Re: Kempner series

On 14.04.2025 14:20, joes wrote:

Am Mon, 14 Apr 2025 13:52:44 +0200 schrieb WM:

All definable sequences of digits are finite. It wouldn't be
possible to define infinitely many numbers individually.

I think it’s possible to define an infinite number sequence, like the
decimal expansion of e.

It is not possible to define all digits. The formula provides the digit at given place , but most n are dark ad therefore cannot be give.

Wrong. The denominators of the harmonic sequence are finite numbers
but the diverging part consists of numbers which are larger than all
definable numbers.

Sounds pretty infinite to me.

None is infinite. If you cannot comprehend the meaning of "definable",
then first try "defined". There are only finitely many numbers defined.

That is wrong already. The set N is infinite.
 

Since this remains so forever, there are also only finitely many numbers
definable.

Does not follow if you have infinite time.

There is no actually infinite time. Every second belongs to a finite time.
Regards, WM