Re: Does the number of nines increase?

On 6/27/2024 1:16 PM, Chris M. Thomasson wrote:

On 6/27/2024 4:49 AM, WM wrote:

Le 26/06/2024 à 12:40, FromTheRafters a écrit :

WM has brought this to us :

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Corollary-question: Does the number of nines grow when in 0.999 the decimal point is shifted by one or more position?

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What do you think multiplying by ten does to a continued decimal expansion representation?

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You must understand that no natural number can be added to the complete set.

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Of course not, a set contains *all* of its elements.

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And all are indices of the nines in 0.999... .

  r[0] = .9
r[n] = r[0] + 10^(-n) * .9

^^^^^^^^^^^^^^
Ahhh shit! Damn typos! That recursion should be:
r[n] = r[n - 1] + 10^(-n) * .9
Sorry everybody!

 lets expand it for a couple of iterations:

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