Re: Does the number of nines increase?

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

Le 03/07/2024 à 20:24, Jim Burns a écrit :

On 6/28/2024 9:41 AM, WM wrote:

A non-terminating digit sequence
does not determine a real number.

>
A non.terminating decimal determines
no less than one real number (line.point) and
no more than one real number (line.point).

>
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).
If it is impossible to constructᵂᴹ or defineᵂᴹ or findᵂᴹ or
  recognizeᵂᴹ or communicateᵂᴹ a non.terminating.decimalⁿᵒᵗᐧᵂᴹ
then that proves that it is unnecessary to
  constructᵂᴹ or defineᵂᴹ or findᵂᴹ or recognizeᵂᴹ or
  communicateᵂᴹ a non.terminating.decimalⁿᵒᵗᐧᵂᴹ

because it cannot be handled with eniugh precision.

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

Always almost all digits are dark.

All.nonempty.digit.setsⁿᵒᵗᐧᵂᴹ hold a first member.
All.digitsⁿᵒᵗᐧᵂᴹ have a first.after.digit and a last.before.digit,
except the first.digit, which has only a first.after.digit.