Sujet : Re: Does the number of nines increase?
De : ross.a.finlayson (at) *nospam* gmail.com (Ross Finlayson)
Groupes : sci.mathDate : 30. Jun 2024, 15:48:04
Autres entêtes
Message-ID : <bvScnc3yo6e97Rz7nZ2dnZfqn_adnZ2d@giganews.com>
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On 06/30/2024 02:55 AM, FromTheRafters wrote:
WM wrote on 6/29/2024 :
Le 29/06/2024 à 11:37, FromTheRafters a écrit :
Ross Finlayson pretended :
>
You know, or it "goes" to.
>
Yes, but the number of nines in the sequence after the radix point is
countably infinite rather than finite, hence NaN in this context.
>
All nines are from the sequence 0.9, 0.09, 0.009, ... None of the ℵo
nines makes its partial sum 0,9, 0.99, 0.999, ... equal to 1
>
Yes it does, the sequence of partial sums approaches/converges to one.
This *complete* ordered field of reals guarantees cauchy sequence
convergence. See how real numbers are defined.
It's axiomatic, and about the usual open topology.
There are others, ....
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