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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: Does the number of nines increase?
Date: Sat, 29 Jun 2024 18:06:46 -0700
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On 6/29/2024 12:11 PM, Chris M. Thomasson wrote:
> On 6/29/2024 10:01 AM, WM wrote:
>> Le 29/06/2024 à 00:23, "Chris M. Thomasson" a écrit :
>>> On 6/28/2024 6:41 AM, WM wrote:
>>>> Le 28/06/2024 à 02:03, Richard Damon a écrit :
>>>>
>>>>> As was saidd, Cardinatality of infinte sets work differently than 
>>>>> that of finite sets.
>>>>
>>>> Here is no cardinality asked for.
>>>>
>>>> A non-terminating digit sequence does not determine a real number.
>>>
>>> Huh? Sure it can. What is:
>>>
>>> .(428571) >
>> That is a formula determining an infinite digit sequence
> 
> Try 3/7 represented in base 10 decimal notation ;^)
> 
>>>
>>> ? It is a non-terminating digit sequence in base ten.
>>
>> No. Like "0.111..." it is a formula.
>>
>> Formulas determine sequences. The other way round is not possible.
> 
> Here is a simple recursive formula that creates infinite 9's during 
> iteration:
> 
> r[0] = .9
> r[n] = r[n - 1] + 10^(-n) * .9 = .(9) = 1 (limit)
> 
> let's expand:
> 
> r[0] = 0

God damn it! r[0] should be equal to .9 in this expansion! Fucking typos!


> r[1] = .9 + 10^(-1) * .9 = .99
> r[2] = .99 + 10^(-2) * .9 = .999
> r[3] = .999 + 10^(-3) * .9 = .9999
> 
> ... on and on ...
> 
> See?