Re: Does the number of nines increase?

Le 04/07/2024 à 05:20, Jim Burns a écrit :

On 7/3/2024 4:00 PM, WM wrote:

But it is impossible to
construct or define or find or recognize or communicate
a non-terminating decimal without using a finite formula,
and be it as simple as "0.111...".

 Answer the questions
"What is a non.terminating.decimalⁿᵒᵗᐧᵂᴹ?"  and
"What is a line.pointⁿᵒᵗᐧᵂᴹ?"
and one can prove from very reasonable assumptions
that non.terminating.decimalsⁿᵒᵗᐧᵂᴹ _exist_
and line.pointsⁿᵒᵗᐧᵂᴹ _exist_
and
a non.terminating.decimalⁿᵒᵗᐧᵂᴹ determines
no less than one real number (line.pointⁿᵒᵗᐧᵂᴹ) and
no more than one real number (line.pointⁿᵒᵗᐧᵂᴹ).

Yes, the line point is the limit of an infinite sequence.
Example: 0.999... --> 1.
But the sequence cannot be given other than by its defining formula like "0.999...".

 If it is impossible to constructᵂᴹ or defineᵂᴹ or findᵂᴹ or
  recognizeᵂᴹ or communicateᵂᴹ a non.terminating.decimalⁿᵒᵗᐧᵂᴹ

It is not impossible to construct every desired digit of the sequence. But it is impossible to do so without a finite formula. And it is impossible to desire all digits. ℵo are always missing.

because it cannot be handled with enough precision.

 Then it _exists_ and is unable to be
  handled.with.enough.precisionᵂᴹ.

It is handled by a formula, sometimes even with absolute precision like 0.999... --> 1.

 

Always almost all digits are dark.

 All.nonempty.digit.setsⁿᵒᵗᐧᵂᴹ hold a first member.
All.digitsⁿᵒᵗᐧᵂᴹ have a first.after.digit

Most are unknown.
Regards, WM