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Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: The truncated harmonic series diverges.
Date: Wed, 5 Mar 2025 11:01:16 +0100
Organization: A noiseless patient Spider
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The harmonic series diverges. Kempner has shown in 1914 that all terms 
containing the digit 9 can be removed without changing the divergence.
Here is a simple derivation: https://www.hs-augsburg.de/~mueckenh/HI/ p. 15.

I think that we can remove all terms containing 1, 2, 3, 4, 5, 6, 7, 8, 
9, 0 in the denominator without changing the divergence.

Further I think we can remove every denominator containig any given 
number like 2025 without changing the divergence.

Further I think that we can remove the chain of all definable numbers 
without changing the divergence.

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

Regards, WM