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Respect is a rational process -- McCoy, "The Galileo Seven", stardate 2822.3


tech / sci.math / Re: Add an infinitesimal to .999 repeating

SubjectAuthor
* Add an infinitesimal to .999 repeatingmitchr...@gmail.com
+- Re: Add an infinitesimal to .999 repeatingsergi o
+- Re: Add an infinitesimal to .999 repeatingChris M. Thomasson
+* Re: Add an infinitesimal to .999 repeatingMichael Moroney
|+- Re: Add an infinitesimal to .999 repeatingLon Ebina
|+* Re: Add an infinitesimal to .999 repeatingRoss A. Finlayson
||`* Re: Add an infinitesimal to .999 repeatingsergi o
|| `- Re: Add an infinitesimal to .999 repeatingRoss A. Finlayson
|`* Re: Add an infinitesimal to .999 repeatingmitchr...@gmail.com
| +- Re: Add an infinitesimal to .999 repeatingsergi o
| `* RE: Re: Add an infinitesimal to .999 repeatingEarle Jones
|  +- Re: Add an infinitesimal to .999 repeatingChris M. Thomasson
|  +- Re: Re: Add an infinitesimal to .999 repeatingmitchr...@gmail.com
|  `- RE: RE: Re: Add an infinitesimal to .999 repeatingEarle Jones
+- Re: Add an infinitesimal to .999 repeatingCleo Hirota
+* Re: Add an infinitesimal to .999 repeatingDan joyce
|+* Re: Add an infinitesimal to .999 repeatingsergi o
||`- Re: Add an infinitesimal to .999 repeatingRoss A. Finlayson
|+- Re: Add an infinitesimal to .999 repeatingmitchr...@gmail.com
|`* Re: Add an infinitesimal to .999 repeatingFromTheRafters
| `* Re: Add an infinitesimal to .999 repeatingChris M. Thomasson
|  `* Re: Add an infinitesimal to .999 repeatingFromTheRafters
|   `* Re: Add an infinitesimal to .999 repeatingChris M. Thomasson
|    `* Re: Add an infinitesimal to .999 repeatingsergi o
|     `* Re: Add an infinitesimal to .999 repeatingChris M. Thomasson
|      +* Re: Add an infinitesimal to .999 repeatingBen
|      |`* Re: Add an infinitesimal to .999 repeatingRoss A. Finlayson
|      | +- Re: Add an infinitesimal to .999 repeatingsergi o
|      | `* Re: Add an infinitesimal to .999 repeatingMichael Moroney
|      |  +* Re: Add an infinitesimal to .999 repeatingChris M. Thomasson
|      |  |`* Re: Add an infinitesimal to .999 repeatingDan joyce
|      |  | +- Re: Add an infinitesimal to .999 repeatingsergi o
|      |  | `* Re: Add an infinitesimal to .999 repeatingChris M. Thomasson
|      |  |  `* Re: Add an infinitesimal to .999 repeatingMichael Moroney
|      |  |   +* Re: Add an infinitesimal to .999 repeatingChris M. Thomasson
|      |  |   |`* Re: Add an infinitesimal to .999 repeatingmitchr...@gmail.com
|      |  |   | +* Re: Add an infinitesimal to .999 repeatingsergi o
|      |  |   | |`* Re: Add an infinitesimal to .999 repeatingRoss A. Finlayson
|      |  |   | | `* Re: Add an infinitesimal to .999 repeatingmitchr...@gmail.com
|      |  |   | |  +* Re: Add an infinitesimal to .999 repeatingsergi o
|      |  |   | |  |`* Re: Add an infinitesimal to .999 repeatingmitchr...@gmail.com
|      |  |   | |  | `* Re: Add an infinitesimal to .999 repeatingRoss A. Finlayson
|      |  |   | |  |  `* Re: Add an infinitesimal to .999 repeatingmitchr...@gmail.com
|      |  |   | |  |   +- Re: Add an infinitesimal to .999 repeatingAtom Hatoyama
|      |  |   | |  |   +* Re: Add an infinitesimal to .999 repeatingmitchr...@gmail.com
|      |  |   | |  |   |+- Re: Add an infinitesimal to .999 repeatingMichael Moroney
|      |  |   | |  |   |+- Re: Add an infinitesimal to .999 repeatingsergi o
|      |  |   | |  |   |`* Re: Add an infinitesimal to .999 repeatingmitchr...@gmail.com
|      |  |   | |  |   | +* Re: Add an infinitesimal to .999 repeatingMichael Moroney
|      |  |   | |  |   | |`- Re: Add an infinitesimal to .999 repeatingLen Deguchi
|      |  |   | |  |   | `* Re: Add an infinitesimal to .999 repeatingmitchr...@gmail.com
|      |  |   | |  |   |  +- Re: Add an infinitesimal to .999 repeatingsergi o
|      |  |   | |  |   |  +* Re: Add an infinitesimal to .999 repeatingMichael Moroney
|      |  |   | |  |   |  |`* Re: Add an infinitesimal to .999 repeatingBlain Nakada
|      |  |   | |  |   |  | `- Re: Add an infinitesimal to .999 repeatingsergi o
|      |  |   | |  |   |  +- Re: Add an infinitesimal to .999 repeatingmitchr...@gmail.com
|      |  |   | |  |   |  `* Re: Add an infinitesimal to .999 repeatingmitchr...@gmail.com
|      |  |   | |  |   |   +* Re: Add an infinitesimal to .999 repeatingMichael Moroney
|      |  |   | |  |   |   |`- Re: Add an infinitesimal to .999 repeatingEarl Iesada
|      |  |   | |  |   |   `* Re: Add an infinitesimal to .999 repeatingmitchr...@gmail.com
|      |  |   | |  |   |    +- Re: Add an infinitesimal to .999 repeatingsergi o
|      |  |   | |  |   |    +- Re: Add an infinitesimal to .999 repeatingRoss A. Finlayson
|      |  |   | |  |   |    `- Re: Add an infinitesimal to .999 repeatingMichael Moroney
|      |  |   | |  |   `- Re: Add an infinitesimal to .999 repeatingsergi o
|      |  |   | |  +- Re: Add an infinitesimal to .999 repeatingRoss A. Finlayson
|      |  |   | |  `* Re: Add an infinitesimal to .999 repeatingzelos...@gmail.com
|      |  |   | |   +- Re: Add an infinitesimal to .999 repeatingRoss A. Finlayson
|      |  |   | |   `* Re: Add an infinitesimal to .999 repeatingmitchr...@gmail.com
|      |  |   | |    +* Re: Add an infinitesimal to .999 repeatingsergi o
|      |  |   | |    |`* Re: Add an infinitesimal to .999 repeatingRoss A. Finlayson
|      |  |   | |    | +* Re: Add an infinitesimal to .999 repeatingsergi o
|      |  |   | |    | |+- Re: Add an infinitesimal to .999 repeatingzelos...@gmail.com
|      |  |   | |    | |`- Re: Add an infinitesimal to .999 repeatingzelos...@gmail.com
|      |  |   | |    | +- Re: Add an infinitesimal to .999 repeatingRoss A. Finlayson
|      |  |   | |    | +* Re: Add an infinitesimal to .999 repeatingmitchr...@gmail.com
|      |  |   | |    | |+- Re: Add an infinitesimal to .999 repeatingMichael Moroney
|      |  |   | |    | |`* Re: Add an infinitesimal to .999 repeatingRoss A. Finlayson
|      |  |   | |    | | +- Re: Add an infinitesimal to .999 repeatingFromTheRafters
|      |  |   | |    | | `- Re: Add an infinitesimal to .999 repeatingRoss A. Finlayson
|      |  |   | |    | +- Re: Add an infinitesimal to .999 repeatingmitchr...@gmail.com
|      |  |   | |    | +- Re: Add an infinitesimal to .999 repeatingRoss A. Finlayson
|      |  |   | |    | `* Re: Add an infinitesimal to .999 repeatingmitchr...@gmail.com
|      |  |   | |    |  `- Re: Add an infinitesimal to .999 repeatingJeff Kajiwara
|      |  |   | |    `- Re: Add an infinitesimal to .999 repeatingzelos...@gmail.com
|      |  |   | `- Re: Add an infinitesimal to .999 repeatingzelos...@gmail.com
|      |  |   `- Re: Add an infinitesimal to .999 repeatingRoss A. Finlayson
|      |  `* Re: Add an infinitesimal to .999 repeatingMandy Ugaki
|      |   `* Re: Add an infinitesimal to .999 repeatingMichael Moroney
|      |    `- Re: Add an infinitesimal to .999 repeatingCoty Hojo
|      `* Re: Add an infinitesimal to .999 repeatingsergi o
|       +* Re: Add an infinitesimal to .999 repeatingChris M. Thomasson
|       |`- Re: Add an infinitesimal to .999 repeatingsergi o
|       +* Re: Add an infinitesimal to .999 repeatingChris M. Thomasson
|       |+- Re: Add an infinitesimal to .999 repeatingsergi o
|       |`- Re: Add an infinitesimal to .999 repeatingChris M. Thomasson
|       `- Re: Add an infinitesimal to .999 repeatingRoss A. Finlayson
+* Re: Add an infinitesimal to .999 repeatingRoss A. Finlayson
|`* Re: Add an infinitesimal to .999 repeatingRoss A. Finlayson
| `* Re: Add an infinitesimal to .999 repeatingzelos...@gmail.com
|  `* Re: Add an infinitesimal to .999 repeatingRoss A. Finlayson
|   +* Re: Add an infinitesimal to .999 repeatingmitchr...@gmail.com
|   `* Re: Add an infinitesimal to .999 repeatingzelos...@gmail.com
+* Re: Add an infinitesimal to .999 repeatingChris M. Thomasson
+- Re: Add an infinitesimal to .999 repeatingSeñor Dingus
`- Re: Add an infinitesimal to .999 repeatingChris M. Thomasson

Pages:12345
Add an infinitesimal to .999 repeating

<be3eec34-7b0d-477f-8259-00341e465163n@googlegroups.com>

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Subject: Add an infinitesimal to .999 repeating
From: mitchrae...@gmail.com (mitchr...@gmail.com)
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 by: mitchr...@gmail.com - Thu, 19 May 2022 17:25 UTC

and you get the first integer.

Re: Add an infinitesimal to .999 repeating

<t66002$uk6$1@gioia.aioe.org>

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https://www.novabbs.com/tech/article-flat.php?id=100515&group=sci.math#100515

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From: inva...@invalid.com (sergi o)
Newsgroups: sci.math
Subject: Re: Add an infinitesimal to .999 repeating
Date: Thu, 19 May 2022 12:49:54 -0500
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 by: sergi o - Thu, 19 May 2022 17:49 UTC

On 5/19/2022 12:25 PM, mitchr...@gmail.com wrote:
> and you get the first integer.

Whoa! hold on there Cowboy, you cant get something for nothing.

did you own the .999 repeating ? if you don't own it, you cant get it.

do you own an infinitesimal ? if you don't own it, you cant get it.

Re: Add an infinitesimal to .999 repeating

<t66beh$1tp$1@dont-email.me>

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https://www.novabbs.com/tech/article-flat.php?id=100525&group=sci.math#100525

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From: chris.m....@gmail.com (Chris M. Thomasson)
Newsgroups: sci.math
Subject: Re: Add an infinitesimal to .999 repeating
Date: Thu, 19 May 2022 14:05:21 -0700
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 by: Chris M. Thomasson - Thu, 19 May 2022 21:05 UTC

On 5/19/2022 10:25 AM, mitchr...@gmail.com wrote:
> and you get the first integer.

Do you mean:

..999... + (1 - .999...) = 1?

Re: Add an infinitesimal to .999 repeating

<t66bsg$d18$2@gioia.aioe.org>

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https://www.novabbs.com/tech/article-flat.php?id=100526&group=sci.math#100526

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From: moro...@world.std.spaamtrap.com (Michael Moroney)
Newsgroups: sci.math
Subject: Re: Add an infinitesimal to .999 repeating
Date: Thu, 19 May 2022 17:13:03 -0400
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 by: Michael Moroney - Thu, 19 May 2022 21:13 UTC

Of course. 1+0=1.

Re: Add an infinitesimal to .999 repeating

<t66emn$12sr$1@gioia.aioe.org>

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From: aio...@nlnnenna.an (Lon Ebina)
Newsgroups: sci.math
Subject: Re: Add an infinitesimal to .999 repeating
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 by: Lon Ebina - Thu, 19 May 2022 22:00 UTC

Michael Moroney wrote:

> Of course. 1+0=1.

come on, it's not my fault aioe banned relativity for posting. I am a nice
man. I rarely insult anyone, an only as an insult in return. You can't
blame me. Blame that gearmon wanker "homepage_designer" not knowing what
he does.

Re: Add an infinitesimal to .999 repeating

<t66f7d$12sr$2@gioia.aioe.org>

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From: aot...@helahrlt.ho (Cleo Hirota)
Newsgroups: sci.math
Subject: Re: Add an infinitesimal to .999 repeating
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 by: Cleo Hirota - Thu, 19 May 2022 22:09 UTC

mitchr...@gmail.com wrote:

> Add an infinitesimal to .999 repeating and you get the first integer.

not true, you can't add anything, the 9 goes to infinity, hence anything
you add, fucks up your integer. One thing is for certain,
*_it_never_converges_*. Just think again, deeper, not faster.

Re: Add an infinitesimal to .999 repeating

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Subject: Re: Add an infinitesimal to .999 repeating
From: ross.fin...@gmail.com (Ross A. Finlayson)
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 by: Ross A. Finlayson - Fri, 20 May 2022 05:42 UTC

On Thursday, May 19, 2022 at 2:12:58 PM UTC-7, Michael Moroney wrote:
> Of course. 1+0=1.

999!

Re: Add an infinitesimal to .999 repeating

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Subject: Re: Add an infinitesimal to .999 repeating
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 by: sergi o - Fri, 20 May 2022 15:50 UTC

On 5/20/2022 12:42 AM, Ross A. Finlayson wrote:
> On Thursday, May 19, 2022 at 2:12:58 PM UTC-7, Michael Moroney wrote:
>> Of course. 1+0=1.
>
> 999!

666 + 999 = 1665

so when you add 9s it pulls out a 1 off the rightmost digit, and puts it in a 1 up front !

999 + 999 = 1998 see !

4 + 9 = 13 !!

22,222,222 + 9,999,999 = 122,222,221 !

Extra credit problem;

when does this not work this way, and why ?

Re: Add an infinitesimal to .999 repeating

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Subject: Re: Add an infinitesimal to .999 repeating
From: mitchrae...@gmail.com (mitchr...@gmail.com)
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 by: mitchr...@gmail.com - Sat, 21 May 2022 17:38 UTC

On Thursday, May 19, 2022 at 2:12:58 PM UTC-7, Michael Moroney wrote:
> Of course. 1+0=1.

But .999... plus zero equals .999...
To get to 1 you need to add an infinitesimal instead.

Mitchell Raemsch

Re: Add an infinitesimal to .999 repeating

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Subject: Re: Add an infinitesimal to .999 repeating
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 by: sergi o - Sat, 21 May 2022 19:07 UTC

On 5/21/2022 12:38 PM, mitchr...@gmail.com wrote:
> On Thursday, May 19, 2022 at 2:12:58 PM UTC-7, Michael Moroney wrote:
>> Of course. 1+0=1.
>
> But .999... plus zero equals .999...
> To get to 1 you need to add an infinitesimal instead.
>
> Mitchell Raemsch

1 - .999... = infinitesimal = 0

Re: Add an infinitesimal to .999 repeating

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Subject: Re: Add an infinitesimal to .999 repeating
From: ross.fin...@gmail.com (Ross A. Finlayson)
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 by: Ross A. Finlayson - Sat, 21 May 2022 21:04 UTC

On Friday, May 20, 2022 at 8:51:06 AM UTC-7, sergi o wrote:
> On 5/20/2022 12:42 AM, Ross A. Finlayson wrote:
> > On Thursday, May 19, 2022 at 2:12:58 PM UTC-7, Michael Moroney wrote:
> >> Of course. 1+0=1.
> >
> > 999!
> 666 + 999 = 1665
>
> so when you add 9s it pulls out a 1 off the rightmost digit, and puts it in a 1 up front !
>
>
> 999 + 999 = 1998 see !
>
>
> 4 + 9 = 13 !!
>
>
> 22,222,222 + 9,999,999 = 122,222,221 !
>
>
>
>
>
> Extra credit problem;
>
> when does this not work this way, and why ?

Seems like "one system is carry, the other is round".

That for both of them it works out
"in the infinite case..." that a limit exists.

Of course I have a mathematics degree and the
curriculum included some usual axioms of algebra's
complete ordered field for real numbers, then also
I simply wrote for myself what theorems implemented
a ring for the usual theorems of calculus (real analysis,
infinitesimal analysis) the "fundamental" theorems.

Having this way models of continuous domains
including line reals, field reals, signal reals, is a
much bigger mathematics while having less.

Of course it's a usual goal of "foundations" what
is the least independent axioms, that result the
most consistent theory.

Then for clock arithmetic and divisor arithmetic,
each regular and modular, it really helps explain
the scalar as real-valued as both rational field,
and, integer and non-integer part.

Now, as to _why_ education is so one-sided that
".999, ..., equals one and is no different", it's because
it follows that the following years of cumulative education
have the "usual" or "standard, after defining LUB and
measure 1.0, after the complete ordered field", that
Cauchy's definition is singular to simplify the entire thing.

Here though it's _not_ without its opposite or alternative,
framed in terms of what is "critical analysis" what involves
maintaining both definitions separately, some "dual representation
..999" and "infinitesimal difference .999".

It's that simple and easy and for constructivists, both.

Re: Add an infinitesimal to .999 repeating

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Subject: Re: Add an infinitesimal to .999 repeating
From: danj4...@gmail.com (Dan joyce)
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 by: Dan joyce - Sat, 21 May 2022 23:59 UTC

On Thursday, May 19, 2022 at 1:25:44 PM UTC-4, mitchr...@gmail.com wrote:
> and you get the first integer.

Think of it this way Mitch.
When .999... becomes so close to being 1,
then what the hell lets call it 1.
When pi or e or any transcendental or irrational
number expressed to 30 decimal place it is perfectly normal
to round up the last digit or not depending if that number is >4
then round up or <5 just leave the same value.
The difference would be a diameter much smaller than a quark
and that is really small. Smaller than any known particle.

In a few words, when the distance is so small it
becomes an incommensurable quantity.
Then it is time to round up or not the last digit of the decimal expansion.
In all cases probably the 30th digit
So what the hell is all the controversy about?

I think what Mitch means is, 0.999...+ (0.000...1) as the infinitesimal
which is also an incommensurable quantity.
That really doesn't make any sense either because the 9's go on forever.

Dan

Re: Add an infinitesimal to .999 repeating

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Subject: Re: Add an infinitesimal to .999 repeating
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 by: sergi o - Sun, 22 May 2022 00:13 UTC

On 5/21/2022 6:59 PM, Dan joyce wrote:
> On Thursday, May 19, 2022 at 1:25:44 PM UTC-4, mitchr...@gmail.com wrote:
>> and you get the first integer.
>
> Think of it this way Mitch.
> When .999... becomes so close to being 1,
> then what the hell lets call it 1.
> When pi or e or any transcendental or irrational
> number expressed to 30 decimal place it is perfectly normal
> to round up the last digit or not depending if that number is >4
> then round up or <5 just leave the same value.
> The difference would be a diameter much smaller than a quark
> and that is really small. Smaller than any known particle.
>
> In a few words, when the distance is so small it
> becomes an incommensurable quantity.
> Then it is time to round up or not the last digit of the decimal expansion.
> In all cases probably the 30th digit
> So what the hell is all the controversy about?
>
> I think what Mitch means is, 0.999...+ (0.000...1) as the infinitesimal
> which is also an incommensurable quantity.
> That really doesn't make any sense either because the 9's go on forever.
>
> Dan

I think Mitch camps out in that infinitesimal

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Subject: Re: Add an infinitesimal to .999 repeating
From: ross.fin...@gmail.com (Ross A. Finlayson)
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 by: Ross A. Finlayson - Sun, 22 May 2022 01:09 UTC

On Saturday, May 21, 2022 at 5:14:12 PM UTC-7, sergi o wrote:
> On 5/21/2022 6:59 PM, Dan joyce wrote:
> > On Thursday, May 19, 2022 at 1:25:44 PM UTC-4, mitchr...@gmail.com wrote:
> >> and you get the first integer.
> >
> > Think of it this way Mitch.
> > When .999... becomes so close to being 1,
> > then what the hell lets call it 1.
> > When pi or e or any transcendental or irrational
> > number expressed to 30 decimal place it is perfectly normal
> > to round up the last digit or not depending if that number is >4
> > then round up or <5 just leave the same value.
> > The difference would be a diameter much smaller than a quark
> > and that is really small. Smaller than any known particle.
> >
> > In a few words, when the distance is so small it
> > becomes an incommensurable quantity.
> > Then it is time to round up or not the last digit of the decimal expansion.
> > In all cases probably the 30th digit
> > So what the hell is all the controversy about?
> >
> > I think what Mitch means is, 0.999...+ (0.000...1) as the infinitesimal
> > which is also an incommensurable quantity.
> > That really doesn't make any sense either because the 9's go on forever.
> >
> > Dan
> I think Mitch camps out in that infinitesimal

Why not - Mitch is a giant troll (gullible troll).

These are infinitesimals because they have properties
of real numbers about zero and between zero and one.

"I.e.: there are only real numbers
everywhere in the real numbers".

Then, the most standard infinitesimals
seem between zero and one, sum to one.

The idea then with Vitali and his sum over
terms, instead of establishing the non-measurable,
doubles the space to gve each the "one-sided"
points on the line filling more than"two-sided".

The Hausdorff and Banach-Tarski are next,
simply increasing in the dimensions the space,
from one dimension, why the everywhere
non-decomposable doubles in the space.

With iota-values here the terms and the
geometry of lines and points and the sides
on the points, then results arithmetic in real
numbers after products in terms.

Having 0, 1 first them also is for symmetry on 1/2
and the modular besides rational, power series, ....

Generating functions in operator spaces, is a
usual automatic, for the "Equivalency Function"
and "Reverse Equivalency Function" and so on.

Re: Add an infinitesimal to .999 repeating

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Subject: Re: Add an infinitesimal to .999 repeating
From: mitchrae...@gmail.com (mitchr...@gmail.com)
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 by: mitchr...@gmail.com - Sun, 22 May 2022 01:53 UTC

On Saturday, May 21, 2022 at 4:59:55 PM UTC-7, Dan joyce wrote:
> On Thursday, May 19, 2022 at 1:25:44 PM UTC-4, mitchr...@gmail.com wrote:
> > and you get the first integer.
> Think of it this way Mitch.
> When .999... becomes so close to being 1,
> then what the hell lets call it 1.

It becomes infinitely close to being 1 without being.

> When pi or e or any transcendental or irrational
> number expressed to 30 decimal place it is perfectly normal
> to round up the last digit or not depending if that number is >4
> then round up or <5 just leave the same value.
> The difference would be a diameter much smaller than a quark
> and that is really small. Smaller than any known particle.
>
> In a few words, when the distance is so small it
> becomes an incommensurable quantity.
> Then it is time to round up or not the last digit of the decimal expansion.
> In all cases probably the 30th digit
> So what the hell is all the controversy about?
>
> I think what Mitch means is, 0.999...+ (0.000...1) as the infinitesimal
> which is also an incommensurable quantity.
> That really doesn't make any sense either because the 9's go on forever.

What about a size of infinity dan?
At its end you can add.

>
> Dan

Re: Add an infinitesimal to .999 repeating

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From: nom...@afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Add an infinitesimal to .999 repeating
Date: Sat, 21 May 2022 19:09:34 -0700
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 by: FromTheRafters - Sun, 22 May 2022 02:09 UTC

Dan joyce presented the following explanation :
> On Thursday, May 19, 2022 at 1:25:44 PM UTC-4, mitchr...@gmail.com wrote:
>> and you get the first integer.
>
> Think of it this way Mitch.
> When .999... becomes so close to being 1,

That number being represented by this symbol is not 'becoming' anything
though. It simply is a representation of a number (the natural number
one in this case) as embedded in the real number system.

Re: Add an infinitesimal to .999 repeating

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From: chris.m....@gmail.com (Chris M. Thomasson)
Newsgroups: sci.math
Subject: Re: Add an infinitesimal to .999 repeating
Date: Sat, 21 May 2022 20:18:13 -0700
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 by: Chris M. Thomasson - Sun, 22 May 2022 03:18 UTC

On 5/21/2022 7:09 PM, FromTheRafters wrote:
> Dan joyce presented the following explanation :
>> On Thursday, May 19, 2022 at 1:25:44 PM UTC-4, mitchr...@gmail.com wrote:
>>> and you get the first integer.
>>
>> Think of it this way Mitch.
>> When .999... becomes so close to being 1,
>
> That number being represented by this symbol is not 'becoming' anything
> though. It simply is a representation of a number (the natural number
> one in this case) as embedded in the real number system.

I wonder if he thinks "becoming" just might be:

[0] = 0
[1] = .9
[2] = .99
[3] = .999
[4] = .9999
[5] = .99999
....

If one takes each individual step into account... The limit is one.

However, wrt the step-by-step accounting, there is no step where 1 - [n] = 0

Just wondering here.

Re: Add an infinitesimal to .999 repeating

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From: nom...@afraid.org (FromTheRafters)
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Subject: Re: Add an infinitesimal to .999 repeating
Date: Sun, 22 May 2022 03:20:41 -0700
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 by: FromTheRafters - Sun, 22 May 2022 10:20 UTC

Chris M. Thomasson used his keyboard to write :
> On 5/21/2022 7:09 PM, FromTheRafters wrote:
>> Dan joyce presented the following explanation :
>>> On Thursday, May 19, 2022 at 1:25:44 PM UTC-4, mitchr...@gmail.com wrote:
>>>> and you get the first integer.
>>>
>>> Think of it this way Mitch.
>>> When .999... becomes so close to being 1,
>>
>> That number being represented by this symbol is not 'becoming' anything
>> though. It simply is a representation of a number (the natural number one
>> in this case) as embedded in the real number system.
>
> I wonder if he thinks "becoming" just might be:
>
> [0] = 0
> [1] = .9
> [2] = .99
> [3] = .999
> [4] = .9999
> [5] = .99999
> ...
>
> If one takes each individual step into account... The limit is one.
>
> However, wrt the step-by-step accounting, there is no step where 1 - [n] = 0
>
> Just wondering here.

It is the mistake of thinking that summation is a step by step process.
Just because there are indices for each member does not mean you have
to add them in any particular order.

Re: Add an infinitesimal to .999 repeating

<t6e2tj$6mu$1@dont-email.me>

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From: chris.m....@gmail.com (Chris M. Thomasson)
Newsgroups: sci.math
Subject: Re: Add an infinitesimal to .999 repeating
Date: Sun, 22 May 2022 12:28:49 -0700
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 by: Chris M. Thomasson - Sun, 22 May 2022 19:28 UTC

On 5/22/2022 3:20 AM, FromTheRafters wrote:
> Chris M. Thomasson used his keyboard to write :
>> On 5/21/2022 7:09 PM, FromTheRafters wrote:
>>> Dan joyce presented the following explanation :
>>>> On Thursday, May 19, 2022 at 1:25:44 PM UTC-4, mitchr...@gmail.com
>>>> wrote:
>>>>> and you get the first integer.
>>>>
>>>> Think of it this way Mitch.
>>>> When .999... becomes so close to being 1,
>>>
>>> That number being represented by this symbol is not 'becoming'
>>> anything though. It simply is a representation of a number (the
>>> natural number one in this case) as embedded in the real number system.
>>
>> I wonder if he thinks "becoming" just might be:
>>
>> [0] = 0
>> [1] = .9
>> [2] = .99
>> [3] = .999
>> [4] = .9999
>> [5] = .99999
>> ...
>>
>> If one takes each individual step into account... The limit is one.
>>
>> However, wrt the step-by-step accounting, there is no step where 1 -
>> [n] = 0
>>
>> Just wondering here.
>
> It is the mistake of thinking that summation is a step by step process.
> Just because there are indices for each member does not mean you have to
> add them in any particular order.

True. Humm... I am wondering if this is kosher wrt the step-by-step
process... If the index of the process is infinity, then it is equal to one.

[infinity] = 1 because the limit is one for the process as a whole?

Is that just, moronic?

I know that .999... is just a representation of one in base 10.

Re: Add an infinitesimal to .999 repeating

<t6e4ed$jci$1@gioia.aioe.org>

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From: inva...@invalid.com (sergi o)
Newsgroups: sci.math
Subject: Re: Add an infinitesimal to .999 repeating
Date: Sun, 22 May 2022 14:54:52 -0500
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 by: sergi o - Sun, 22 May 2022 19:54 UTC

On 5/22/2022 2:28 PM, Chris M. Thomasson wrote:
> On 5/22/2022 3:20 AM, FromTheRafters wrote:
>> Chris M. Thomasson used his keyboard to write :
>>> On 5/21/2022 7:09 PM, FromTheRafters wrote:
>>>> Dan joyce presented the following explanation :
>>>>> On Thursday, May 19, 2022 at 1:25:44 PM UTC-4, mitchr...@gmail.com wrote:
>>>>>> and you get the first integer.
>>>>>
>>>>> Think of it this way Mitch.
>>>>> When .999... becomes so close to being 1,
>>>>
>>>> That number being represented by this symbol is not 'becoming' anything though. It simply is a representation of a number (the natural number one in
>>>> this case) as embedded in the real number system.
>>>
>>> I wonder if he thinks "becoming" just might be:
>>>
>>> [0] = 0
>>> [1] = .9
>>> [2] = .99
>>> [3] = .999
>>> [4] = .9999
>>> [5] = .99999
>>> ...
>>>
>>> If one takes each individual step into account... The limit is one.
>>>
>>> However, wrt the step-by-step accounting, there is no step where 1 - [n] = 0
>>>
>>> Just wondering here.
>>
>> It is the mistake of thinking that summation is a step by step process. Just because there are indices for each member does not mean you have to add
>> them in any particular order.
>
> True. Humm... I am wondering if this is kosher wrt the step-by-step process... If the index of the process is infinity, then it is equal to one.

"step by step" implies you are at a step number, came from previous step, and have not gone to the next step. so you are stuck at k. it is just one
line in the code and needs the outside loop to drive all the steps

s=.9
for i = 1 to oo
s= s + s *.1 ; the step by step process dependent upon i
next i
Print s

Ill wait till it prints s

>
> [infinity] = 1 because the limit is one for the process as a whole?
>
> Is that just, moronic?
>
> I know that .999... is just a representation of one in base 10.

Re: Add an infinitesimal to .999 repeating

<t6e93n$iui$1@dont-email.me>

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From: chris.m....@gmail.com (Chris M. Thomasson)
Newsgroups: sci.math
Subject: Re: Add an infinitesimal to .999 repeating
Date: Sun, 22 May 2022 14:14:31 -0700
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 by: Chris M. Thomasson - Sun, 22 May 2022 21:14 UTC

On 5/22/2022 12:54 PM, sergi o wrote:
> On 5/22/2022 2:28 PM, Chris M. Thomasson wrote:
>> On 5/22/2022 3:20 AM, FromTheRafters wrote:
>>> Chris M. Thomasson used his keyboard to write :
>>>> On 5/21/2022 7:09 PM, FromTheRafters wrote:
>>>>> Dan joyce presented the following explanation :
>>>>>> On Thursday, May 19, 2022 at 1:25:44 PM UTC-4, mitchr...@gmail.com
>>>>>> wrote:
>>>>>>> and you get the first integer.
>>>>>>
>>>>>> Think of it this way Mitch.
>>>>>> When .999... becomes so close to being 1,
>>>>>
>>>>> That number being represented by this symbol is not 'becoming'
>>>>> anything though. It simply is a representation of a number (the
>>>>> natural number one in this case) as embedded in the real number
>>>>> system.
>>>>
>>>> I wonder if he thinks "becoming" just might be:
>>>>
>>>> [0] = 0
>>>> [1] = .9
>>>> [2] = .99
>>>> [3] = .999
>>>> [4] = .9999
>>>> [5] = .99999
>>>> ...
>>>>
>>>> If one takes each individual step into account... The limit is one.
>>>>
>>>> However, wrt the step-by-step accounting, there is no step where 1 -
>>>> [n] = 0
>>>>
>>>> Just wondering here.
>>>
>>> It is the mistake of thinking that summation is a step by step
>>> process. Just because there are indices for each member does not mean
>>> you have to add them in any particular order.
>>
>> True. Humm... I am wondering if this is kosher wrt the step-by-step
>> process... If the index of the process is infinity, then it is equal
>> to one.
>
>
> "step by step" implies you are at a step number, came from previous
> step, and have not gone to the next step.  so you are stuck at k. it is
> just one line in the code and needs the outside loop to drive all the steps
>
> s=.9
> for i = 1 to oo
> s= s + s *.1    ; the step by step process dependent upon i
> next i
> Print s
>
> Ill wait till it prints s

We can define a limit? Perhaps even an epsilon that terminates the loop
when things get "close enough", so to speak... ?

>
>>
>> [infinity] = 1 because the limit is one for the process as a whole?
>>
>> Is that just, moronic?
>>
>> I know that .999... is just a representation of one in base 10.
>
>
>

Re: Add an infinitesimal to .999 repeating

<87czg51caj.fsf@bsb.me.uk>

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Subject: Re: Add an infinitesimal to .999 repeating
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 by: Ben - Sun, 22 May 2022 21:35 UTC

"Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:

> On 5/22/2022 12:54 PM, sergi o wrote:
>> On 5/22/2022 2:28 PM, Chris M. Thomasson wrote:
>>> On 5/22/2022 3:20 AM, FromTheRafters wrote:
>>>> Chris M. Thomasson used his keyboard to write :
>>>>> On 5/21/2022 7:09 PM, FromTheRafters wrote:
>>>>>> Dan joyce presented the following explanation :
>>>>>>> On Thursday, May 19, 2022 at 1:25:44 PM UTC-4, mitchr...@gmail.com wrote:
>>>>>>>> and you get the first integer.
>>>>>>>
>>>>>>> Think of it this way Mitch.
>>>>>>> When .999... becomes so close to being 1,
>>>>>>
>>>>>> That number being represented by this symbol is not 'becoming' anything though. It simply is a representation of a number (the
>>>>>> natural number one in this case) as embedded in the real number system.
>>>>>
>>>>> I wonder if he thinks "becoming" just might be:
>>>>>
>>>>> [0] = 0
>>>>> [1] = .9
>>>>> [2] = .99
>>>>> [3] = .999
>>>>> [4] = .9999
>>>>> [5] = .99999
>>>>> ...
>>>>>
>>>>> If one takes each individual step into account... The limit is one.
>>>>>
>>>>> However, wrt the step-by-step accounting, there is no step where 1 - [n] = 0
>>>>>
>>>>> Just wondering here.
>>>>
>>>> It is the mistake of thinking that summation is a step by step process. Just because there are indices for each member does not mean
>>>> you have to add them in any particular order.
>>>
>>> True. Humm... I am wondering if this is kosher wrt the step-by-step process... If the index of the process is infinity, then it is equal
>>> to one.
>>
>> "step by step" implies you are at a step number, came from previous step, and have not gone to the next step.  so you are stuck at k. it is
>> just one line in the code and needs the outside loop to drive all the steps
>> s=.9
>> for i = 1 to oo
>> s= s + s *.1    ; the step by step process dependent upon i
>> next i
>> Print s
>> Ill wait till it prints s
>
> We can define a limit?

Of course we can. Look at any text on real analysis.

The reason that 0.999... = 1 is that the sequence of partial sums is not
bounded by any r less than one. Every real >=1 is an upper bound of the
sequence of partial sums, but 1 is the least upper bound.

The existence of least upper bounds (for the right kinds of convergent
sequences) is no accident. It's how the reals are defined and why the
reals are useful for doing analysis (essentially calculus).

--
Ben.

Re: Add an infinitesimal to .999 repeating

<t6eao4$11k4$1@gioia.aioe.org>

 copy mid

https://www.novabbs.com/tech/article-flat.php?id=100759&group=sci.math#100759

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From: inva...@invalid.com (sergi o)
Newsgroups: sci.math
Subject: Re: Add an infinitesimal to .999 repeating
Date: Sun, 22 May 2022 16:42:27 -0500
Organization: Aioe.org NNTP Server
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 by: sergi o - Sun, 22 May 2022 21:42 UTC

On 5/22/2022 4:14 PM, Chris M. Thomasson wrote:
> On 5/22/2022 12:54 PM, sergi o wrote:
>> On 5/22/2022 2:28 PM, Chris M. Thomasson wrote:
>>> On 5/22/2022 3:20 AM, FromTheRafters wrote:
>>>> Chris M. Thomasson used his keyboard to write :
>>>>> On 5/21/2022 7:09 PM, FromTheRafters wrote:
>>>>>> Dan joyce presented the following explanation :
>>>>>>> On Thursday, May 19, 2022 at 1:25:44 PM UTC-4, mitchr...@gmail.com wrote:
>>>>>>>> and you get the first integer.
>>>>>>>
>>>>>>> Think of it this way Mitch.
>>>>>>> When .999... becomes so close to being 1,
>>>>>>
>>>>>> That number being represented by this symbol is not 'becoming' anything though. It simply is a representation of a number (the natural number one
>>>>>> in this case) as embedded in the real number system.
>>>>>
>>>>> I wonder if he thinks "becoming" just might be:
>>>>>
>>>>> [0] = 0
>>>>> [1] = .9
>>>>> [2] = .99
>>>>> [3] = .999
>>>>> [4] = .9999
>>>>> [5] = .99999
>>>>> ...
>>>>>
>>>>> If one takes each individual step into account... The limit is one.
>>>>>
>>>>> However, wrt the step-by-step accounting, there is no step where 1 - [n] = 0
>>>>>
>>>>> Just wondering here.
>>>>
>>>> It is the mistake of thinking that summation is a step by step process. Just because there are indices for each member does not mean you have to add
>>>> them in any particular order.
>>>
>>> True. Humm... I am wondering if this is kosher wrt the step-by-step process... If the index of the process is infinity, then it is equal to one.
>>
>>
>> "step by step" implies you are at a step number, came from previous step, and have not gone to the next step.  so you are stuck at k. it is just one
>> line in the code and needs the outside loop to drive all the steps
>>
>> s=.9
>> for i = 1 to oo
>> s= s + s *.1    ; the step by step process dependent upon i
>> next i
>> Print s
>>
>> Ill wait till it prints s
>
> We can define a limit? Perhaps even an epsilon that terminates the loop when things get "close enough", so to speak... ?

could use Mitches infinitesimal, call it e, where e is really very very super tiny smallish, 10^(-20) or less ...

if s*.1 is less than e or
if s - 1 is less than e or
if i > 200

Input e
s=.9
for i = 1 to oo
s= s + s *.1 ; the step by step process dependent upon i
if s*.1 is less than e
if s - 1 is less than e
if i > 200
bail out to Print s
Endif
Endif
Endif
next i
Print s

but you need a program that deals with huge number precision, I know a guys website, he had a calculator, used to post in here too, professor from south
America, I guess you could make this "step by step process" by spitting out the s*.1 factor, then have the operator hit continue, and have some external
guy add it up. (yes using punch tape from the 60's)

anyhow, How do they get the precision on fractals and zooming ?

>
>
>>
>>>
>>> [infinity] = 1 because the limit is one for the process as a whole?
>>>
>>> Is that just, moronic?
>>>
>>> I know that .999... is just a representation of one in base 10.
>>
>>
>>
>

Re: Add an infinitesimal to .999 repeating

<t6ecls$c8r$1@dont-email.me>

 copy mid

https://www.novabbs.com/tech/article-flat.php?id=100761&group=sci.math#100761

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Path: i2pn2.org!i2pn.org!eternal-september.org!reader02.eternal-september.org!.POSTED!not-for-mail
From: chris.m....@gmail.com (Chris M. Thomasson)
Newsgroups: sci.math
Subject: Re: Add an infinitesimal to .999 repeating
Date: Sun, 22 May 2022 15:15:22 -0700
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 by: Chris M. Thomasson - Sun, 22 May 2022 22:15 UTC

On 5/22/2022 2:42 PM, sergi o wrote:
> On 5/22/2022 4:14 PM, Chris M. Thomasson wrote:
>> On 5/22/2022 12:54 PM, sergi o wrote:
>>> On 5/22/2022 2:28 PM, Chris M. Thomasson wrote:
>>>> On 5/22/2022 3:20 AM, FromTheRafters wrote:
>>>>> Chris M. Thomasson used his keyboard to write :
>>>>>> On 5/21/2022 7:09 PM, FromTheRafters wrote:
>>>>>>> Dan joyce presented the following explanation :
>>>>>>>> On Thursday, May 19, 2022 at 1:25:44 PM UTC-4,
>>>>>>>> mitchr...@gmail.com wrote:
>>>>>>>>> and you get the first integer.
>>>>>>>>
>>>>>>>> Think of it this way Mitch.
>>>>>>>> When .999... becomes so close to being 1,
>>>>>>>
>>>>>>> That number being represented by this symbol is not 'becoming'
>>>>>>> anything though. It simply is a representation of a number (the
>>>>>>> natural number one in this case) as embedded in the real number
>>>>>>> system.
>>>>>>
>>>>>> I wonder if he thinks "becoming" just might be:
>>>>>>
>>>>>> [0] = 0
>>>>>> [1] = .9
>>>>>> [2] = .99
>>>>>> [3] = .999
>>>>>> [4] = .9999
>>>>>> [5] = .99999
>>>>>> ...
>>>>>>
>>>>>> If one takes each individual step into account... The limit is one.
>>>>>>
>>>>>> However, wrt the step-by-step accounting, there is no step where 1
>>>>>> - [n] = 0
>>>>>>
>>>>>> Just wondering here.
>>>>>
>>>>> It is the mistake of thinking that summation is a step by step
>>>>> process. Just because there are indices for each member does not
>>>>> mean you have to add them in any particular order.
>>>>
>>>> True. Humm... I am wondering if this is kosher wrt the step-by-step
>>>> process... If the index of the process is infinity, then it is equal
>>>> to one.
>>>
>>>
>>> "step by step" implies you are at a step number, came from previous
>>> step, and have not gone to the next step.  so you are stuck at k. it
>>> is just one line in the code and needs the outside loop to drive all
>>> the steps
>>>
>>> s=.9
>>> for i = 1 to oo
>>> s= s + s *.1    ; the step by step process dependent upon i
>>> next i
>>> Print s
>>>
>>> Ill wait till it prints s
>>
>> We can define a limit? Perhaps even an epsilon that terminates the
>> loop when things get "close enough", so to speak... ?

Wait a minute here... You s gets larger than one right?

s[0] = .9
s[1] = .9 + .9 *.1 = .99
s[2] = .99 + .99 * .1 = 1.089

Oops!

s[3] = 1.089 + 1.089 * .1 = 1.1979

Oh shit... Does it even have a limit?

What am I missing here?

>
>
> could use Mitches infinitesimal, call it e, where e is really very very
> super tiny smallish, 10^(-20) or less ...
>
> if s*.1 is less than e    or
> if s - 1 is less than e   or
> if i > 200
>
> Input e
> s=.9
> for i = 1 to oo
> s= s + s *.1    ; the step by step process dependent upon i
> if s*.1 is less than e
>  if s - 1 is less than e
>   if i > 200
>    bail out to Print s
>   Endif
>  Endif
> Endif
> next i
> Print s
>
> but you need a program that deals with huge number precision, I know a
> guys website, he had a calculator, used to post in here too, professor
> from south America, I guess you could make this "step by step process"
> by spitting out the s*.1 factor, then have the operator hit continue,
> and have some external guy add it up. (yes using punch tape from the 60's)
>
> anyhow, How do they get the precision on fractals and zooming ?

It depends on far you want to zoom in. Shaders use 32-bit floats and
they are okay. However, if you want to get a really deep zoom... Well,
we are going to have to use arbitrary precision....

;^)

>
>>
>>
>>>
>>>>
>>>> [infinity] = 1 because the limit is one for the process as a whole?
>>>>
>>>> Is that just, moronic?
>>>>
>>>> I know that .999... is just a representation of one in base 10.
>>>
>>>
>>>
>>
>

Re: Add an infinitesimal to .999 repeating

<t6edmu$htf$1@dont-email.me>

 copy mid

https://www.novabbs.com/tech/article-flat.php?id=100762&group=sci.math#100762

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From: chris.m....@gmail.com (Chris M. Thomasson)
Newsgroups: sci.math
Subject: Re: Add an infinitesimal to .999 repeating
Date: Sun, 22 May 2022 15:33:00 -0700
Organization: A noiseless patient Spider
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 by: Chris M. Thomasson - Sun, 22 May 2022 22:33 UTC

On 5/22/2022 2:42 PM, sergi o wrote:
> On 5/22/2022 4:14 PM, Chris M. Thomasson wrote:
>> On 5/22/2022 12:54 PM, sergi o wrote:
>>> On 5/22/2022 2:28 PM, Chris M. Thomasson wrote:
>>>> On 5/22/2022 3:20 AM, FromTheRafters wrote:
>>>>> Chris M. Thomasson used his keyboard to write :
>>>>>> On 5/21/2022 7:09 PM, FromTheRafters wrote:
>>>>>>> Dan joyce presented the following explanation :
>>>>>>>> On Thursday, May 19, 2022 at 1:25:44 PM UTC-4,
>>>>>>>> mitchr...@gmail.com wrote:
>>>>>>>>> and you get the first integer.
>>>>>>>>
>>>>>>>> Think of it this way Mitch.
>>>>>>>> When .999... becomes so close to being 1,
>>>>>>>
>>>>>>> That number being represented by this symbol is not 'becoming'
>>>>>>> anything though. It simply is a representation of a number (the
>>>>>>> natural number one in this case) as embedded in the real number
>>>>>>> system.
>>>>>>
>>>>>> I wonder if he thinks "becoming" just might be:
>>>>>>
>>>>>> [0] = 0
>>>>>> [1] = .9
>>>>>> [2] = .99
>>>>>> [3] = .999
>>>>>> [4] = .9999
>>>>>> [5] = .99999
>>>>>> ...
>>>>>>
>>>>>> If one takes each individual step into account... The limit is one.
>>>>>>
>>>>>> However, wrt the step-by-step accounting, there is no step where 1
>>>>>> - [n] = 0
>>>>>>
>>>>>> Just wondering here.
>>>>>
>>>>> It is the mistake of thinking that summation is a step by step
>>>>> process. Just because there are indices for each member does not
>>>>> mean you have to add them in any particular order.
>>>>
>>>> True. Humm... I am wondering if this is kosher wrt the step-by-step
>>>> process... If the index of the process is infinity, then it is equal
>>>> to one.
>>>
>>>
>>> "step by step" implies you are at a step number, came from previous
>>> step, and have not gone to the next step.  so you are stuck at k. it
>>> is just one line in the code and needs the outside loop to drive all
>>> the steps
>>>
>>> s=.9
>>> for i = 1 to oo
>>> s= s + s *.1    ; the step by step process dependent upon i
>>> next i
>>> Print s
>>>
>>> Ill wait till it prints s
[...]

Did you mean something like:

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

on and on, getting closer to one...

[0] = 0
[n + 1] = [n] + .9 * .1^n

This converges on 1 at infinity... right?

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