novaBBS - sci.math - Re: .999 repeating add zero

Re: .999 repeating add zero

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Subject: Re: .999 repeating add zero
From: mitchrae...@gmail.com (mitchr...@gmail.com)
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by: mitchr...@gmail.com - Tue, 7 Dec 2021 18:40 UTC

On Sunday, December 5, 2021 at 9:28:39 PM UTC-8, zelos...@gmail.com wrote:
> lördag 4 december 2021 kl. 22:00:44 UTC+1 skrev mitchr...@gmail.com:
> > On Saturday, December 4, 2021 at 12:06:18 AM UTC-8, FromTheRafters wrote:
> > > Chris M. Thomasson wrote :
> > > > On 12/2/2021 7:29 PM, Serg io wrote:
> > > >> On 12/2/2021 4:42 PM, Chris M. Thomasson wrote:
> > > >>> On 12/2/2021 2:38 PM, Chris M. Thomasson wrote:
> > > >>>> On 12/2/2021 2:15 PM, FromTheRafters wrote:
> > > >>>>> Chris M. Thomasson submitted this idea :
> > > >>>>>> On 12/2/2021 10:38 AM, mitchr...@gmail.com wrote:
> > > >>>>>>> On Thursday, December 2, 2021 at 5:20:12 AM UTC-8, Serg io wrote:
> > > >>>>>>>> On 12/1/2021 10:34 PM, Chris M. Thomasson wrote:
> > > >>>>>>>>> On 12/1/2021 8:06 PM, Serg io wrote:
> > > >>>>>>>>>> On 12/1/2021 5:57 PM, mitchr...@gmail.com wrote:
> > > >>>>>>>>>>> On Wednesday, December 1, 2021 at 3:07:47 PM UTC-8, Michael
> > > >>>>>>>>>>> Moroney wrote:
> > > >>>>>>>>>>>> On 12/1/2021 3:46 PM, mitchr...@gmail.com wrote:
> > > >>>>>>>>>>>>> you get .999 repeating again not 1 instead...
> > > >>>>>>>>>>>>>
> > > >>>>>>>>>>>> I get 1.
> > > >>>>>>>>>>>
> > > >>>>>>>>>>> You don't get it...
> > > >>>>>>>>>>>
> > > >>>>>>>>>>
> > > >>>>>>>>>> just use 1 base(.999 repeating) = 1
> > > >>>>>>>>>
> > > >>>>>>>>> .999 repeating is the representation of 1 in base 10.
> > > >>>>>>>> I see the mistake;
> > > >>>>>>>>
> > > >>>>>>>> .999repeating in base(.999 repeating) = 1
> > > >>>>>>>
> > > >>>>>>> ..999 repeating does not reach1.
> > > >>>>>>
> > > >>>>>> If you take it on a step-by-step basis, yeah, you are correct.
> > > >>>>>
> > > >>>>> How does a number reach?
> > > >>>>
> > > >>>> On a step-by-step basis, say:
> > > >>>>
> > > >>>> 1 = .9 = false
> > > >>>> 1 = .99 = false
> > > >>>> 1 = .999 = false
> > > >>>> 1 = .9999 = false
> > > >>>>
> > > >>>> We will never get there. However, it does get infinitely close to 1...
> > > >>>
> > > >>> On a step-by-step basis:
> > > >>>
> > > >>> 1 = .9 + .1 = true
> > > >>> 1 = .99 + .01 = true
> > > >>> 1 = .999 + .001 = true
> > > >>> 1 = .9999 + .0001 = true
> > > >>>
> > > >>> lol. ;^)
> > > >>
> > > >>
> > > >>
> > > >> by golly! that IS the solution!
> > > >>
> > > >>
> > > >> so 1 = .999 repeating + 0 = true
> > > >
> > > > .999... is one of the ways for base 10 to represent 1. just writing 1 is
> > > > another, one. ;^)
> > > >
> > > > Its limit is 1, it is one. Okay. Then for fun, sometimes I imagine a fantasy
> > > > scenario that involves two beings that live forever... lol... ;^)
> > > >
> > > > Being_0 tells Being_1 to report when the following recursion equals one:
> > > >
> > > > r[0] = .9 / 10^0 = .9
> > > > r[1] = r[0] + .9 / 10^1 = 0.99
> > > > r[2] = r[1] + .9 / 10^2 = 0.999
> > > > r[3] = r[2] + .9 / 10^3 = 0.9999
> > > > r[4] = r[3] + .9 / 10^4 = 0.99999
> > > > ...
> > > >
> > > > Basically:
> > > >
> > > > r[0] = .9 / 10^0 = .9
> > > > r[n] = r[n - 1] + .9 / 10^[n]
> > > >
> > > > At what iteration n will Being_1 report to Being_0 that r[n] is equal to
> > > > zero?
> > > >
> > > > ;^)
> > > It won't. It only gives a successively better rational approximation
> > > with each iteration.
> > .999 repeating and the first integer are not the same quantity.
> > They share a different kind of equality. One that is by the
> > beginning quantity of Calculus...
> >
> > Mitchell Raemsch
> they are the same, get over it

Plot them on a number line...
Not the same quantity just closest to one another on a number line instead....

Mitchell Raemsch

Re: .999 repeating add zero

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From: inva...@invalid.com (Serg io)
Newsgroups: sci.math
Subject: Re: .999 repeating add zero
Date: Tue, 7 Dec 2021 15:24:33 -0600
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by: Serg io - Tue, 7 Dec 2021 21:24 UTC

On 12/7/2021 12:40 PM, mitchr...@gmail.com wrote:
> On Sunday, December 5, 2021 at 9:28:39 PM UTC-8, zelos...@gmail.com wrote:
>> lördag 4 december 2021 kl. 22:00:44 UTC+1 skrev mitchr...@gmail.com:
>>> On Saturday, December 4, 2021 at 12:06:18 AM UTC-8, FromTheRafters wrote:
>>>> Chris M. Thomasson wrote :
>>>>> On 12/2/2021 7:29 PM, Serg io wrote:
>>>>>> On 12/2/2021 4:42 PM, Chris M. Thomasson wrote:
>>>>>>> On 12/2/2021 2:38 PM, Chris M. Thomasson wrote:
>>>>>>>> On 12/2/2021 2:15 PM, FromTheRafters wrote:
>>>>>>>>> Chris M. Thomasson submitted this idea :
>>>>>>>>>> On 12/2/2021 10:38 AM, mitchr...@gmail.com wrote:
>>>>>>>>>>> On Thursday, December 2, 2021 at 5:20:12 AM UTC-8, Serg io wrote:
>>>>>>>>>>>> On 12/1/2021 10:34 PM, Chris M. Thomasson wrote:
>>>>>>>>>>>>> On 12/1/2021 8:06 PM, Serg io wrote:
>>>>>>>>>>>>>> On 12/1/2021 5:57 PM, mitchr...@gmail.com wrote:
>>>>>>>>>>>>>>> On Wednesday, December 1, 2021 at 3:07:47 PM UTC-8, Michael
>>>>>>>>>>>>>>> Moroney wrote:
>>>>>>>>>>>>>>>> On 12/1/2021 3:46 PM, mitchr...@gmail.com wrote:
>>>>>>>>>>>>>>>>> you get .999 repeating again not 1 instead...
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> I get 1.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> You don't get it...
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> just use 1 base(.999 repeating) = 1
>>>>>>>>>>>>>
>>>>>>>>>>>>> .999 repeating is the representation of 1 in base 10.
>>>>>>>>>>>> I see the mistake;
>>>>>>>>>>>>
>>>>>>>>>>>> .999repeating in base(.999 repeating) = 1
>>>>>>>>>>>
>>>>>>>>>>> ..999 repeating does not reach1.
>>>>>>>>>>
>>>>>>>>>> If you take it on a step-by-step basis, yeah, you are correct.
>>>>>>>>>
>>>>>>>>> How does a number reach?
>>>>>>>>
>>>>>>>> On a step-by-step basis, say:
>>>>>>>>
>>>>>>>> 1 = .9 = false
>>>>>>>> 1 = .99 = false
>>>>>>>> 1 = .999 = false
>>>>>>>> 1 = .9999 = false
>>>>>>>>
>>>>>>>> We will never get there. However, it does get infinitely close to 1...
>>>>>>>
>>>>>>> On a step-by-step basis:
>>>>>>>
>>>>>>> 1 = .9 + .1 = true
>>>>>>> 1 = .99 + .01 = true
>>>>>>> 1 = .999 + .001 = true
>>>>>>> 1 = .9999 + .0001 = true
>>>>>>>
>>>>>>> lol. ;^)
>>>>>>
>>>>>>
>>>>>>
>>>>>> by golly! that IS the solution!
>>>>>>
>>>>>>
>>>>>> so 1 = .999 repeating + 0 = true
>>>>>
>>>>> .999... is one of the ways for base 10 to represent 1. just writing 1 is
>>>>> another, one. ;^)
>>>>>
>>>>> Its limit is 1, it is one. Okay. Then for fun, sometimes I imagine a fantasy
>>>>> scenario that involves two beings that live forever... lol... ;^)
>>>>>
>>>>> Being_0 tells Being_1 to report when the following recursion equals one:
>>>>>
>>>>> r[0] = .9 / 10^0 = .9
>>>>> r[1] = r[0] + .9 / 10^1 = 0.99
>>>>> r[2] = r[1] + .9 / 10^2 = 0.999
>>>>> r[3] = r[2] + .9 / 10^3 = 0.9999
>>>>> r[4] = r[3] + .9 / 10^4 = 0.99999
>>>>> ...
>>>>>
>>>>> Basically:
>>>>>
>>>>> r[0] = .9 / 10^0 = .9
>>>>> r[n] = r[n - 1] + .9 / 10^[n]
>>>>>
>>>>> At what iteration n will Being_1 report to Being_0 that r[n] is equal to
>>>>> zero?
>>>>>
>>>>> ;^)
>>>> It won't. It only gives a successively better rational approximation
>>>> with each iteration.
>>> .999 repeating and the first integer are not the same quantity.
>>> They share a different kind of equality. One that is by the
>>> beginning quantity of Calculus...
>>>
>>> Mitchell Raemsch
>> they are the same, get over it
>
> Plot them on a number line...
> Not the same quantity just closest to one another on a number line instead...
>
> Mitchell Raemsch
>

how close ? so close you cannot tell them apart. that means they are equal.

Re: .999 repeating add zero

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Subject: Re: .999 repeating add zero
From: mitchrae...@gmail.com (mitchr...@gmail.com)
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by: mitchr...@gmail.com - Tue, 7 Dec 2021 22:58 UTC

On Tuesday, December 7, 2021 at 1:24:44 PM UTC-8, Serg io wrote:
> On 12/7/2021 12:40 PM, mitchr...@gmail.com wrote:
> > On Sunday, December 5, 2021 at 9:28:39 PM UTC-8, zelos...@gmail.com wrote:
> >> lördag 4 december 2021 kl. 22:00:44 UTC+1 skrev mitchr...@gmail.com:
> >>> On Saturday, December 4, 2021 at 12:06:18 AM UTC-8, FromTheRafters wrote:
> >>>> Chris M. Thomasson wrote :
> >>>>> On 12/2/2021 7:29 PM, Serg io wrote:
> >>>>>> On 12/2/2021 4:42 PM, Chris M. Thomasson wrote:
> >>>>>>> On 12/2/2021 2:38 PM, Chris M. Thomasson wrote:
> >>>>>>>> On 12/2/2021 2:15 PM, FromTheRafters wrote:
> >>>>>>>>> Chris M. Thomasson submitted this idea :
> >>>>>>>>>> On 12/2/2021 10:38 AM, mitchr...@gmail.com wrote:
> >>>>>>>>>>> On Thursday, December 2, 2021 at 5:20:12 AM UTC-8, Serg io wrote:
> >>>>>>>>>>>> On 12/1/2021 10:34 PM, Chris M. Thomasson wrote:
> >>>>>>>>>>>>> On 12/1/2021 8:06 PM, Serg io wrote:
> >>>>>>>>>>>>>> On 12/1/2021 5:57 PM, mitchr...@gmail.com wrote:
> >>>>>>>>>>>>>>> On Wednesday, December 1, 2021 at 3:07:47 PM UTC-8, Michael
> >>>>>>>>>>>>>>> Moroney wrote:
> >>>>>>>>>>>>>>>> On 12/1/2021 3:46 PM, mitchr...@gmail.com wrote:
> >>>>>>>>>>>>>>>>> you get .999 repeating again not 1 instead...
> >>>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>> I get 1.
> >>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>> You don't get it...
> >>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>
> >>>>>>>>>>>>>> just use 1 base(.999 repeating) = 1
> >>>>>>>>>>>>>
> >>>>>>>>>>>>> .999 repeating is the representation of 1 in base 10.
> >>>>>>>>>>>> I see the mistake;
> >>>>>>>>>>>>
> >>>>>>>>>>>> .999repeating in base(.999 repeating) = 1
> >>>>>>>>>>>
> >>>>>>>>>>> ..999 repeating does not reach1.
> >>>>>>>>>>
> >>>>>>>>>> If you take it on a step-by-step basis, yeah, you are correct.
> >>>>>>>>>
> >>>>>>>>> How does a number reach?
> >>>>>>>>
> >>>>>>>> On a step-by-step basis, say:
> >>>>>>>>
> >>>>>>>> 1 = .9 = false
> >>>>>>>> 1 = .99 = false
> >>>>>>>> 1 = .999 = false
> >>>>>>>> 1 = .9999 = false
> >>>>>>>>
> >>>>>>>> We will never get there. However, it does get infinitely close to 1...
> >>>>>>>
> >>>>>>> On a step-by-step basis:
> >>>>>>>
> >>>>>>> 1 = .9 + .1 = true
> >>>>>>> 1 = .99 + .01 = true
> >>>>>>> 1 = .999 + .001 = true
> >>>>>>> 1 = .9999 + .0001 = true
> >>>>>>>
> >>>>>>> lol. ;^)
> >>>>>>
> >>>>>>
> >>>>>>
> >>>>>> by golly! that IS the solution!
> >>>>>>
> >>>>>>
> >>>>>> so 1 = .999 repeating + 0 = true
> >>>>>
> >>>>> .999... is one of the ways for base 10 to represent 1. just writing 1 is
> >>>>> another, one. ;^)
> >>>>>
> >>>>> Its limit is 1, it is one. Okay. Then for fun, sometimes I imagine a fantasy
> >>>>> scenario that involves two beings that live forever... lol... ;^)
> >>>>>
> >>>>> Being_0 tells Being_1 to report when the following recursion equals one:
> >>>>>
> >>>>> r[0] = .9 / 10^0 = .9
> >>>>> r[1] = r[0] + .9 / 10^1 = 0.99
> >>>>> r[2] = r[1] + .9 / 10^2 = 0.999
> >>>>> r[3] = r[2] + .9 / 10^3 = 0.9999
> >>>>> r[4] = r[3] + .9 / 10^4 = 0.99999
> >>>>> ...
> >>>>>
> >>>>> Basically:
> >>>>>
> >>>>> r[0] = .9 / 10^0 = .9
> >>>>> r[n] = r[n - 1] + .9 / 10^[n]
> >>>>>
> >>>>> At what iteration n will Being_1 report to Being_0 that r[n] is equal to
> >>>>> zero?
> >>>>>
> >>>>> ;^)
> >>>> It won't. It only gives a successively better rational approximation
> >>>> with each iteration.
> >>> .999 repeating and the first integer are not the same quantity.
> >>> They share a different kind of equality. One that is by the
> >>> beginning quantity of Calculus...
> >>>
> >>> Mitchell Raemsch
> >> they are the same, get over it
> >
> > Plot them on a number line...
> > Not the same quantity just closest to one another on a number line instead...
> >
> > Mitchell Raemsch
> >
> how close ? so close you cannot tell them apart. that means they are equal.

They are not separate by zero but by calculus first quantity....
Their difference is not by null but by inverse of infinity...

Mitchell Raemsch

Re: .999 repeating add zero

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From: inva...@invalid.com (Serg io)
Newsgroups: sci.math
Subject: Re: .999 repeating add zero
Date: Tue, 7 Dec 2021 17:25:02 -0600
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by: Serg io - Tue, 7 Dec 2021 23:25 UTC

On 12/7/2021 4:58 PM, mitchr...@gmail.com wrote:
> On Tuesday, December 7, 2021 at 1:24:44 PM UTC-8, Serg io wrote:
>> On 12/7/2021 12:40 PM, mitchr...@gmail.com wrote:
>>> On Sunday, December 5, 2021 at 9:28:39 PM UTC-8, zelos...@gmail.com wrote:
>>>> lördag 4 december 2021 kl. 22:00:44 UTC+1 skrev mitchr...@gmail.com:
>>>>> On Saturday, December 4, 2021 at 12:06:18 AM UTC-8, FromTheRafters wrote:
>>>>>> Chris M. Thomasson wrote :
>>>>>>> On 12/2/2021 7:29 PM, Serg io wrote:
>>>>>>>> On 12/2/2021 4:42 PM, Chris M. Thomasson wrote:
>>>>>>>>> On 12/2/2021 2:38 PM, Chris M. Thomasson wrote:
>>>>>>>>>> On 12/2/2021 2:15 PM, FromTheRafters wrote:
>>>>>>>>>>> Chris M. Thomasson submitted this idea :
>>>>>>>>>>>> On 12/2/2021 10:38 AM, mitchr...@gmail.com wrote:
>>>>>>>>>>>>> On Thursday, December 2, 2021 at 5:20:12 AM UTC-8, Serg io wrote:
>>>>>>>>>>>>>> On 12/1/2021 10:34 PM, Chris M. Thomasson wrote:
>>>>>>>>>>>>>>> On 12/1/2021 8:06 PM, Serg io wrote:
>>>>>>>>>>>>>>>> On 12/1/2021 5:57 PM, mitchr...@gmail.com wrote:
>>>>>>>>>>>>>>>>> On Wednesday, December 1, 2021 at 3:07:47 PM UTC-8, Michael
>>>>>>>>>>>>>>>>> Moroney wrote:
>>>>>>>>>>>>>>>>>> On 12/1/2021 3:46 PM, mitchr...@gmail.com wrote:
>>>>>>>>>>>>>>>>>>> you get .999 repeating again not 1 instead...
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> I get 1.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> You don't get it...
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> just use 1 base(.999 repeating) = 1
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> .999 repeating is the representation of 1 in base 10.
>>>>>>>>>>>>>> I see the mistake;
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> .999repeating in base(.999 repeating) = 1
>>>>>>>>>>>>>
>>>>>>>>>>>>> ..999 repeating does not reach1.
>>>>>>>>>>>>
>>>>>>>>>>>> If you take it on a step-by-step basis, yeah, you are correct.
>>>>>>>>>>>
>>>>>>>>>>> How does a number reach?
>>>>>>>>>>
>>>>>>>>>> On a step-by-step basis, say:
>>>>>>>>>>
>>>>>>>>>> 1 = .9 = false
>>>>>>>>>> 1 = .99 = false
>>>>>>>>>> 1 = .999 = false
>>>>>>>>>> 1 = .9999 = false
>>>>>>>>>>
>>>>>>>>>> We will never get there. However, it does get infinitely close to 1...
>>>>>>>>>
>>>>>>>>> On a step-by-step basis:
>>>>>>>>>
>>>>>>>>> 1 = .9 + .1 = true
>>>>>>>>> 1 = .99 + .01 = true
>>>>>>>>> 1 = .999 + .001 = true
>>>>>>>>> 1 = .9999 + .0001 = true
>>>>>>>>>
>>>>>>>>> lol. ;^)
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> by golly! that IS the solution!
>>>>>>>>
>>>>>>>>
>>>>>>>> so 1 = .999 repeating + 0 = true
>>>>>>>
>>>>>>> .999... is one of the ways for base 10 to represent 1. just writing 1 is
>>>>>>> another, one. ;^)
>>>>>>>
>>>>>>> Its limit is 1, it is one. Okay. Then for fun, sometimes I imagine a fantasy
>>>>>>> scenario that involves two beings that live forever... lol... ;^)
>>>>>>>
>>>>>>> Being_0 tells Being_1 to report when the following recursion equals one:
>>>>>>>
>>>>>>> r[0] = .9 / 10^0 = .9
>>>>>>> r[1] = r[0] + .9 / 10^1 = 0.99
>>>>>>> r[2] = r[1] + .9 / 10^2 = 0.999
>>>>>>> r[3] = r[2] + .9 / 10^3 = 0.9999
>>>>>>> r[4] = r[3] + .9 / 10^4 = 0.99999
>>>>>>> ...
>>>>>>>
>>>>>>> Basically:
>>>>>>>
>>>>>>> r[0] = .9 / 10^0 = .9
>>>>>>> r[n] = r[n - 1] + .9 / 10^[n]
>>>>>>>
>>>>>>> At what iteration n will Being_1 report to Being_0 that r[n] is equal to
>>>>>>> zero?
>>>>>>>
>>>>>>> ;^)
>>>>>> It won't. It only gives a successively better rational approximation
>>>>>> with each iteration.
>>>>> .999 repeating and the first integer are not the same quantity.
>>>>> They share a different kind of equality. One that is by the
>>>>> beginning quantity of Calculus...
>>>>>
>>>>> Mitchell Raemsch
>>>> they are the same, get over it
>>>
>>> Plot them on a number line...
>>> Not the same quantity just closest to one another on a number line instead...
>>>
>>> Mitchell Raemsch
>>>
>> how close ? so close you cannot tell them apart. that means they are equal.
>
> They are not separate by zero but by calculus first quantity....
> Their difference is not by null but by inverse of infinity...
>
> Mitchell Raemsch
>

but they are separated by 0
they are also separated by null

the inverse of infinity is 1/oo = 0 but so is 214/oo = 0 so that is no good

Re: .999 repeating add zero

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Subject: Re: .999 repeating add zero
From: mitchrae...@gmail.com (mitchr...@gmail.com)
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by: mitchr...@gmail.com - Tue, 7 Dec 2021 23:46 UTC

On Tuesday, December 7, 2021 at 3:25:13 PM UTC-8, Serg io wrote:
> On 12/7/2021 4:58 PM, mitchr...@gmail.com wrote:
> > On Tuesday, December 7, 2021 at 1:24:44 PM UTC-8, Serg io wrote:
> >> On 12/7/2021 12:40 PM, mitchr...@gmail.com wrote:
> >>> On Sunday, December 5, 2021 at 9:28:39 PM UTC-8, zelos...@gmail.com wrote:
> >>>> lördag 4 december 2021 kl. 22:00:44 UTC+1 skrev mitchr...@gmail..com:
> >>>>> On Saturday, December 4, 2021 at 12:06:18 AM UTC-8, FromTheRafters wrote:
> >>>>>> Chris M. Thomasson wrote :
> >>>>>>> On 12/2/2021 7:29 PM, Serg io wrote:
> >>>>>>>> On 12/2/2021 4:42 PM, Chris M. Thomasson wrote:
> >>>>>>>>> On 12/2/2021 2:38 PM, Chris M. Thomasson wrote:
> >>>>>>>>>> On 12/2/2021 2:15 PM, FromTheRafters wrote:
> >>>>>>>>>>> Chris M. Thomasson submitted this idea :
> >>>>>>>>>>>> On 12/2/2021 10:38 AM, mitchr...@gmail.com wrote:
> >>>>>>>>>>>>> On Thursday, December 2, 2021 at 5:20:12 AM UTC-8, Serg io wrote:
> >>>>>>>>>>>>>> On 12/1/2021 10:34 PM, Chris M. Thomasson wrote:
> >>>>>>>>>>>>>>> On 12/1/2021 8:06 PM, Serg io wrote:
> >>>>>>>>>>>>>>>> On 12/1/2021 5:57 PM, mitchr...@gmail.com wrote:
> >>>>>>>>>>>>>>>>> On Wednesday, December 1, 2021 at 3:07:47 PM UTC-8, Michael
> >>>>>>>>>>>>>>>>> Moroney wrote:
> >>>>>>>>>>>>>>>>>> On 12/1/2021 3:46 PM, mitchr...@gmail.com wrote:
> >>>>>>>>>>>>>>>>>>> you get .999 repeating again not 1 instead...
> >>>>>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>>>> I get 1.
> >>>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>>> You don't get it...
> >>>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>> just use 1 base(.999 repeating) = 1
> >>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>> .999 repeating is the representation of 1 in base 10.
> >>>>>>>>>>>>>> I see the mistake;
> >>>>>>>>>>>>>>
> >>>>>>>>>>>>>> .999repeating in base(.999 repeating) = 1
> >>>>>>>>>>>>>
> >>>>>>>>>>>>> ..999 repeating does not reach1.
> >>>>>>>>>>>>
> >>>>>>>>>>>> If you take it on a step-by-step basis, yeah, you are correct.
> >>>>>>>>>>>
> >>>>>>>>>>> How does a number reach?
> >>>>>>>>>>
> >>>>>>>>>> On a step-by-step basis, say:
> >>>>>>>>>>
> >>>>>>>>>> 1 = .9 = false
> >>>>>>>>>> 1 = .99 = false
> >>>>>>>>>> 1 = .999 = false
> >>>>>>>>>> 1 = .9999 = false
> >>>>>>>>>>
> >>>>>>>>>> We will never get there. However, it does get infinitely close to 1...
> >>>>>>>>>
> >>>>>>>>> On a step-by-step basis:
> >>>>>>>>>
> >>>>>>>>> 1 = .9 + .1 = true
> >>>>>>>>> 1 = .99 + .01 = true
> >>>>>>>>> 1 = .999 + .001 = true
> >>>>>>>>> 1 = .9999 + .0001 = true
> >>>>>>>>>
> >>>>>>>>> lol. ;^)
> >>>>>>>>
> >>>>>>>>
> >>>>>>>>
> >>>>>>>> by golly! that IS the solution!
> >>>>>>>>
> >>>>>>>>
> >>>>>>>> so 1 = .999 repeating + 0 = true
> >>>>>>>
> >>>>>>> .999... is one of the ways for base 10 to represent 1. just writing 1 is
> >>>>>>> another, one. ;^)
> >>>>>>>
> >>>>>>> Its limit is 1, it is one. Okay. Then for fun, sometimes I imagine a fantasy
> >>>>>>> scenario that involves two beings that live forever... lol... ;^)
> >>>>>>>
> >>>>>>> Being_0 tells Being_1 to report when the following recursion equals one:
> >>>>>>>
> >>>>>>> r[0] = .9 / 10^0 = .9
> >>>>>>> r[1] = r[0] + .9 / 10^1 = 0.99
> >>>>>>> r[2] = r[1] + .9 / 10^2 = 0.999
> >>>>>>> r[3] = r[2] + .9 / 10^3 = 0.9999
> >>>>>>> r[4] = r[3] + .9 / 10^4 = 0.99999
> >>>>>>> ...
> >>>>>>>
> >>>>>>> Basically:
> >>>>>>>
> >>>>>>> r[0] = .9 / 10^0 = .9
> >>>>>>> r[n] = r[n - 1] + .9 / 10^[n]
> >>>>>>>
> >>>>>>> At what iteration n will Being_1 report to Being_0 that r[n] is equal to
> >>>>>>> zero?
> >>>>>>>
> >>>>>>> ;^)
> >>>>>> It won't. It only gives a successively better rational approximation
> >>>>>> with each iteration.
> >>>>> .999 repeating and the first integer are not the same quantity.
> >>>>> They share a different kind of equality. One that is by the
> >>>>> beginning quantity of Calculus...
> >>>>>
> >>>>> Mitchell Raemsch
> >>>> they are the same, get over it
> >>>
> >>> Plot them on a number line...
> >>> Not the same quantity just closest to one another on a number line instead...
> >>>
> >>> Mitchell Raemsch
> >>>
> >> how close ? so close you cannot tell them apart. that means they are equal.
> >
> > They are not separate by zero but by calculus first quantity....
> > Their difference is not by null but by inverse of infinity...
> >
> > Mitchell Raemsch
> >
> but they are separated by 0
> they are also separated by null
>

They are different by inverse infinity
that is calculus sameness to no quantity.

Mitchell Raemsch

Re: .999 repeating add zero

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From: chris.m....@gmail.com (Chris M. Thomasson)
Newsgroups: sci.math
Subject: Re: .999 repeating add zero
Date: Tue, 7 Dec 2021 21:02:57 -0800
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by: Chris M. Thomasson - Wed, 8 Dec 2021 05:02 UTC

On 12/7/2021 1:24 PM, Serg io wrote:
> On 12/7/2021 12:40 PM, mitchr...@gmail.com wrote:
>> On Sunday, December 5, 2021 at 9:28:39 PM UTC-8, zelos...@gmail.com
>> wrote:
>>> lördag 4 december 2021 kl. 22:00:44 UTC+1 skrev mitchr...@gmail.com:
>>>> On Saturday, December 4, 2021 at 12:06:18 AM UTC-8, FromTheRafters
>>>> wrote:
>>>>> Chris M. Thomasson wrote :
>>>>>> On 12/2/2021 7:29 PM, Serg io wrote:
>>>>>>> On 12/2/2021 4:42 PM, Chris M. Thomasson wrote:
>>>>>>>> On 12/2/2021 2:38 PM, Chris M. Thomasson wrote:
>>>>>>>>> On 12/2/2021 2:15 PM, FromTheRafters wrote:
>>>>>>>>>> Chris M. Thomasson submitted this idea :
>>>>>>>>>>> On 12/2/2021 10:38 AM, mitchr...@gmail.com wrote:
>>>>>>>>>>>> On Thursday, December 2, 2021 at 5:20:12 AM UTC-8, Serg io
>>>>>>>>>>>> wrote:
>>>>>>>>>>>>> On 12/1/2021 10:34 PM, Chris M. Thomasson wrote:
>>>>>>>>>>>>>> On 12/1/2021 8:06 PM, Serg io wrote:
>>>>>>>>>>>>>>> On 12/1/2021 5:57 PM, mitchr...@gmail.com wrote:
>>>>>>>>>>>>>>>> On Wednesday, December 1, 2021 at 3:07:47 PM UTC-8, Michael
>>>>>>>>>>>>>>>> Moroney wrote:
>>>>>>>>>>>>>>>>> On 12/1/2021 3:46 PM, mitchr...@gmail.com wrote:
>>>>>>>>>>>>>>>>>> you get .999 repeating again not 1 instead...
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> I get 1.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> You don't get it...
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> just use 1 base(.999 repeating) = 1
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> .999 repeating is the representation of 1 in base 10.
>>>>>>>>>>>>> I see the mistake;
>>>>>>>>>>>>>
>>>>>>>>>>>>> .999repeating in base(.999 repeating) = 1
>>>>>>>>>>>>
>>>>>>>>>>>> ..999 repeating does not reach1.
>>>>>>>>>>>
>>>>>>>>>>> If you take it on a step-by-step basis, yeah, you are correct.
>>>>>>>>>>
>>>>>>>>>> How does a number reach?
>>>>>>>>>
>>>>>>>>> On a step-by-step basis, say:
>>>>>>>>>
>>>>>>>>> 1 = .9 = false
>>>>>>>>> 1 = .99 = false
>>>>>>>>> 1 = .999 = false
>>>>>>>>> 1 = .9999 = false
>>>>>>>>>
>>>>>>>>> We will never get there. However, it does get infinitely close
>>>>>>>>> to 1...
>>>>>>>>
>>>>>>>> On a step-by-step basis:
>>>>>>>>
>>>>>>>> 1 = .9 + .1 = true
>>>>>>>> 1 = .99 + .01 = true
>>>>>>>> 1 = .999 + .001 = true
>>>>>>>> 1 = .9999 + .0001 = true
>>>>>>>>
>>>>>>>> lol. ;^)
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> by golly! that IS the solution!
>>>>>>>
>>>>>>>
>>>>>>> so 1 = .999 repeating + 0 = true
>>>>>>
>>>>>> .999... is one of the ways for base 10 to represent 1. just
>>>>>> writing 1 is
>>>>>> another, one. ;^)
>>>>>>
>>>>>> Its limit is 1, it is one. Okay. Then for fun, sometimes I imagine
>>>>>> a fantasy
>>>>>> scenario that involves two beings that live forever... lol... ;^)
>>>>>>
>>>>>> Being_0 tells Being_1 to report when the following recursion
>>>>>> equals one:
>>>>>>
>>>>>> r[0] = .9 / 10^0 = .9
>>>>>> r[1] = r[0] + .9 / 10^1 = 0.99
>>>>>> r[2] = r[1] + .9 / 10^2 = 0.999
>>>>>> r[3] = r[2] + .9 / 10^3 = 0.9999
>>>>>> r[4] = r[3] + .9 / 10^4 = 0.99999
>>>>>> ...
>>>>>>
>>>>>> Basically:
>>>>>>
>>>>>> r[0] = .9 / 10^0 = .9
>>>>>> r[n] = r[n - 1] + .9 / 10^[n]
>>>>>>
>>>>>> At what iteration n will Being_1 report to Being_0 that r[n] is
>>>>>> equal to
>>>>>> zero?
>>>>>>
>>>>>> ;^)
>>>>> It won't. It only gives a successively better rational approximation
>>>>> with each iteration.
>>>> .999 repeating and the first integer are not the same quantity.
>>>> They share a different kind of equality. One that is by the
>>>> beginning quantity of Calculus...
>>>>
>>>> Mitchell Raemsch
>>> they are the same, get over it
>>
>> Plot them on a number line...
>> Not the same quantity just closest to one another on a number line
>> instead...
>>
>> Mitchell Raemsch
>>
>
> how close ? so close you cannot tell them apart. that means they are
> equal.

Humm... Imagine using an arbitrary precision floating point lib... Just
because two points happen to visually look on top of one another so to
speak at the current view, zoom in on it. Then we can see they are
actually far apart from one another. Exploring fractals really shows
this off.

Re: .999 repeating add zero

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Subject: Re: .999 repeating add zero
From: zelos.ma...@gmail.com (zelos...@gmail.com)
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by: zelos...@gmail.com - Wed, 8 Dec 2021 05:36 UTC

tisdag 7 december 2021 kl. 19:40:36 UTC+1 skrev mitchr...@gmail.com:
> On Sunday, December 5, 2021 at 9:28:39 PM UTC-8, zelos...@gmail.com wrote:
> > lördag 4 december 2021 kl. 22:00:44 UTC+1 skrev mitchr...@gmail.com:
> > > On Saturday, December 4, 2021 at 12:06:18 AM UTC-8, FromTheRafters wrote:
> > > > Chris M. Thomasson wrote :
> > > > > On 12/2/2021 7:29 PM, Serg io wrote:
> > > > >> On 12/2/2021 4:42 PM, Chris M. Thomasson wrote:
> > > > >>> On 12/2/2021 2:38 PM, Chris M. Thomasson wrote:
> > > > >>>> On 12/2/2021 2:15 PM, FromTheRafters wrote:
> > > > >>>>> Chris M. Thomasson submitted this idea :
> > > > >>>>>> On 12/2/2021 10:38 AM, mitchr...@gmail.com wrote:
> > > > >>>>>>> On Thursday, December 2, 2021 at 5:20:12 AM UTC-8, Serg io wrote:
> > > > >>>>>>>> On 12/1/2021 10:34 PM, Chris M. Thomasson wrote:
> > > > >>>>>>>>> On 12/1/2021 8:06 PM, Serg io wrote:
> > > > >>>>>>>>>> On 12/1/2021 5:57 PM, mitchr...@gmail.com wrote:
> > > > >>>>>>>>>>> On Wednesday, December 1, 2021 at 3:07:47 PM UTC-8, Michael
> > > > >>>>>>>>>>> Moroney wrote:
> > > > >>>>>>>>>>>> On 12/1/2021 3:46 PM, mitchr...@gmail.com wrote:
> > > > >>>>>>>>>>>>> you get .999 repeating again not 1 instead...
> > > > >>>>>>>>>>>>>
> > > > >>>>>>>>>>>> I get 1.
> > > > >>>>>>>>>>>
> > > > >>>>>>>>>>> You don't get it...
> > > > >>>>>>>>>>>
> > > > >>>>>>>>>>
> > > > >>>>>>>>>> just use 1 base(.999 repeating) = 1
> > > > >>>>>>>>>
> > > > >>>>>>>>> .999 repeating is the representation of 1 in base 10.
> > > > >>>>>>>> I see the mistake;
> > > > >>>>>>>>
> > > > >>>>>>>> .999repeating in base(.999 repeating) = 1
> > > > >>>>>>>
> > > > >>>>>>> ..999 repeating does not reach1.
> > > > >>>>>>
> > > > >>>>>> If you take it on a step-by-step basis, yeah, you are correct.
> > > > >>>>>
> > > > >>>>> How does a number reach?
> > > > >>>>
> > > > >>>> On a step-by-step basis, say:
> > > > >>>>
> > > > >>>> 1 = .9 = false
> > > > >>>> 1 = .99 = false
> > > > >>>> 1 = .999 = false
> > > > >>>> 1 = .9999 = false
> > > > >>>>
> > > > >>>> We will never get there. However, it does get infinitely close to 1...
> > > > >>>
> > > > >>> On a step-by-step basis:
> > > > >>>
> > > > >>> 1 = .9 + .1 = true
> > > > >>> 1 = .99 + .01 = true
> > > > >>> 1 = .999 + .001 = true
> > > > >>> 1 = .9999 + .0001 = true
> > > > >>>
> > > > >>> lol. ;^)
> > > > >>
> > > > >>
> > > > >>
> > > > >> by golly! that IS the solution!
> > > > >>
> > > > >>
> > > > >> so 1 = .999 repeating + 0 = true
> > > > >
> > > > > .999... is one of the ways for base 10 to represent 1. just writing 1 is
> > > > > another, one. ;^)
> > > > >
> > > > > Its limit is 1, it is one. Okay. Then for fun, sometimes I imagine a fantasy
> > > > > scenario that involves two beings that live forever... lol... ;^)
> > > > >
> > > > > Being_0 tells Being_1 to report when the following recursion equals one:
> > > > >
> > > > > r[0] = .9 / 10^0 = .9
> > > > > r[1] = r[0] + .9 / 10^1 = 0.99
> > > > > r[2] = r[1] + .9 / 10^2 = 0.999
> > > > > r[3] = r[2] + .9 / 10^3 = 0.9999
> > > > > r[4] = r[3] + .9 / 10^4 = 0.99999
> > > > > ...
> > > > >
> > > > > Basically:
> > > > >
> > > > > r[0] = .9 / 10^0 = .9
> > > > > r[n] = r[n - 1] + .9 / 10^[n]
> > > > >
> > > > > At what iteration n will Being_1 report to Being_0 that r[n] is equal to
> > > > > zero?
> > > > >
> > > > > ;^)
> > > > It won't. It only gives a successively better rational approximation
> > > > with each iteration.
> > > .999 repeating and the first integer are not the same quantity.
> > > They share a different kind of equality. One that is by the
> > > beginning quantity of Calculus...
> > >
> > > Mitchell Raemsch
> > they are the same, get over it
> Plot them on a number line...
> Not the same quantity just closest to one another on a number line instead...
>
> Mitchell Raemsch

They are the exact same line so yes, still the same.

Re: .999 repeating add zero

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Subject: Re: .999 repeating add zero
From: mitchrae...@gmail.com (mitchr...@gmail.com)
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by: mitchr...@gmail.com - Wed, 8 Dec 2021 20:10 UTC

On Tuesday, December 7, 2021 at 9:36:40 PM UTC-8, zelos...@gmail.com wrote:
> tisdag 7 december 2021 kl. 19:40:36 UTC+1 skrev mitchr...@gmail.com:
> > On Sunday, December 5, 2021 at 9:28:39 PM UTC-8, zelos...@gmail.com wrote:
> > > lördag 4 december 2021 kl. 22:00:44 UTC+1 skrev mitchr...@gmail.com:
> > > > On Saturday, December 4, 2021 at 12:06:18 AM UTC-8, FromTheRafters wrote:
> > > > > Chris M. Thomasson wrote :
> > > > > > On 12/2/2021 7:29 PM, Serg io wrote:
> > > > > >> On 12/2/2021 4:42 PM, Chris M. Thomasson wrote:
> > > > > >>> On 12/2/2021 2:38 PM, Chris M. Thomasson wrote:
> > > > > >>>> On 12/2/2021 2:15 PM, FromTheRafters wrote:
> > > > > >>>>> Chris M. Thomasson submitted this idea :
> > > > > >>>>>> On 12/2/2021 10:38 AM, mitchr...@gmail.com wrote:
> > > > > >>>>>>> On Thursday, December 2, 2021 at 5:20:12 AM UTC-8, Serg io wrote:
> > > > > >>>>>>>> On 12/1/2021 10:34 PM, Chris M. Thomasson wrote:
> > > > > >>>>>>>>> On 12/1/2021 8:06 PM, Serg io wrote:
> > > > > >>>>>>>>>> On 12/1/2021 5:57 PM, mitchr...@gmail.com wrote:
> > > > > >>>>>>>>>>> On Wednesday, December 1, 2021 at 3:07:47 PM UTC-8, Michael
> > > > > >>>>>>>>>>> Moroney wrote:
> > > > > >>>>>>>>>>>> On 12/1/2021 3:46 PM, mitchr...@gmail.com wrote:
> > > > > >>>>>>>>>>>>> you get .999 repeating again not 1 instead...
> > > > > >>>>>>>>>>>>>
> > > > > >>>>>>>>>>>> I get 1.
> > > > > >>>>>>>>>>>
> > > > > >>>>>>>>>>> You don't get it...
> > > > > >>>>>>>>>>>
> > > > > >>>>>>>>>>
> > > > > >>>>>>>>>> just use 1 base(.999 repeating) = 1
> > > > > >>>>>>>>>
> > > > > >>>>>>>>> .999 repeating is the representation of 1 in base 10.
> > > > > >>>>>>>> I see the mistake;
> > > > > >>>>>>>>
> > > > > >>>>>>>> .999repeating in base(.999 repeating) = 1
> > > > > >>>>>>>
> > > > > >>>>>>> ..999 repeating does not reach1.
> > > > > >>>>>>
> > > > > >>>>>> If you take it on a step-by-step basis, yeah, you are correct.
> > > > > >>>>>
> > > > > >>>>> How does a number reach?
> > > > > >>>>
> > > > > >>>> On a step-by-step basis, say:
> > > > > >>>>
> > > > > >>>> 1 = .9 = false
> > > > > >>>> 1 = .99 = false
> > > > > >>>> 1 = .999 = false
> > > > > >>>> 1 = .9999 = false
> > > > > >>>>
> > > > > >>>> We will never get there. However, it does get infinitely close to 1...
> > > > > >>>
> > > > > >>> On a step-by-step basis:
> > > > > >>>
> > > > > >>> 1 = .9 + .1 = true
> > > > > >>> 1 = .99 + .01 = true
> > > > > >>> 1 = .999 + .001 = true
> > > > > >>> 1 = .9999 + .0001 = true
> > > > > >>>
> > > > > >>> lol. ;^)
> > > > > >>
> > > > > >>
> > > > > >>
> > > > > >> by golly! that IS the solution!
> > > > > >>
> > > > > >>
> > > > > >> so 1 = .999 repeating + 0 = true
> > > > > >
> > > > > > .999... is one of the ways for base 10 to represent 1. just writing 1 is
> > > > > > another, one. ;^)
> > > > > >
> > > > > > Its limit is 1, it is one. Okay. Then for fun, sometimes I imagine a fantasy
> > > > > > scenario that involves two beings that live forever... lol... ;^)
> > > > > >
> > > > > > Being_0 tells Being_1 to report when the following recursion equals one:
> > > > > >
> > > > > > r[0] = .9 / 10^0 = .9
> > > > > > r[1] = r[0] + .9 / 10^1 = 0.99
> > > > > > r[2] = r[1] + .9 / 10^2 = 0.999
> > > > > > r[3] = r[2] + .9 / 10^3 = 0.9999
> > > > > > r[4] = r[3] + .9 / 10^4 = 0.99999
> > > > > > ...
> > > > > >
> > > > > > Basically:
> > > > > >
> > > > > > r[0] = .9 / 10^0 = .9
> > > > > > r[n] = r[n - 1] + .9 / 10^[n]
> > > > > >
> > > > > > At what iteration n will Being_1 report to Being_0 that r[n] is equal to
> > > > > > zero?
> > > > > >
> > > > > > ;^)
> > > > > It won't. It only gives a successively better rational approximation
> > > > > with each iteration.
> > > > .999 repeating and the first integer are not the same quantity.
> > > > They share a different kind of equality. One that is by the
> > > > beginning quantity of Calculus...
> > > >
> > > > Mitchell Raemsch
> > > they are the same, get over it
> > Plot them on a number line...
> > Not the same quantity just closest to one another on a number line instead...
> >
> > Mitchell Raemsch
> They are the exact same line so yes, still the same.

No. They are separate on a number line...

Re: .999 repeating add zero

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by: zelos...@gmail.com - Thu, 9 Dec 2021 05:33 UTC

onsdag 8 december 2021 kl. 21:10:16 UTC+1 skrev mitchr...@gmail.com:
> On Tuesday, December 7, 2021 at 9:36:40 PM UTC-8, zelos...@gmail.com wrote:
> > tisdag 7 december 2021 kl. 19:40:36 UTC+1 skrev mitchr...@gmail.com:
> > > On Sunday, December 5, 2021 at 9:28:39 PM UTC-8, zelos...@gmail.com wrote:
> > > > lördag 4 december 2021 kl. 22:00:44 UTC+1 skrev mitchr...@gmail.com:
> > > > > On Saturday, December 4, 2021 at 12:06:18 AM UTC-8, FromTheRafters wrote:
> > > > > > Chris M. Thomasson wrote :
> > > > > > > On 12/2/2021 7:29 PM, Serg io wrote:
> > > > > > >> On 12/2/2021 4:42 PM, Chris M. Thomasson wrote:
> > > > > > >>> On 12/2/2021 2:38 PM, Chris M. Thomasson wrote:
> > > > > > >>>> On 12/2/2021 2:15 PM, FromTheRafters wrote:
> > > > > > >>>>> Chris M. Thomasson submitted this idea :
> > > > > > >>>>>> On 12/2/2021 10:38 AM, mitchr...@gmail.com wrote:
> > > > > > >>>>>>> On Thursday, December 2, 2021 at 5:20:12 AM UTC-8, Serg io wrote:
> > > > > > >>>>>>>> On 12/1/2021 10:34 PM, Chris M. Thomasson wrote:
> > > > > > >>>>>>>>> On 12/1/2021 8:06 PM, Serg io wrote:
> > > > > > >>>>>>>>>> On 12/1/2021 5:57 PM, mitchr...@gmail.com wrote:
> > > > > > >>>>>>>>>>> On Wednesday, December 1, 2021 at 3:07:47 PM UTC-8, Michael
> > > > > > >>>>>>>>>>> Moroney wrote:
> > > > > > >>>>>>>>>>>> On 12/1/2021 3:46 PM, mitchr...@gmail.com wrote:
> > > > > > >>>>>>>>>>>>> you get .999 repeating again not 1 instead...
> > > > > > >>>>>>>>>>>>>
> > > > > > >>>>>>>>>>>> I get 1.
> > > > > > >>>>>>>>>>>
> > > > > > >>>>>>>>>>> You don't get it...
> > > > > > >>>>>>>>>>>
> > > > > > >>>>>>>>>>
> > > > > > >>>>>>>>>> just use 1 base(.999 repeating) = 1
> > > > > > >>>>>>>>>
> > > > > > >>>>>>>>> .999 repeating is the representation of 1 in base 10.
> > > > > > >>>>>>>> I see the mistake;
> > > > > > >>>>>>>>
> > > > > > >>>>>>>> .999repeating in base(.999 repeating) = 1
> > > > > > >>>>>>>
> > > > > > >>>>>>> ..999 repeating does not reach1.
> > > > > > >>>>>>
> > > > > > >>>>>> If you take it on a step-by-step basis, yeah, you are correct.
> > > > > > >>>>>
> > > > > > >>>>> How does a number reach?
> > > > > > >>>>
> > > > > > >>>> On a step-by-step basis, say:
> > > > > > >>>>
> > > > > > >>>> 1 = .9 = false
> > > > > > >>>> 1 = .99 = false
> > > > > > >>>> 1 = .999 = false
> > > > > > >>>> 1 = .9999 = false
> > > > > > >>>>
> > > > > > >>>> We will never get there. However, it does get infinitely close to 1...
> > > > > > >>>
> > > > > > >>> On a step-by-step basis:
> > > > > > >>>
> > > > > > >>> 1 = .9 + .1 = true
> > > > > > >>> 1 = .99 + .01 = true
> > > > > > >>> 1 = .999 + .001 = true
> > > > > > >>> 1 = .9999 + .0001 = true
> > > > > > >>>
> > > > > > >>> lol. ;^)
> > > > > > >>
> > > > > > >>
> > > > > > >>
> > > > > > >> by golly! that IS the solution!
> > > > > > >>
> > > > > > >>
> > > > > > >> so 1 = .999 repeating + 0 = true
> > > > > > >
> > > > > > > .999... is one of the ways for base 10 to represent 1. just writing 1 is
> > > > > > > another, one. ;^)
> > > > > > >
> > > > > > > Its limit is 1, it is one. Okay. Then for fun, sometimes I imagine a fantasy
> > > > > > > scenario that involves two beings that live forever... lol... ;^)
> > > > > > >
> > > > > > > Being_0 tells Being_1 to report when the following recursion equals one:
> > > > > > >
> > > > > > > r[0] = .9 / 10^0 = .9
> > > > > > > r[1] = r[0] + .9 / 10^1 = 0.99
> > > > > > > r[2] = r[1] + .9 / 10^2 = 0.999
> > > > > > > r[3] = r[2] + .9 / 10^3 = 0.9999
> > > > > > > r[4] = r[3] + .9 / 10^4 = 0.99999
> > > > > > > ...
> > > > > > >
> > > > > > > Basically:
> > > > > > >
> > > > > > > r[0] = .9 / 10^0 = .9
> > > > > > > r[n] = r[n - 1] + .9 / 10^[n]
> > > > > > >
> > > > > > > At what iteration n will Being_1 report to Being_0 that r[n] is equal to
> > > > > > > zero?
> > > > > > >
> > > > > > > ;^)
> > > > > > It won't. It only gives a successively better rational approximation
> > > > > > with each iteration.
> > > > > .999 repeating and the first integer are not the same quantity.
> > > > > They share a different kind of equality. One that is by the
> > > > > beginning quantity of Calculus...
> > > > >
> > > > > Mitchell Raemsch
> > > > they are the same, get over it
> > > Plot them on a number line...
> > > Not the same quantity just closest to one another on a number line instead...
> > >
> > > Mitchell Raemsch
> > They are the exact same line so yes, still the same.
> No. They are separate on a number line...
nope, they are same line cause they are equal

Re: .999 repeating add zero

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Subject: Re: .999 repeating add zero
From: timbandt...@gmail.com (Timothy Golden)
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by: Timothy Golden - Thu, 9 Dec 2021 11:46 UTC

On Wednesday, December 8, 2021 at 3:10:16 PM UTC-5, mitchr...@gmail.com wrote:
> On Tuesday, December 7, 2021 at 9:36:40 PM UTC-8, zelos...@gmail.com wrote:
> > tisdag 7 december 2021 kl. 19:40:36 UTC+1 skrev mitchr...@gmail.com:
> > > On Sunday, December 5, 2021 at 9:28:39 PM UTC-8, zelos...@gmail.com wrote:
> > > > lördag 4 december 2021 kl. 22:00:44 UTC+1 skrev mitchr...@gmail.com:
> > > > > On Saturday, December 4, 2021 at 12:06:18 AM UTC-8, FromTheRafters wrote:
> > > > > > Chris M. Thomasson wrote :
> > > > > > > On 12/2/2021 7:29 PM, Serg io wrote:
> > > > > > >> On 12/2/2021 4:42 PM, Chris M. Thomasson wrote:
> > > > > > >>> On 12/2/2021 2:38 PM, Chris M. Thomasson wrote:
> > > > > > >>>> On 12/2/2021 2:15 PM, FromTheRafters wrote:
> > > > > > >>>>> Chris M. Thomasson submitted this idea :
> > > > > > >>>>>> On 12/2/2021 10:38 AM, mitchr...@gmail.com wrote:
> > > > > > >>>>>>> On Thursday, December 2, 2021 at 5:20:12 AM UTC-8, Serg io wrote:
> > > > > > >>>>>>>> On 12/1/2021 10:34 PM, Chris M. Thomasson wrote:
> > > > > > >>>>>>>>> On 12/1/2021 8:06 PM, Serg io wrote:
> > > > > > >>>>>>>>>> On 12/1/2021 5:57 PM, mitchr...@gmail.com wrote:
> > > > > > >>>>>>>>>>> On Wednesday, December 1, 2021 at 3:07:47 PM UTC-8, Michael
> > > > > > >>>>>>>>>>> Moroney wrote:
> > > > > > >>>>>>>>>>>> On 12/1/2021 3:46 PM, mitchr...@gmail.com wrote:
> > > > > > >>>>>>>>>>>>> you get .999 repeating again not 1 instead...
> > > > > > >>>>>>>>>>>>>
> > > > > > >>>>>>>>>>>> I get 1.
> > > > > > >>>>>>>>>>>
> > > > > > >>>>>>>>>>> You don't get it...
> > > > > > >>>>>>>>>>>
> > > > > > >>>>>>>>>>
> > > > > > >>>>>>>>>> just use 1 base(.999 repeating) = 1
> > > > > > >>>>>>>>>
> > > > > > >>>>>>>>> .999 repeating is the representation of 1 in base 10.
> > > > > > >>>>>>>> I see the mistake;
> > > > > > >>>>>>>>
> > > > > > >>>>>>>> .999repeating in base(.999 repeating) = 1
> > > > > > >>>>>>>
> > > > > > >>>>>>> ..999 repeating does not reach1.
> > > > > > >>>>>>
> > > > > > >>>>>> If you take it on a step-by-step basis, yeah, you are correct.
> > > > > > >>>>>
> > > > > > >>>>> How does a number reach?
> > > > > > >>>>
> > > > > > >>>> On a step-by-step basis, say:
> > > > > > >>>>
> > > > > > >>>> 1 = .9 = false
> > > > > > >>>> 1 = .99 = false
> > > > > > >>>> 1 = .999 = false
> > > > > > >>>> 1 = .9999 = false
> > > > > > >>>>
> > > > > > >>>> We will never get there. However, it does get infinitely close to 1...
> > > > > > >>>
> > > > > > >>> On a step-by-step basis:
> > > > > > >>>
> > > > > > >>> 1 = .9 + .1 = true
> > > > > > >>> 1 = .99 + .01 = true
> > > > > > >>> 1 = .999 + .001 = true
> > > > > > >>> 1 = .9999 + .0001 = true
> > > > > > >>>
> > > > > > >>> lol. ;^)
> > > > > > >>
> > > > > > >>
> > > > > > >>
> > > > > > >> by golly! that IS the solution!
> > > > > > >>
> > > > > > >>
> > > > > > >> so 1 = .999 repeating + 0 = true
> > > > > > >
> > > > > > > .999... is one of the ways for base 10 to represent 1. just writing 1 is
> > > > > > > another, one. ;^)
> > > > > > >
> > > > > > > Its limit is 1, it is one. Okay. Then for fun, sometimes I imagine a fantasy
> > > > > > > scenario that involves two beings that live forever... lol... ;^)
> > > > > > >
> > > > > > > Being_0 tells Being_1 to report when the following recursion equals one:
> > > > > > >
> > > > > > > r[0] = .9 / 10^0 = .9
> > > > > > > r[1] = r[0] + .9 / 10^1 = 0.99
> > > > > > > r[2] = r[1] + .9 / 10^2 = 0.999
> > > > > > > r[3] = r[2] + .9 / 10^3 = 0.9999
> > > > > > > r[4] = r[3] + .9 / 10^4 = 0.99999
> > > > > > > ...
> > > > > > >
> > > > > > > Basically:
> > > > > > >
> > > > > > > r[0] = .9 / 10^0 = .9
> > > > > > > r[n] = r[n - 1] + .9 / 10^[n]
> > > > > > >
> > > > > > > At what iteration n will Being_1 report to Being_0 that r[n] is equal to
> > > > > > > zero?
> > > > > > >
> > > > > > > ;^)
> > > > > > It won't. It only gives a successively better rational approximation
> > > > > > with each iteration.
> > > > > .999 repeating and the first integer are not the same quantity.
> > > > > They share a different kind of equality. One that is by the
> > > > > beginning quantity of Calculus...
> > > > >
> > > > > Mitchell Raemsch
> > > > they are the same, get over it
> > > Plot them on a number line...
> > > Not the same quantity just closest to one another on a number line instead...
> > >
> > > Mitchell Raemsch
> > They are the exact same line so yes, still the same.
> No. They are separate on a number line...

I've been reading Richard Dedekind, and the Dedekind cut and its interpretation is relevant here I think.
No doubt students do bring this to their math teachers regularly.
Cut the real line at 1 so as to keep 1 on the high side.
It is rare to be able to name a number's predecessor, but clearly
0.99999...
is that number. So it is possible that this counterexample does have some influence.
As we admit that 0.99999... is unity then we are admitting that a cut does in fact leave the same value on either side. It was clear already that the values are awfully close, but this would secure yet another freedom of the cut, and how one ever could land so precisely on a continuum... only the mathematician can manage that one.

Re: .999 repeating add zero

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From: erra...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: .999 repeating add zero
Date: Thu, 09 Dec 2021 06:54:42 -0500
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by: FromTheRafters - Thu, 9 Dec 2021 11:54 UTC

Timothy Golden used his keyboard to write :
> On Wednesday, December 8, 2021 at 3:10:16 PM UTC-5, mitchr...@gmail.com
> wrote:
>> On Tuesday, December 7, 2021 at 9:36:40 PM UTC-8, zelos...@gmail.com wrote:
>>> tisdag 7 december 2021 kl. 19:40:36 UTC+1 skrev mitchr...@gmail.com:
>>>> On Sunday, December 5, 2021 at 9:28:39 PM UTC-8, zelos...@gmail.com wrote:
>>>>> lördag 4 december 2021 kl. 22:00:44 UTC+1 skrev mitchr...@gmail.com:
>>>>>> On Saturday, December 4, 2021 at 12:06:18 AM UTC-8, FromTheRafters
>>>>>> wrote:
>>>>>>> Chris M. Thomasson wrote :
>>>>>>>> On 12/2/2021 7:29 PM, Serg io wrote:
>>>>>>>>> On 12/2/2021 4:42 PM, Chris M. Thomasson wrote:
>>>>>>>>>> On 12/2/2021 2:38 PM, Chris M. Thomasson wrote:
>>>>>>>>>>> On 12/2/2021 2:15 PM, FromTheRafters wrote:
>>>>>>>>>>>> Chris M. Thomasson submitted this idea :
>>>>>>>>>>>>> On 12/2/2021 10:38 AM, mitchr...@gmail.com wrote:
>>>>>>>>>>>>>> On Thursday, December 2, 2021 at 5:20:12 AM UTC-8, Serg io
>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>> On 12/1/2021 10:34 PM, Chris M. Thomasson wrote:
>>>>>>>>>>>>>>>> On 12/1/2021 8:06 PM, Serg io wrote:
>>>>>>>>>>>>>>>>> On 12/1/2021 5:57 PM, mitchr...@gmail.com wrote:
>>>>>>>>>>>>>>>>>> On Wednesday, December 1, 2021 at 3:07:47 PM UTC-8, Michael
>>>>>>>>>>>>>>>>>> Moroney wrote:
>>>>>>>>>>>>>>>>>>> On 12/1/2021 3:46 PM, mitchr...@gmail.com wrote:
>>>>>>>>>>>>>>>>>>>> you get .999 repeating again not 1 instead...
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> I get 1.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> You don't get it...
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> just use 1 base(.999 repeating) = 1
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> .999 repeating is the representation of 1 in base 10.
>>>>>>>>>>>>>>> I see the mistake;
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> .999repeating in base(.999 repeating) = 1
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> ..999 repeating does not reach1.
>>>>>>>>>>>>>
>>>>>>>>>>>>> If you take it on a step-by-step basis, yeah, you are correct.
>>>>>>>>>>>>
>>>>>>>>>>>> How does a number reach?
>>>>>>>>>>>
>>>>>>>>>>> On a step-by-step basis, say:
>>>>>>>>>>>
>>>>>>>>>>> 1 = .9 = false
>>>>>>>>>>> 1 = .99 = false
>>>>>>>>>>> 1 = .999 = false
>>>>>>>>>>> 1 = .9999 = false
>>>>>>>>>>>
>>>>>>>>>>> We will never get there. However, it does get infinitely close to
>>>>>>>>>>> 1...
>>>>>>>>>>
>>>>>>>>>> On a step-by-step basis:
>>>>>>>>>>
>>>>>>>>>> 1 = .9 + .1 = true
>>>>>>>>>> 1 = .99 + .01 = true
>>>>>>>>>> 1 = .999 + .001 = true
>>>>>>>>>> 1 = .9999 + .0001 = true
>>>>>>>>>>
>>>>>>>>>> lol. ;^)
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> by golly! that IS the solution!
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> so 1 = .999 repeating + 0 = true
>>>>>>>>
>>>>>>>> .999... is one of the ways for base 10 to represent 1. just writing 1
>>>>>>>> is another, one. ;^)
>>>>>>>>
>>>>>>>> Its limit is 1, it is one. Okay. Then for fun, sometimes I imagine a
>>>>>>>> fantasy scenario that involves two beings that live forever... lol...
>>>>>>>> ;^)
>>>>>>>>
>>>>>>>> Being_0 tells Being_1 to report when the following recursion equals
>>>>>>>> one:
>>>>>>>>
>>>>>>>> r[0] = .9 / 10^0 = .9
>>>>>>>> r[1] = r[0] + .9 / 10^1 = 0.99
>>>>>>>> r[2] = r[1] + .9 / 10^2 = 0.999
>>>>>>>> r[3] = r[2] + .9 / 10^3 = 0.9999
>>>>>>>> r[4] = r[3] + .9 / 10^4 = 0.99999
>>>>>>>> ...
>>>>>>>>
>>>>>>>> Basically:
>>>>>>>>
>>>>>>>> r[0] = .9 / 10^0 = .9
>>>>>>>> r[n] = r[n - 1] + .9 / 10^[n]
>>>>>>>>
>>>>>>>> At what iteration n will Being_1 report to Being_0 that r[n] is equal
>>>>>>>> to zero?
>>>>>>>>
>>>>>>>> ;^)
>>>>>>> It won't. It only gives a successively better rational approximation
>>>>>>> with each iteration.
>>>>>> .999 repeating and the first integer are not the same quantity.
>>>>>> They share a different kind of equality. One that is by the
>>>>>> beginning quantity of Calculus...
>>>>>>
>>>>>> Mitchell Raemsch
>>>>> they are the same, get over it
>>>> Plot them on a number line...
>>>> Not the same quantity just closest to one another on a number line
>>>> instead...
>>>>
>>>> Mitchell Raemsch
>>> They are the exact same line so yes, still the same.
>> No. They are separate on a number line...
>
> I've been reading Richard Dedekind, and the Dedekind cut and its
> interpretation is relevant here I think. No doubt students do bring this to
> their math teachers regularly. Cut the real line at 1 so as to keep 1 on the
> high side. It is rare to be able to name a number's predecessor, but clearly
> 0.99999...
> is that number.

That representation does not precede the other representation.

Re: .999 repeating add zero

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Subject: Re: .999 repeating add zero
From: timbandt...@gmail.com (Timothy Golden)
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by: Timothy Golden - Thu, 9 Dec 2021 12:12 UTC

On Thursday, December 9, 2021 at 6:55:31 AM UTC-5, FromTheRafters wrote:
> Timothy Golden used his keyboard to write :
> > On Wednesday, December 8, 2021 at 3:10:16 PM UTC-5, mitchr...@gmail.com
> > wrote:
> >> On Tuesday, December 7, 2021 at 9:36:40 PM UTC-8, zelos...@gmail.com wrote:
> >>> tisdag 7 december 2021 kl. 19:40:36 UTC+1 skrev mitchr...@gmail.com:
> >>>> On Sunday, December 5, 2021 at 9:28:39 PM UTC-8, zelos...@gmail.com wrote:
> >>>>> lördag 4 december 2021 kl. 22:00:44 UTC+1 skrev mitchr...@gmail.com:
> >>>>>> On Saturday, December 4, 2021 at 12:06:18 AM UTC-8, FromTheRafters
> >>>>>> wrote:
> >>>>>>> Chris M. Thomasson wrote :
> >>>>>>>> On 12/2/2021 7:29 PM, Serg io wrote:
> >>>>>>>>> On 12/2/2021 4:42 PM, Chris M. Thomasson wrote:
> >>>>>>>>>> On 12/2/2021 2:38 PM, Chris M. Thomasson wrote:
> >>>>>>>>>>> On 12/2/2021 2:15 PM, FromTheRafters wrote:
> >>>>>>>>>>>> Chris M. Thomasson submitted this idea :
> >>>>>>>>>>>>> On 12/2/2021 10:38 AM, mitchr...@gmail.com wrote:
> >>>>>>>>>>>>>> On Thursday, December 2, 2021 at 5:20:12 AM UTC-8, Serg io
> >>>>>>>>>>>>>> wrote:
> >>>>>>>>>>>>>>> On 12/1/2021 10:34 PM, Chris M. Thomasson wrote:
> >>>>>>>>>>>>>>>> On 12/1/2021 8:06 PM, Serg io wrote:
> >>>>>>>>>>>>>>>>> On 12/1/2021 5:57 PM, mitchr...@gmail.com wrote:
> >>>>>>>>>>>>>>>>>> On Wednesday, December 1, 2021 at 3:07:47 PM UTC-8, Michael
> >>>>>>>>>>>>>>>>>> Moroney wrote:
> >>>>>>>>>>>>>>>>>>> On 12/1/2021 3:46 PM, mitchr...@gmail.com wrote:
> >>>>>>>>>>>>>>>>>>>> you get .999 repeating again not 1 instead...
> >>>>>>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>>>>> I get 1.
> >>>>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>>>> You don't get it...
> >>>>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>>> just use 1 base(.999 repeating) = 1
> >>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>> .999 repeating is the representation of 1 in base 10.
> >>>>>>>>>>>>>>> I see the mistake;
> >>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>> .999repeating in base(.999 repeating) = 1
> >>>>>>>>>>>>>>
> >>>>>>>>>>>>>> ..999 repeating does not reach1.
> >>>>>>>>>>>>>
> >>>>>>>>>>>>> If you take it on a step-by-step basis, yeah, you are correct.
> >>>>>>>>>>>>
> >>>>>>>>>>>> How does a number reach?
> >>>>>>>>>>>
> >>>>>>>>>>> On a step-by-step basis, say:
> >>>>>>>>>>>
> >>>>>>>>>>> 1 = .9 = false
> >>>>>>>>>>> 1 = .99 = false
> >>>>>>>>>>> 1 = .999 = false
> >>>>>>>>>>> 1 = .9999 = false
> >>>>>>>>>>>
> >>>>>>>>>>> We will never get there. However, it does get infinitely close to
> >>>>>>>>>>> 1...
> >>>>>>>>>>
> >>>>>>>>>> On a step-by-step basis:
> >>>>>>>>>>
> >>>>>>>>>> 1 = .9 + .1 = true
> >>>>>>>>>> 1 = .99 + .01 = true
> >>>>>>>>>> 1 = .999 + .001 = true
> >>>>>>>>>> 1 = .9999 + .0001 = true
> >>>>>>>>>>
> >>>>>>>>>> lol. ;^)
> >>>>>>>>>
> >>>>>>>>>
> >>>>>>>>>
> >>>>>>>>> by golly! that IS the solution!
> >>>>>>>>>
> >>>>>>>>>
> >>>>>>>>> so 1 = .999 repeating + 0 = true
> >>>>>>>>
> >>>>>>>> .999... is one of the ways for base 10 to represent 1. just writing 1
> >>>>>>>> is another, one. ;^)
> >>>>>>>>
> >>>>>>>> Its limit is 1, it is one. Okay. Then for fun, sometimes I imagine a
> >>>>>>>> fantasy scenario that involves two beings that live forever... lol...
> >>>>>>>> ;^)
> >>>>>>>>
> >>>>>>>> Being_0 tells Being_1 to report when the following recursion equals
> >>>>>>>> one:
> >>>>>>>>
> >>>>>>>> r[0] = .9 / 10^0 = .9
> >>>>>>>> r[1] = r[0] + .9 / 10^1 = 0.99
> >>>>>>>> r[2] = r[1] + .9 / 10^2 = 0.999
> >>>>>>>> r[3] = r[2] + .9 / 10^3 = 0.9999
> >>>>>>>> r[4] = r[3] + .9 / 10^4 = 0.99999
> >>>>>>>> ...
> >>>>>>>>
> >>>>>>>> Basically:
> >>>>>>>>
> >>>>>>>> r[0] = .9 / 10^0 = .9
> >>>>>>>> r[n] = r[n - 1] + .9 / 10^[n]
> >>>>>>>>
> >>>>>>>> At what iteration n will Being_1 report to Being_0 that r[n] is equal
> >>>>>>>> to zero?
> >>>>>>>>
> >>>>>>>> ;^)
> >>>>>>> It won't. It only gives a successively better rational approximation
> >>>>>>> with each iteration.
> >>>>>> .999 repeating and the first integer are not the same quantity.
> >>>>>> They share a different kind of equality. One that is by the
> >>>>>> beginning quantity of Calculus...
> >>>>>>
> >>>>>> Mitchell Raemsch
> >>>>> they are the same, get over it
> >>>> Plot them on a number line...
> >>>> Not the same quantity just closest to one another on a number line
> >>>> instead...
> >>>>
> >>>> Mitchell Raemsch
> >>> They are the exact same line so yes, still the same.
> >> No. They are separate on a number line...
> >
> > I've been reading Richard Dedekind, and the Dedekind cut and its
> > interpretation is relevant here I think. No doubt students do bring this to
> > their math teachers regularly. Cut the real line at 1 so as to keep 1 on the
> > high side. It is rare to be able to name a number's predecessor, but clearly
> > 0.99999...
> > is that number.
> That representation does not precede the other representation.

And so under this interpretation that you sleazily make here Dedekind is falsified.

Re: .999 repeating add zero

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From: erra...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: .999 repeating add zero
Date: Thu, 09 Dec 2021 08:04:45 -0500
Organization: Peripheral Visions
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by: FromTheRafters - Thu, 9 Dec 2021 13:04 UTC

Timothy Golden presented the following explanation :
> On Thursday, December 9, 2021 at 6:55:31 AM UTC-5, FromTheRafters wrote:
>> Timothy Golden used his keyboard to write :
>>> On Wednesday, December 8, 2021 at 3:10:16 PM UTC-5, mitchr...@gmail.com
>>> wrote:
>>>> On Tuesday, December 7, 2021 at 9:36:40 PM UTC-8, zelos...@gmail.com
>>>> wrote:
>>>>> tisdag 7 december 2021 kl. 19:40:36 UTC+1 skrev mitchr...@gmail.com:
>>>>>> On Sunday, December 5, 2021 at 9:28:39 PM UTC-8, zelos...@gmail.com
>>>>>> wrote:
>>>>>>> lördag 4 december 2021 kl. 22:00:44 UTC+1 skrev mitchr...@gmail.com:
>>>>>>>> On Saturday, December 4, 2021 at 12:06:18 AM UTC-8, FromTheRafters
>>>>>>>> wrote:
>>>>>>>>> Chris M. Thomasson wrote :
>>>>>>>>>> On 12/2/2021 7:29 PM, Serg io wrote:
>>>>>>>>>>> On 12/2/2021 4:42 PM, Chris M. Thomasson wrote:
>>>>>>>>>>>> On 12/2/2021 2:38 PM, Chris M. Thomasson wrote:
>>>>>>>>>>>>> On 12/2/2021 2:15 PM, FromTheRafters wrote:
>>>>>>>>>>>>>> Chris M. Thomasson submitted this idea :
>>>>>>>>>>>>>>> On 12/2/2021 10:38 AM, mitchr...@gmail.com wrote:
>>>>>>>>>>>>>>>> On Thursday, December 2, 2021 at 5:20:12 AM UTC-8, Serg io
>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>> On 12/1/2021 10:34 PM, Chris M. Thomasson wrote:
>>>>>>>>>>>>>>>>>> On 12/1/2021 8:06 PM, Serg io wrote:
>>>>>>>>>>>>>>>>>>> On 12/1/2021 5:57 PM, mitchr...@gmail.com wrote:
>>>>>>>>>>>>>>>>>>>> On Wednesday, December 1, 2021 at 3:07:47 PM UTC-8,
>>>>>>>>>>>>>>>>>>>> Michael Moroney wrote:
>>>>>>>>>>>>>>>>>>>>> On 12/1/2021 3:46 PM, mitchr...@gmail.com wrote:
>>>>>>>>>>>>>>>>>>>>>> you get .999 repeating again not 1 instead...
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> I get 1.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> You don't get it...
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> just use 1 base(.999 repeating) = 1
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> .999 repeating is the representation of 1 in base 10.
>>>>>>>>>>>>>>>>> I see the mistake;
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> .999repeating in base(.999 repeating) = 1
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> ..999 repeating does not reach1.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> If you take it on a step-by-step basis, yeah, you are correct.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> How does a number reach?
>>>>>>>>>>>>>
>>>>>>>>>>>>> On a step-by-step basis, say:
>>>>>>>>>>>>>
>>>>>>>>>>>>> 1 = .9 = false
>>>>>>>>>>>>> 1 = .99 = false
>>>>>>>>>>>>> 1 = .999 = false
>>>>>>>>>>>>> 1 = .9999 = false
>>>>>>>>>>>>>
>>>>>>>>>>>>> We will never get there. However, it does get infinitely close to
>>>>>>>>>>>>> 1...
>>>>>>>>>>>>
>>>>>>>>>>>> On a step-by-step basis:
>>>>>>>>>>>>
>>>>>>>>>>>> 1 = .9 + .1 = true
>>>>>>>>>>>> 1 = .99 + .01 = true
>>>>>>>>>>>> 1 = .999 + .001 = true
>>>>>>>>>>>> 1 = .9999 + .0001 = true
>>>>>>>>>>>>
>>>>>>>>>>>> lol. ;^)
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> by golly! that IS the solution!
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> so 1 = .999 repeating + 0 = true
>>>>>>>>>>
>>>>>>>>>> .999... is one of the ways for base 10 to represent 1. just writing
>>>>>>>>>> 1 is another, one. ;^)
>>>>>>>>>>
>>>>>>>>>> Its limit is 1, it is one. Okay. Then for fun, sometimes I imagine a
>>>>>>>>>> fantasy scenario that involves two beings that live forever...
>>>>>>>>>> lol... ;^)
>>>>>>>>>>
>>>>>>>>>> Being_0 tells Being_1 to report when the following recursion equals
>>>>>>>>>> one:
>>>>>>>>>>
>>>>>>>>>> r[0] = .9 / 10^0 = .9
>>>>>>>>>> r[1] = r[0] + .9 / 10^1 = 0.99
>>>>>>>>>> r[2] = r[1] + .9 / 10^2 = 0.999
>>>>>>>>>> r[3] = r[2] + .9 / 10^3 = 0.9999
>>>>>>>>>> r[4] = r[3] + .9 / 10^4 = 0.99999
>>>>>>>>>> ...
>>>>>>>>>>
>>>>>>>>>> Basically:
>>>>>>>>>>
>>>>>>>>>> r[0] = .9 / 10^0 = .9
>>>>>>>>>> r[n] = r[n - 1] + .9 / 10^[n]
>>>>>>>>>>
>>>>>>>>>> At what iteration n will Being_1 report to Being_0 that r[n] is
>>>>>>>>>> equal to zero?
>>>>>>>>>>
>>>>>>>>>> ;^)
>>>>>>>>> It won't. It only gives a successively better rational approximation
>>>>>>>>> with each iteration.
>>>>>>>> .999 repeating and the first integer are not the same quantity.
>>>>>>>> They share a different kind of equality. One that is by the
>>>>>>>> beginning quantity of Calculus...
>>>>>>>>
>>>>>>>> Mitchell Raemsch
>>>>>>> they are the same, get over it
>>>>>> Plot them on a number line...
>>>>>> Not the same quantity just closest to one another on a number line
>>>>>> instead...
>>>>>>
>>>>>> Mitchell Raemsch
>>>>> They are the exact same line so yes, still the same.
>>>> No. They are separate on a number line...
>>>
>>> I've been reading Richard Dedekind, and the Dedekind cut and its
>>> interpretation is relevant here I think. No doubt students do bring this to
>>> their math teachers regularly. Cut the real line at 1 so as to keep 1 on
>>> the high side. It is rare to be able to name a number's predecessor, but
>>> clearly 0.99999...
>>> is that number.
>> That representation does not precede the other representation.
>
> And so under this interpretation that you sleazily make here Dedekind is
> falsified.

I don't see how that follows. Are you sleasily suggesting that there
are no rational numbers between every two distinct/different/unique
rational numbers, or is it again just the base ten fractional
positional notation you disagree with?

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Re: .999 repeating add zero

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Subject: Re: .999 repeating add zero
From: mitchrae...@gmail.com (mitchr...@gmail.com)
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by: mitchr...@gmail.com - Thu, 9 Dec 2021 19:16 UTC

On Wednesday, December 8, 2021 at 9:33:39 PM UTC-8, zelos...@gmail.com wrote:
> onsdag 8 december 2021 kl. 21:10:16 UTC+1 skrev mitchr...@gmail.com:
> > On Tuesday, December 7, 2021 at 9:36:40 PM UTC-8, zelos...@gmail.com wrote:
> > > tisdag 7 december 2021 kl. 19:40:36 UTC+1 skrev mitchr...@gmail.com:
> > > > On Sunday, December 5, 2021 at 9:28:39 PM UTC-8, zelos...@gmail.com wrote:
> > > > > lördag 4 december 2021 kl. 22:00:44 UTC+1 skrev mitchr...@gmail.com:
> > > > > > On Saturday, December 4, 2021 at 12:06:18 AM UTC-8, FromTheRafters wrote:
> > > > > > > Chris M. Thomasson wrote :
> > > > > > > > On 12/2/2021 7:29 PM, Serg io wrote:
> > > > > > > >> On 12/2/2021 4:42 PM, Chris M. Thomasson wrote:
> > > > > > > >>> On 12/2/2021 2:38 PM, Chris M. Thomasson wrote:
> > > > > > > >>>> On 12/2/2021 2:15 PM, FromTheRafters wrote:
> > > > > > > >>>>> Chris M. Thomasson submitted this idea :
> > > > > > > >>>>>> On 12/2/2021 10:38 AM, mitchr...@gmail.com wrote:
> > > > > > > >>>>>>> On Thursday, December 2, 2021 at 5:20:12 AM UTC-8, Serg io wrote:
> > > > > > > >>>>>>>> On 12/1/2021 10:34 PM, Chris M. Thomasson wrote:
> > > > > > > >>>>>>>>> On 12/1/2021 8:06 PM, Serg io wrote:
> > > > > > > >>>>>>>>>> On 12/1/2021 5:57 PM, mitchr...@gmail.com wrote:
> > > > > > > >>>>>>>>>>> On Wednesday, December 1, 2021 at 3:07:47 PM UTC-8, Michael
> > > > > > > >>>>>>>>>>> Moroney wrote:
> > > > > > > >>>>>>>>>>>> On 12/1/2021 3:46 PM, mitchr...@gmail.com wrote:
> > > > > > > >>>>>>>>>>>>> you get .999 repeating again not 1 instead...
> > > > > > > >>>>>>>>>>>>>
> > > > > > > >>>>>>>>>>>> I get 1.
> > > > > > > >>>>>>>>>>>
> > > > > > > >>>>>>>>>>> You don't get it...
> > > > > > > >>>>>>>>>>>
> > > > > > > >>>>>>>>>>
> > > > > > > >>>>>>>>>> just use 1 base(.999 repeating) = 1
> > > > > > > >>>>>>>>>
> > > > > > > >>>>>>>>> .999 repeating is the representation of 1 in base 10.
> > > > > > > >>>>>>>> I see the mistake;
> > > > > > > >>>>>>>>
> > > > > > > >>>>>>>> .999repeating in base(.999 repeating) = 1
> > > > > > > >>>>>>>
> > > > > > > >>>>>>> ..999 repeating does not reach1.
> > > > > > > >>>>>>
> > > > > > > >>>>>> If you take it on a step-by-step basis, yeah, you are correct.
> > > > > > > >>>>>
> > > > > > > >>>>> How does a number reach?
> > > > > > > >>>>
> > > > > > > >>>> On a step-by-step basis, say:
> > > > > > > >>>>
> > > > > > > >>>> 1 = .9 = false
> > > > > > > >>>> 1 = .99 = false
> > > > > > > >>>> 1 = .999 = false
> > > > > > > >>>> 1 = .9999 = false
> > > > > > > >>>>
> > > > > > > >>>> We will never get there. However, it does get infinitely close to 1...
> > > > > > > >>>
> > > > > > > >>> On a step-by-step basis:
> > > > > > > >>>
> > > > > > > >>> 1 = .9 + .1 = true
> > > > > > > >>> 1 = .99 + .01 = true
> > > > > > > >>> 1 = .999 + .001 = true
> > > > > > > >>> 1 = .9999 + .0001 = true
> > > > > > > >>>
> > > > > > > >>> lol. ;^)
> > > > > > > >>
> > > > > > > >>
> > > > > > > >>
> > > > > > > >> by golly! that IS the solution!
> > > > > > > >>
> > > > > > > >>
> > > > > > > >> so 1 = .999 repeating + 0 = true
> > > > > > > >
> > > > > > > > .999... is one of the ways for base 10 to represent 1. just writing 1 is
> > > > > > > > another, one. ;^)
> > > > > > > >
> > > > > > > > Its limit is 1, it is one. Okay. Then for fun, sometimes I imagine a fantasy
> > > > > > > > scenario that involves two beings that live forever... lol.... ;^)
> > > > > > > >
> > > > > > > > Being_0 tells Being_1 to report when the following recursion equals one:
> > > > > > > >
> > > > > > > > r[0] = .9 / 10^0 = .9
> > > > > > > > r[1] = r[0] + .9 / 10^1 = 0.99
> > > > > > > > r[2] = r[1] + .9 / 10^2 = 0.999
> > > > > > > > r[3] = r[2] + .9 / 10^3 = 0.9999
> > > > > > > > r[4] = r[3] + .9 / 10^4 = 0.99999
> > > > > > > > ...
> > > > > > > >
> > > > > > > > Basically:
> > > > > > > >
> > > > > > > > r[0] = .9 / 10^0 = .9
> > > > > > > > r[n] = r[n - 1] + .9 / 10^[n]
> > > > > > > >
> > > > > > > > At what iteration n will Being_1 report to Being_0 that r[n] is equal to
> > > > > > > > zero?
> > > > > > > >
> > > > > > > > ;^)
> > > > > > > It won't. It only gives a successively better rational approximation
> > > > > > > with each iteration.
> > > > > > .999 repeating and the first integer are not the same quantity.
> > > > > > They share a different kind of equality. One that is by the
> > > > > > beginning quantity of Calculus...
> > > > > >
> > > > > > Mitchell Raemsch
> > > > > they are the same, get over it
> > > > Plot them on a number line...
> > > > Not the same quantity just closest to one another on a number line instead...
> > > >
> > > > Mitchell Raemsch
> > > They are the exact same line so yes, still the same.
> > No. They are separate on a number line...
> nope, they are same line cause they are equal

They are separate on a number line...
or show otherwise.. .999 comes
first then the first integer after...

Mitchell Raemsch

In computing, the mean time to failure keeps getting shorter.

tech / sci.math / Re: .999 repeating add zero

tech / sci.math / Re: .999 repeating add zero

Subject	Author
.999 repeating add zero	mitchr...@gmail.com
Re: .999 repeating add zero	Michael Moroney
Re: .999 repeating add zero	mitchr...@gmail.com
Re: .999 repeating add zero	Serg io
Re: .999 repeating add zero	Chris M. Thomasson
Re: .999 repeating add zero	FromTheRafters
Re: .999 repeating add zero	Chris M. Thomasson
Re: .999 repeating add zero	Serg io
Re: .999 repeating add zero	mitchr...@gmail.com
Re: .999 repeating add zero	Chris M. Thomasson
Re: .999 repeating add zero	FromTheRafters
Re: .999 repeating add zero	Chris M. Thomasson
Re: .999 repeating add zero	Chris M. Thomasson
Re: .999 repeating add zero	Serg io
Re: .999 repeating add zero	Chris M. Thomasson
Re: .999 repeating add zero	Chris M. Thomasson
Re: .999 repeating add zero	Chris M. Thomasson
Re: .999 repeating add zero	Serg io
Re: .999 repeating add zero	FromTheRafters
Re: .999 repeating add zero	mitchr...@gmail.com
Re: .999 repeating add zero	zelos...@gmail.com
Re: .999 repeating add zero	mitchr...@gmail.com
Re: .999 repeating add zero	Serg io
Re: .999 repeating add zero	mitchr...@gmail.com
Re: .999 repeating add zero	Serg io
Re: .999 repeating add zero	mitchr...@gmail.com
Re: .999 repeating add zero	Chris M. Thomasson
Re: .999 repeating add zero	zelos...@gmail.com
Re: .999 repeating add zero	mitchr...@gmail.com
Re: .999 repeating add zero	zelos...@gmail.com
Re: .999 repeating add zero	mitchr...@gmail.com
Re: .999 repeating add zero	Timothy Golden
Re: .999 repeating add zero	FromTheRafters
Re: .999 repeating add zero	Timothy Golden
Re: .999 repeating add zero	FromTheRafters
Re: .999 repeating add zero	Jim Burns
Re: .999 repeating add zero	Serg io
Re: .999 repeating add zero	zelos...@gmail.com
Re: .999 repeating add zero	zelos...@gmail.com