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  • The existence of dark numbers proved by the thinned out harmonic, serie

    From WM@21:1/5 to All on Wed Mar 12 07:50:55 2025
    The harmonic series diverges. Kempner has shown in 1914 that when all
    terms containing the digit 9 are removed, the series converges. Here is
    a simple derivation: https://www.hs-augsburg.de/~mueckenh/HI/ p. 15.

    That means that the terms containing 9 diverge. Same is true when all
    terms containing 8 are removed. That means all terms containing 8 and 9 simultaneously diverge.

    We can continue and remove all terms containing 1, 2, 3, 4, 5, 6, 7, 8,
    9, 0 in the denominator without changing this. That means that only the
    terms containing all these digits together constitute the diverging
    series. (*)

    But that's not the end! We can remove any number, like 2025, and the
    remaining series will converge. For proof use base 2026. This extends to
    every definable number. Therefore the diverging part of the harmonic
    series is constituted only by terms containing a digit sequence of all definable numbers.

    Note that here not only the first terms are cut off but that many
    following terms are excluded from the diverging remainder.

    This is a proof of the huge set of undefinable or dark numbers.

    (*) At this point the diverging series starts with the smallest term
    1023456789 and contains further terms like 1203456789 or 1234567891010
    or 123456789111 or 1234567891011. Only those containing the digit
    sequence 10 will survive the next step, and only those containing the
    digit sequence 1234567891011 (where the order of the first nine digits
    is irrelevant) will survive the next step.

    Regards, WM

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  • From Julio Di Egidio@21:1/5 to org on Wed Mar 12 08:31:16 2025
    On 12/03/2025 07:50, WM <invalid@no org> wrote:
    The harmonic series diverges. Kempner has shown in 1914 that when all
    terms containing the digit 9 are removed, the series converges. Here is
    a simple derivation: https://www.hs-augsburg.de/~mueckenh/HI/ p. 15.
    That means that the terms containing 9 diverge.

    The existence of chronic nazi-retarded polluters of all ponds.

    There are insanities that can only be cured by amputation, and only
    if it is not too late. WM should die a.s.a.p., but lots of people,
    especially the spammers and polluters of all ponds, meanwhile the Weltanschauung and modus operandi of our entire society, should
    simply and directly be shot in the face.

    TL;DR Stupid fucking white man...

    *Plonk*

    -Julio

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Julio Di Egidio@21:1/5 to Julio Di Egidio on Wed Mar 12 11:48:42 2025
    On 12/03/2025 08:31, Julio Di Egidio wrote:
    On 12/03/2025 07:50, WM <invalid@no org> wrote:
    The harmonic series diverges. Kempner has shown in 1914 that when all
    terms containing the digit 9 are removed, the series converges. Here
    is a simple derivation: https://www.hs-augsburg.de/~mueckenh/HI/ p. 15.
    That means that the terms containing 9 diverge.

    The existence of chronic nazi-retarded polluters of all ponds.

    There are insanities that can only be cured by amputation, and only
    if it is not too late.  WM should die a.s.a.p.,

    That's poorly phrased, to the point that I must apologise, to WM personally, even if you *are* a spammer: I meant of old age there.

    but lots of people,
    especially the spammers and polluters of all ponds, meanwhile the Weltanschauung and modus operandi of our entire society, should
    simply and directly be shot in the face.

    TL;DR  Stupid fucking white man...

    *Plonk*

    To be clear: those are insults, and the measure of my own in-sanity, as
    I don't really hate anybody.

    TL;DR  Try and do the right thing for a change.

    -Julio

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