Re: Does the number of nines increase?

On 6/28/2024 9:05 PM, Ross Finlayson wrote:

On 06/28/2024 02:01 PM, FromTheRafters wrote:

The number of nines is not a number.

>
I thought .999... = 1, ....

1 is near almost.all (all.but.finitely.many) of
  0.9  0.99  0.999  0.9999  0.99999  ...
for any sense > 0 of 'near'
For that reason,
we assign 1 to 0.999...
The values of infinite.length decimals
are assigned by a different method from how
the values of finite.length decimals are assigned.

You know, or it "goes" to.

<RF>

 This recalls the "First of Zen Koans" bit again,
 Two Buddhist priests observe a flag in the wind.
 The first says, "the wind, moves, the flag".
The second says, "ah, that flag, moves, in the wind."
 A third says "it is your mind that moves".
>

</RF>
Date: Fri, 28 Jun 2024 21:38:40 -0700
The sequence
  0.9  0.99  0.999  0.9999  0.99999  ...
does not move.
It is your mind that moves,
imagining the next, and the next, and the next.
Remember that
  0.9  0.99  0.999  0.9999  0.99999  ...
doesn't "go to" even Avogadroᴬᵛᵒᵍᵃᵈʳᵒ 9s
not inside our 13.8×10⁹.year.old universe.
However,
we can reason about Avogadroᴬᵛᵒᵍᵃᵈʳᵒ 9s
by finite not.first.false claim.sequence
without going to them.
It's the same for infinitely.many 9s  in that
we can't go to them,  but
we can reason about them.
But
'infinite' is different from 'humongous' and
different conclusions get concluded.