Re: Does the number of nines increase?

Le 26/06/2024 à 12:36, FromTheRafters a écrit :

Ross Finlayson has brought this to us :

On 06/25/2024 04:17 PM, FromTheRafters wrote:

WM used his keyboard to write :

Let the infinite sequence 0.999... be multiplied by 10. Does the
number of nines grow?

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No, both sequences are infinite.
>

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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What does Simon Stevin say?
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The number of nines left of the radix grows, ....

And the number right of the radix point decreases.

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Though, one might aver it's the "count" of nines,
it's also its number.
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Counting and numbering are two different things,
though they're often conflated, not to be confused.
>
Numbers "have" a number and "make" a count.

 ...000099.999...
 There are countably many nines on either side of the radix point.

"Countably" is an unsharp notion because there are countably many prime numbers and countably many algebraic numbers but obviously there are algebraic numbers which are not prime numbers but all prime numbers are algebraic numbers. So this notion too unsharp to measure the fact that {1, 2, 3, ...} has one number less than {0, 1, 2, 3, ...} although this is an obvious fact.
Regards, WM