Re: Does the number of nines increase?

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 :
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As was saidd, Cardinatality of infinte sets work differently than that of finite sets.

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Here is no cardinality asked for.
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A non-terminating digit sequence does not determine a real number.

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Huh? Sure it can. What is:
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.(428571) >

That is a formula determining an infinite digit sequence

 Try 3/7 represented in base 10 decimal notation ;^)
 

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? It is a non-terminating digit sequence in base ten.

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No. Like "0.111..." it is a formula.
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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

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?