.999 and 1 separate on a number line

mitchr...@gmail.com

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Nov 6, 2021, 12:57:11 PM11/6/21

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plotting them shows they are separate...

Mitchell Raemsch

Serg io

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Nov 6, 2021, 12:59:26 PM11/6/21

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On 11/6/2021 11:57 AM, mitchr...@gmail.com wrote:
> plotting them shows they are separate...
>
> Mitchell Raemsch
>

did you plot them ?

show your work.

mitchr...@gmail.com

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Nov 6, 2021, 1:02:39 PM11/6/21

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On Saturday, November 6, 2021 at 9:59:26 AM UTC-7, Serg io wrote:
> On 11/6/2021 11:57 AM, mitchr...@gmail.com wrote:
> > plotting them shows they are separate...
> >
> > Mitchell Raemsch
> >
> did you plot them ?

On my paper...

Show they are not...
>
>
> show your work.

they are separate..

Mitchell Raemsch

Serg io

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Nov 6, 2021, 2:45:26 PM11/6/21

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they should be, by 1 thousandth

1 - .999 = 0.001

Python

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Nov 6, 2021, 4:01:34 PM11/6/21

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smitchI...@gmail.com wrote:
> plotting them shows they are separate...

If you plot them correctly they are not.

FromTheRafters

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Nov 6, 2021, 6:21:31 PM11/6/21

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Python laid this down on his screen :

> smitchI...@gmail.com wrote:
>> plotting them shows they are separate...
>
> If you plot them correctly they are not.

He left out the 'repeating' part.

mitchr...@gmail.com

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Nov 6, 2021, 10:09:12 PM11/6/21

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Zero math is the win. Beyond it
is the first absolute value...

zelos...@gmail.com

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Nov 8, 2021, 1:03:44 AM11/8/21

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lördag 6 november 2021 kl. 17:57:11 UTC+1 skrev mitchr...@gmail.com:
> plotting them shows they are separate...
>
> Mitchell Raemsch

Nope, they are the same.

FromTheRafters

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Nov 8, 2021, 4:05:56 AM11/8/21

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zelos...@gmail.com brought next idea :

Without the ellipsis, there are different.

zelos...@gmail.com

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Nov 8, 2021, 4:20:34 AM11/8/21

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Yepp, but we both know what the shithead means and thinks

mitchr...@gmail.com

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Nov 8, 2021, 1:00:56 PM11/8/21

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On Monday, November 8, 2021 at 1:20:34 AM UTC-8, zelos...@gmail.com wrote:
> måndag 8 november 2021 kl. 10:05:56 UTC+1 skrev FromTheRafters:
> > zelos...@gmail.com brought next idea :
> > > lördag 6 november 2021 kl. 17:57:11 UTC+1 skrev mitchr...@gmail.com:
> > >> plotting them shows they are separate...
> > >>
> > >> Mitchell Raemsch
> > > Nope, they are the same.

They are different on a number line.

zelos...@gmail.com

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Nov 9, 2021, 12:57:43 AM11/9/21

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nope, they are equal. Educate yourself

Timothy Golden

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Mar 8, 2023, 10:09:36 AM3/8/23

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Clearly:
1.000...00 - 0.999...99 = 0.000...01
Proof is by induction:
1.000 - 0.999 = 0.001
1.0000 - 0.9999 = 0.0001
...
1.000...00 - 0.999...99 = 0.000...01

I think it's a bit more interesting to try to assess something like:
1/7 + 0.000...01
0.142857142857...142857142857 + 0.000...01
= 0.142857142857...142857142858

and I believe that this is correct, but now the meaning of the ellipsis along with the repeated form length has more detail.
It can as well be said that:
0.142857142857...142857142 + 0.000...01
= 0.142857142857...142857143
which goes to show that numbers have heads and tails, and any who wish to specify such extreme values ought to bother to specify them precisely.
If you are going to let in infinite digit strings then let them in fully.
If you are not going to let in infinite digit strings then prevent them fully.
The status quo system is incongruent.

All of this work is ridiculous to the practicing physicist and engineer. There is no access to these long numbers; much as they love to chase digits. How strange it is that the mathematician and the others disagree at such a coarse level... all the while avoiding the debate.
The idea of compatibility, probably in much of mathematics, is simply an agreement not to step on each others' feet.
Yet for the student this then implies the integration of all of this; yet it will not integrate.
The purist formulation is found one author at a time apparently.
In some ways this is good, but few bother any more.
Why? Because this dogma, as explained above, is ambiguous.
For one man to espouse his interpretation will not hold up to the others.
It's like academia sits in a pool of concrete waiting for the cure.
Then comes the regurgitant to top it all off.
No: the real number ends in digit chasing; just as Dedekind had it.
You had better choose a radix, sir.