Re: Does the number of nines increase?

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.
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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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What does Simon Stevin say?
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The number of nines left of the radix grows, ....
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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.
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Numbers "have" a number and "make" a count.

...000099.999...
There are countably many nines on either side of the radix point. This is a 'representation' of a number which has a countably infinite sequence of symbols left *and* right of the radix. Left of the radix point it has countably infinitely many zeroes and finitely many non-zero symbols. Right of the radix it has countably infinitely many symbols which in this case is all nines and possibly finitely many non-zero and non-nine leading symbols.
...000100.000...
Same number but no nines.