits without infinitely many successors are existing at all.

Regards, WM

FromTheRafters

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Apr 17, 2021, 10:43:38 AM4/17/21
to
Sergio submitted this idea :
> On 4/16/2021 5:59 AM, WM wrote:
>> zelos...@gmail.com schrieb am Freitag, 16. April 2021 um 07:20:40 UTC+2:
>>>> Then prove me wrong.
>>>
>>> I haave a thousand times.
>>>> .999 repeating is different by the unlimited small you moron..
>>> This is false cause real numbers are archimedian.
>>
>> 0.999...is not anumber but an infinite sequence/series.
>
> no.
>
> If so, then 0.991... is not a number.

But 0.99(1)... or 0.9(91)... or 0.(991)... would all be members of Q as
expressed in CDEs.

WM

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Apr 17, 2021, 10:46:33 AM4/17/21
to
No. Only the limits are rational numbers.

Regards, WM

Timothy Golden

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Apr 17, 2021, 10:52:08 AM4/17/21
to
I think the usage of the ellipsis here really needs to be explored more seriously. There is what is know as the halting problem. In this way the ellipsis cannot end and so the page fills out with information ad nauseum. Consider for instance raising the problem further by the discussion of my new ultimate set of axioms that go beyond mathematics, philosophy, and physics, and yield a whole new generation of superiority complex; possibly even another level of academic lable beyond and above the PhD!

Axiom 1: Everything I say is True...

Doesn't this say it all? I will happily instantiate some more usages for you if this one is not convincing enough. Come now, let's have at the ellipsis here for those who bow out on this front are weaklings who halt too easily.

FromTheRafters

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Apr 17, 2021, 10:54:18 AM4/17/21
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WM formulated on Saturday :
> FromTheRafters schrieb am Samstag, 17. April 2021 um 09:42:22 UTC+2:
>> Chris M. Thomasson formulated on Friday :
>
>>> There are two ways to look at it. .999... is equal to 1
>> And the other one is wrong. :)
>>
>> Zero point all nines and one point all zeroes are both representations
>> of real (rational) numbers which if they were 'different' real
>> (rational) numbers being represented would necessitate there being
>> other reals (rational and not) in between them.
>
> The usual mistaken argument. Try to think:
>
> There is no number between every unit fraction 1/n and zero. Nevertheless no
> unit fraction is the same number as zero.

Sure, with discrete n you have no assurance that there will be
convergence of strictly monotonic decending sequences. Get REAL.

WM

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Apr 17, 2021, 10:59:02 AM4/17/21
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FromTheRafters schrieb am Samstag, 17. April 2021 um 16:54:18 UTC+2:
> WM formulated on Saturday :

> > There is no number between every unit fraction 1/n and zero. Nevertheless no
> > unit fraction is the same number as zero.
> Sure, with discrete n you have no assurance that there will be
> convergence of strictly monotonic decending sequences.

The sequence is (1/n). It is of same character as the sequence 0.999... . All terms are discrete.

Regards, WM

FromTheRafters

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Apr 17, 2021, 11:09:59 AM4/17/21
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Timothy Golden explained :
The usual interpretation I have is "continues on in like manner" and
such manner does not need to be obvious, but does need to exist. Take
Liouville numbers for instance, it might not be obvious from the CDE
that there is a 'pattern' to follow -- but there is.

Sergio's contribution offered no hint as to pattern, but I offered a
few possibilities of repeating sequences.

Sergio

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Apr 17, 2021, 1:20:32 PM4/17/21
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On 4/17/2021 9:11 AM, WM wrote:
> Sergio schrieb am Freitag, 16. April 2021 um 23:41:30 UTC+2:
>> On 4/16/2021 5:59 AM, WM wrote:
>>> zelos...@gmail.com schrieb am Freitag, 16. April 2021 um 07:20:40 UTC+2:
>>>>> Then prove me wrong.
>>>>
>>>> I haave a thousand times.
>>>>> .999 repeating is different by the unlimited small you moron..
>>>> This is false cause real numbers are archimedian.
>>>
>>> 0.999...is not anumber but an infinite sequence/series.
>> no.
>>
>> If so, then 0.991... is not a number.
>
> What number should it be? Of course it is no a number.

I see you still fail at understanding what the three little dots mean in
math, ...

>>
>> in fact all numbers with decimial representations and expansions would
>> not be numbers.
>
> Wrong. Every decimal representation is an infinite sequence, but those ending with only zeros have reached their limit because they are not strictly increasing. Therefore thieir limit can directly be read.

wrong.

You cannot read it, because it has not been generated,
and you do not know if it will remain all zeros,
and you do not know what the limit will be,
and you cannot read the limit.



> All infinite decimal representations are sequences,

wrong, they are summations.

> but common use assumes that the the limit is meant.

common use Ant

> That is not reprehensible. Unfortunately, caused by this habit many zealous mathematicians think the limit is not required but 0.999... = 1. That is wrong.

wrong.

the values on both sides are the same

0.999... = 1



google ...



>
> Regards, WM
>
>

mitchr...@gmail.com

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Apr 17, 2021, 1:23:37 PM4/17/21
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Roy Masters? You claim you can beat all genius...
Don't resent me for that. God creates gravity
gravity does not create the universe you moron.

Mitchell Raemsch

Timothy Golden

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Apr 18, 2021, 9:25:57 AM4/18/21
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It is only a slightly more ambiguous usage than the standard usage.
You are portraying a representation of a representation when you use the ellipsis.
In the case of a converging sequence you have raised the strength a bit since the tail end peters off.
When induction wipes out the ellipsis then all is well.
When the ellipsis remains there is still something missing.
That is why we use the ellipsis.
It is not a clean representation sir.
It always means that information is not present.

A compiler will have to be very smart when I write:

int DeriveBlackHole()
{
...
}

It is exactly these other potential uses of the ellipsis that will bring it to its knees.
It is a tender trick that when used wisely goes away.
I accept that
0.99999... = 1
but are we going to accept that the difference is
0.000...1 ?
Will we have to engage a digit analysis in n where n goes to infinity to settle?
With just a bit more freedom can we write
0.000...123123... ?
Why is the one valid and the other invalid?
You see we can play games with the ellipsis.
To what degree when we write:
2.0
do we really mean
2.000000... ?
The real analyst must destroy the gaps.
What we see is varying interpretations of the usage and when those variances fail to compile then we have a problem. Already we have a halting problem for when a compiler encounters the ellipsis that thread will live on until some other condition halts it. for instance a RAM limitation. Poor Cantor ran out of paper perhaps when he expanded it. That halted him. Maybe not. Maybe he created the first global paper shortage.

Come on: we all have to admit the weakness of the ellipsis. To claim its perfection is never going to work. Wasn't it one of you who were claiming that the set intersection happens automatically? Again a halting problem, and you choose to look the other way while you slide your hands behind your back to preserve the status quo.

Things which have the sort of perseverance that the ellipsis is claiming are structurally rather different. Axioms are never supposed to go away. They go on and on holding up so should it be that every axiom ends in the ellipsis? To achieve a GhD which is far higher than the PhD one must adopt:
Axiom 1. I am always right...
and then you will be all set for the rest of your life. You'll be walking the easy street, sir.

FromTheRafters

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Apr 18, 2021, 9:31:29 AM4/18/21
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Why should we when it is clear that equality means the difference is
zero?

Eram semper recta

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Apr 18, 2021, 9:47:41 AM4/18/21
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Nothing is "clear" and the use of the word clear an instant red flag.

The "equality" is a <<decree>>. You cannot prove anything about 0.999... being equal to 1 because they are different objects. Equality only holds when objects are identical. The false belief that 0.999... and 1 are equal originated with the mighty crank Euler who claimed S = Lim S.

https://drive.google.com/file/d/12oUJAfIMFMcXFb8DvgsYxuPfdaB99XYH

A primary school student can understand these things, but you first need a PhD in mythmatics before you can say absurd things like 1/3 = 0.3333... and 1 = 0.999....

FromTheRafters

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Apr 18, 2021, 9:48:53 AM4/18/21
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Timothy Golden brought next idea :

> When the ellipsis remains there is still something missing.
> That is why we use the ellipsis.
> It is not a clean representation sir.

http://www.solving-math-problems.com/ellipsis.html#Ellipsis

Something is missing and/or a pattern continues. Sergio's contribution
was ambiguous and didn't represent a number.

Timothy Golden

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Apr 18, 2021, 10:33:59 AM4/18/21
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The format of that link is not great but it does eventually introduce vertical, horizontal, and diagonal ellipses.
Further it introduced a stronger form as with the less controversial:
a, b, c, d, ..., z .
where clearly the alphabet characters of the English language are implied. Certainly this usage might compile and it is the stongest usage of the bunch.
So good on you Rafters for finding a version of the ellipsis that does not suffer the halting problem. The complete representation is in fact possible in these circumstances and this then establishes the form
0.333...
as a weaker form.

There is still a possible weakness left as to the reader versus the writer and if it is possible to find another pattern in the instance then the reader will have options for interpretation that should cause conflict with the down-stream analysis. This then should disambiguate with that analysis and the reader then return to the other option; presuming they are in fact performing their own computations rather than just reading along; something I am quite guilty of. It is an impossible task to claim that the writer has exhaustively extinguished all possible conflating patterns and so even the strongest usage of the ellipsis could be attacked in this way.

In effect when we refer to standards such as the English alphabet and abbreviate via the ellipsis are we then forming an indirect reference to a prior definition? This is relevant as one could interpret
0, 1, 2, 3, ..., 20
to expand with A, B, 1B, and 1F being elements in the progression in the case of hexadecimal digits. Serious linguists will pick over my presumed implied modern English alphabet as well, whereas Old English is a possibility too. I doubt we would disagree, but another reader could. I had a teacher like that in high school and I did not enjoy him. Hopefully I'm not going that way here. I'd rather stay at covering the ground and your instance does help do that. That notation in mathematics could be weak is problematic. It's not supposed to work like that is it?

Sergio

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Apr 18, 2021, 12:15:25 PM4/18/21
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good link, the Ellipsis Symbol ...


what we are missing here, in this ascii world, is the vinculum Symbol

that line over the last repeating decimals

_
0.9 = 0.9999999999999999999999999...

___
0.991 = .991991991991991991991...


__
.94873882 = 94873882828282828282828282...



https://en.wikipedia.org/wiki/Vinculum_(symbol)


So, I call out JG and WM for Zero Math content, they argue over trivial
number representation

Sergio

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Apr 18, 2021, 12:50:07 PM4/18/21
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On 4/17/2021 9:25 AM, WM wrote:
> Mostowski Collapse schrieb am Samstag, 17. April 2021 um 02:37:17 UTC+2:
>> "The limit is 1 when taken to infinity.", nope.
>> You cannot take an iteration to infinity.
>
> Therefore the diagonal of the folklore Cantor-list is not a real number.
>>
>> All you can observe is that 1-1/10^n is
>> always below 1, and there is nothing inbetween
>
> Like the sequence 1/10^n has the GLB 0.
>>
>> so 1 is the L.U.B., similar reasoning for limit.
>
> And why do so many zealous mathematician believe that the digit sequence is its limit? Why do they try to avoid sequence of digits 9 in Cantor lists? Since 0.0999... is not 0.1000... there is no reason to avoid it!

you squawk, but you cannot show they have different values

_ _
0.0999... = 0.09 = 0.1000... = 0.10


you cannot show there exists any different value between them, therefore
they are equal. Deal with it.


>
> When Felix Klein made this precaution in 1895 [Felix Klein: "Vorträge über ausgewählte Fragen der Elementargeometrie", Teubner, Leipzig (1895) p. 42] he showed that he did not understand this basic fact.

you negate Klein! so why do you reference him ?

>
> Regards, WM
>

FromTheRafters

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Apr 18, 2021, 2:35:38 PM4/18/21
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on 4/18/2021, Sergio supposed :
> On 4/18/2021 8:48 AM, FromTheRafters wrote:
>> Timothy Golden brought next idea :
>>
>>> When the ellipsis remains there is still something missing.
>>> That is why we use the ellipsis.
>>> It is not a clean representation sir.
>>
>> http://www.solving-math-problems.com/ellipsis.html#Ellipsis
>>
>> Something is missing and/or a pattern continues. Sergio's contribution
>> was ambiguous and didn't represent a number.
>
>
> good link, the Ellipsis Symbol ...
>
>
> what we are missing here, in this ascii world, is the vinculum Symbol
>
> that line over the last repeating decimals
>
> _
> 0.9 = 0.9999999999999999999999999...
>
> ___
> 0.991 = .991991991991991991991...

Yes, I believe we discussed this before. The best ASCII replacement for
the vinculum is to couch the repeated pattern in parentheses.
> __
> .94873882 = 94873882828282828282828282...

This works in my reply (compose) view (fixed width) but not in my
reading view.

> https://en.wikipedia.org/wiki/Vinculum_(symbol)

> So, I call out JG and WM for Zero Math content, they argue over trivial
> number representation

It is seemingly a mental block they have. I guess some people just
don't get mathematics, especially the use of abstraction.

Sergio

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Apr 18, 2021, 6:11:59 PM4/18/21
to
no. your sequence of discretes, 0.9, 0.09, 0.009, 0.0009, ... does not
result in 0.999...

you have to *ADD* them all together, then you get 0.999... = 1

you forgot to add. don't you recognize that ?

your statement "There is no number between every unit fraction 1/n and
zero." is malformed. if there is no number between, they are equal.
However you state "every unit fraction 1/n" and zero, which is not the
case at all. 1/3 and zero.

Sergio

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Apr 18, 2021, 6:19:31 PM4/18/21
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On 4/17/2021 9:18 AM, WM wrote:
> Chris M. Thomasson schrieb am Samstag, 17. April 2021 um 02:09:20 UTC+2:
>
>> There are two ways to look at it. .999... is equal to 1 when you take
>> limits into account. However, if you use a step-by-step process, then it
>> will never equal 1. It will keep getting closer and closer to it, but
>> never equal it.
>
> Very good. Once you have understood this, you shoudl be able to understand the consequence.

it is only because you stop at k, n or p. why do you stop ?

>
> An infinite sequence without defining formula will never represent a number, because the limit cannot exist:

wrong. random numbers are generated without formulas, and there are no
limits involved.


> Upon every digit that you can read there are infinitely many further digits following.

you are missing context.

what about pre digits ? before the decimal point?


Chris M. Thomasson

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Apr 18, 2021, 7:56:48 PM4/18/21
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On 4/18/2021 3:19 PM, Sergio wrote:
> On 4/17/2021 9:18 AM, WM wrote:
>> Chris M. Thomasson schrieb am Samstag, 17. April 2021 um 02:09:20 UTC+2:
>>
>>> There are two ways to look at it. .999... is equal to 1 when you take
>>> limits into account. However, if you use a step-by-step process, then it
>>> will never equal 1. It will keep getting closer and closer to it, but
>>> never equal it.
>>
>> Very good. Once you have understood this, you shoudl be able to understand the consequence.
>
> it is only because you stop at k, n or p. why do you stop ?

i[0] = 0
i[n + 1] = i[n] + 9 / 10^(n + 1)

This recursion converges on, or tends to, 1. It has a limit of 1.

For some reason I still want to say when this step-by-step process is
taken as a whole, it is equal to 1. As if infinite steps were executed
in one single shot.

zelos...@gmail.com

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Apr 19, 2021, 12:45:49 AM4/19/21
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>0.999...is not anumber but an infinite sequence/series.

It is a number, we can define it from notation by many methods.

>0.999... = (...(((0.9)9)9)...) but nothing else.Therefore 0.999... =/= 1.

Incorrect, they are equal.

zelos...@gmail.com

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Apr 19, 2021, 12:47:04 AM4/19/21
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>LMAO. That phrase has been repeated by morons for many decades, but it's untrue. Archimedes did not acknowledge any other numbers besides the RATIONAL NUMBERS. There are ONLY rational numbers in Classical Greece.

How is that relevant in any case? We are not talking about archimedes and what he thought. We are talking about the archimedean property.

>Fef. There is no such thing as an infinitesimal. LMAO.

In REAL numbers, in hyperreals there are :)

zelos...@gmail.com

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Apr 19, 2021, 12:49:08 AM4/19/21
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>I think the usage of the ellipsis here really needs to be explored more seriously

Why? WE know exactly what it means.

>There is what is know as the halting problem.

Which is irrelevant here.

Timothy Golden

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Apr 19, 2021, 7:31:20 AM4/19/21
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Let's see now, what is that highest degree that can be achieved called?
Was it Doctorate of Philosophy? In a given subject?
Is this to say that philosophy indeed in not yet dead?
We'll just put your philosophy over in a little box over here, and we'll keep shuffling papers making sure that nobody does a complete duplicate of anyone elses paper. Keep making more boxes and be careful not to blend them too much. We need more room for more papers. Yes, alright, some of the papers fit in between the boxes, but we will eventually pigeon-hole them too. Roll it up and drop it in and you are golden, yeah?

Well; I am already Golden, so there is nothing left to do but bitch and moan here.

I do believe that we can call on the halting problem and apply an interpretation onto the standard usage of the ellipsis particularly in light of the notion of representation, which is key to mathematics. The ellipsis does take us to a representation of a representation, which is a dubious place. Shall we engage further in a representation of a representation of a representation? Will this validate my criticism? Can we go two deep structurally but not three deep? If you had something to say but chose not to say it all and just dropped some periods down is that communication? Informationally speaking we do have a problem when what goes unsaid is unsayable.

Oops: Compiler Error in Z5.C at line 403: Substitution required. Guessing substitution now... five possible solutions exist. Please select one of five and code will be autonotated.

Yeah, and this compiler will wipe your ass for you too.
In review:
https://en.wikipedia.org/wiki/Computability_theory
Oh, nothingburger, eh?

No application whatsoever... Hey Z, why don't you take up politics? Your style is perfect for that genera.

zelos...@gmail.com

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Apr 19, 2021, 8:02:36 AM4/19/21
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>Let's see now, what is that highest degree that can be achieved called?

None of the rest in this was of any relevance.

>Well; I am already Golden, so there is nothing left to do but bitch and moan here.

So far you seem to be quite cranky.

>I do believe that we can call on the halting problem and apply an interpretation onto the standard usage of the ellipsis particularly in light of the notion of representatio

And you'd be wrong, halting problem is a problem of computer science and the nature lf algorithms. Elipses is a notational shorthand and nothing else.

It is notation for thigns in mathematics, it is not an algorithm. Get over it

Sergio

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Apr 19, 2021, 9:54:26 AM4/19/21
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On 4/18/2021 6:56 PM, Chris M. Thomasson wrote:
> On 4/18/2021 3:19 PM, Sergio wrote:
>> On 4/17/2021 9:18 AM, WM wrote:
>>> Chris M. Thomasson schrieb am Samstag, 17. April 2021 um 02:09:20 UTC+2:
>>>
>>>> There are two ways to look at it. .999... is equal to 1 when you take
>>>> limits into account. However, if you use a step-by-step process,
>>>> then it
>>>> will never equal 1. It will keep getting closer and closer to it, but
>>>> never equal it.
>>>
>>> Very good. Once you have understood this, you shoudl be able to
>>> understand the consequence.
>>
>> it is only because you stop at k, n or p.  why do you stop ?
>
> i[0] = 0
> i[n + 1] = i[n] + 9 / 10^(n + 1)
>
> This recursion converges on, or tends to, 1. It has a limit of 1.
>
> For some reason I still want to say when this step-by-step process is
> taken as a whole, it is equal to 1. As if infinite steps were executed
> in one single shot.

it is in one shot, no time required for any operation.

A time element cannot be involved. --- consider this line of reasoning,
If there were a time element that has to be considered, what would that
time value be? who would set it, how does one know he has the right time
value, if he doesnt, his work is nada ? -- no, time is in implementation.

WM thrives on applying words/sentances that imply time required per
operation, "processed", "identified", "instantanted" "removed" to make a
opening for his theories. Like counting rocks one at a time (or ants).

WM also stops at some number, (or implies stopping).
If you stop, there is a difference, if not, there is no difference, so
they are equal.

FromTheRafters

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Apr 19, 2021, 10:15:40 AM4/19/21
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Sergio formulated on Monday :
> On 4/18/2021 6:56 PM, Chris M. Thomasson wrote:
>> On 4/18/2021 3:19 PM, Sergio wrote:
>>> On 4/17/2021 9:18 AM, WM wrote:
>>>> Chris M. Thomasson schrieb am Samstag, 17. April 2021 um 02:09:20 UTC+2:
>>>>
>>>>> There are two ways to look at it. .999... is equal to 1 when you take
>>>>> limits into account. However, if you use a step-by-step process,
>>>>> then it
>>>>> will never equal 1. It will keep getting closer and closer to it, but
>>>>> never equal it.
>>>>
>>>> Very good. Once you have understood this, you shoudl be able to
>>>> understand the consequence.
>>>
>>> it is only because you stop at k, n or p.  why do you stop ?
>>
>> i[0] = 0
>> i[n + 1] = i[n] + 9 / 10^(n + 1)
>>
>> This recursion converges on, or tends to, 1. It has a limit of 1.
>>
>> For some reason I still want to say when this step-by-step process is
>> taken as a whole, it is equal to 1. As if infinite steps were executed
>> in one single shot.
>
> it is in one shot, no time required for any operation.
>
> A time element cannot be involved. --- consider this line of reasoning,
> If there were a time element that has to be considered, what would that
> time value be? who would set it, how does one know he has the right time
> value, if he doesnt, his work is nada ? -- no, time is in implementation.

He would have a devil of a time calculating the 36th triangular number
by going step-by-step one plus two plus three plus four plus five ...
plus thirty-six. He would likely never find the thirteen quadrillionth
one even though it has now been "named" as such.

He refuses to see that *another way* to find sums does not require this
arduous method and numbers don't require it anyway.

WM

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Apr 19, 2021, 10:22:27 AM4/19/21
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Chris M. Thomasson schrieb am Montag, 19. April 2021 um 01:56:48 UTC+2:
> On 4/18/2021 3:19 PM, Sergio wrote:
> > On 4/17/2021 9:18 AM, WM wrote:
> >> Chris M. Thomasson schrieb am Samstag, 17. April 2021 um 02:09:20 UTC+2:
> >>
> >>> There are two ways to look at it. .999... is equal to 1 when you take
> >>> limits into account. However, if you use a step-by-step process, then it
> >>> will never equal 1. It will keep getting closer and closer to it, but
> >>> never equal it.
> >>
> >> Very good. Once you have understood this, you shoudl be able to understand the consequence.
> >
> > it is only because you stop at k, n or p. why do you stop ?
> i[0] = 0
> i[n + 1] = i[n] + 9 / 10^(n + 1)
> This recursion converges on, or tends to, 1. It has a limit of 1.

Right. It does not stop. Sergio has some mental illness repeatimng this nonsense again and again. Useless to try to correct him.
>
> For some reason I still want to say when this step-by-step process is
> taken as a whole, it is equal to 1.

Of course, when it is taken as a whole, then the limit is taken, because it does not stop.

> As if infinite steps were executed

Right! At no step before omega 1 is reached.

Regards, WM

WM

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Apr 19, 2021, 10:38:00 AM4/19/21
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At no term of the sequence before omega 1 is reached. Clear?
0.9
0.99
0.999
...

But the omegath term does not beelong to the terms of the sequence. It is the limit.

Regards, WM

FromTheRafters

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Apr 19, 2021, 10:51:43 AM4/19/21
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Chris M. Thomasson formulated the question :
> On 4/18/2021 3:19 PM, Sergio wrote:
>> On 4/17/2021 9:18 AM, WM wrote:
>>> Chris M. Thomasson schrieb am Samstag, 17. April 2021 um 02:09:20 UTC+2:
>>>
>>>> There are two ways to look at it. .999... is equal to 1 when you take
>>>> limits into account. However, if you use a step-by-step process, then it
>>>> will never equal 1. It will keep getting closer and closer to it, but
>>>> never equal it.
>>>
>>> Very good. Once you have understood this, you shoudl be able to understand
>>> the consequence.
>>
>> it is only because you stop at k, n or p. why do you stop ?
>
> i[0] = 0
> i[n + 1] = i[n] + 9 / 10^(n + 1)
>
> This recursion converges on, or tends to, 1. It has a limit of 1.

The series equals one because the summation is accomplished by taking
the limit of the sequence of partial sums.

> For some reason I still want to say when this step-by-step process is taken
> as a whole, it is equal to 1. As if infinite steps were executed in one
> single shot.

It is more like an 'end around' where the sum is arrived at by other
means than by the implied (by the representation used) step-by-step
process. Like Gauss did with the sum of the natural numbers up through
one hundred. He did not use the "this will take a long while" method
his teacher expected.

mitchr...@gmail.com

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Apr 19, 2021, 2:21:55 PM4/19/21
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What about the infinite sequence set of every integer?

Mitchell Raemsch

Sergio

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Apr 19, 2021, 2:48:19 PM4/19/21
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good, you finally got to the limit by NOT STOPing, which has always been
my point.

WM

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Apr 19, 2021, 4:29:30 PM4/19/21
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You cannot go to the limit because at every step aleph_0 are between itself and omega. They are dark steps.

FredJeffries

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Apr 19, 2021, 10:21:00 PM4/19/21
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On Monday, April 19, 2021 at 11:48:19 AM UTC-7, Sergio wrote:

> good, you finally got to the limit by NOT STOPing, which has always been
> my point.

That seems to me to be an extremely silly point.

Limits are not 'gotten to'.

Limits are calculated. We calculate a limit because we CAN NOT get to it. Limits are what we do instead.

Instead of examining each term of an infinite sequence one-by-one.

Instead of performing infinitely many binary additions.

Instead of evaluating a function at a point that is not in its domain.

. . .

Chris M. Thomasson

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Apr 19, 2021, 11:41:43 PM4/19/21
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Fwiw, I do like using the step-by-step method for creating fractals. It
allows me to break, say, a single line segment up into pieces, and do
interesting things with each segment. If I were to take the line segment
as one shot, I would miss the journey, so to speak. When I say break a
line apart, think of something like, just typing in the news reader
sorry for any typos:

{
vec3 p0 = { -1, 0, 0 };
vec3 p1 = { 1, 0, 0 };

vec3 dif = p1 - p0;

unsigned long n = 13;

float normal_base = 1.f / (n - 1.f);

float normal = 0.f;
float radius = normal_base;

for (unsigned long i = 0; i < n; ++i)
{
vec3 seg = p0 + dif * normal;
// draw a circle at point seg using radius
normal = normal + normal_base;
}
}

This line, from p0 to p1, is of length 2 centered at the origin (0, 0,
0). It creates 13 tangent circles, simple. One circle per step.

https://i.ibb.co/4tXJQVn/ct-line-fractal-p0.png

Now, I can do some fun things with this base data.

zelos...@gmail.com

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Apr 20, 2021, 1:02:19 AM4/20/21
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none of those is 0.999... however :)

WM

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Apr 20, 2021, 6:40:44 AM4/20/21
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> none of those is 0.999... however :)

0.999... is obtained by writing all into a single line. Or do you find some 9 missing?

Regards, WM

WM

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Apr 20, 2021, 6:44:32 AM4/20/21
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FredJeffries schrieb am Dienstag, 20. April 2021 um 04:21:00 UTC+2:
> On Monday, April 19, 2021 at 11:48:19 AM UTC-7, Sergio wrote:
>
> > good, you finally got to the limit by NOT STOPing, which has always been
> > my point.
> That seems to me to be an extremely silly point.
>
> Limits are not 'gotten to'.
>
> Limits are calculated. We calculate a limit because we CAN NOT get to it.

Ser theorists can. At least the claim it:

But that is what matheology claims:

Hausdorff: Before that (axiom of choice) it was usual to argue as follows: From the set A to be well-ordered take by arbitrary choice an element and denote it as a0, then from the set A \ {a0} an element a1, then an element from the set A \ {a0, a1} and so on. If the set {a0, a1, a2, ...} is not yet the complete set A, we can choose from A \ {a0, a1, a2, ...} an element aω, then an element aω+1, and so on. This procedure must come to an end, because beyond the set W of ordinal numbers which are mapped on elements of A, there are greater numbers; these obviously cannot be mapped on elements of A.

That is what Jerabek, Hamkins, and Cohen claim. Hamkins has explicitly endorsed the above method. And Jerabek has the effrontery to claim that this does not violate the Peano axioms, because here not natural numbers but ordinal numbers are used. He must believe in a very stupid auditory.

Regards, WM

Timothy Golden

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Apr 20, 2021, 8:15:51 AM4/20/21
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In that claims of the quantity of atoms in the universe can be substantiated and validated, then upon assigning say 10,000 atoms per counting character (something quite modest ) at somewhere around 10^78 you would run out of material and have no further ability to do any formal accounting. This figure should be worked down by rather many orders of magnitude no different than the computation on alien civilizations, but as a simple upper bound we can establish some figure.

The Euclidean presumption of geometry which goes on forever is likewise challenged by physical cosmology, and perhaps it is time that the modern human gets over their forever thing. It seems to be a teenage wasteland. The burden of proof of your work and the seriousness of that work lays not in the mathematical; you have bridged branches by going here. You have entered the domain of physics and philosophy and it should be known to all that these branches are merely artifices. That you have opted to stay in one and refuse to dip your toes in any other does not speak well of you nor of your culture. This is the culture of modern academia.

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