Actually, I meant the series 1 + 2 + 3 + ... rather than the harmonic series. Sorry about that. This is the Wikipedia article https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_⋯ <https://en.wikipedia.org/wiki/1_+_2_+_3_+_4_+_%E2%8B%AF> Plus, I was reporting from memory — which was correct not too long ago — but apparently the non-Yahoos have finally won and the article no longer insists that a false statement is true. —Dan
On Sep 9, 2015, at 11:33 AM, Allan Wechsler <acwacw@gmail.com> wrote:
Dan, can you give a reference to which Wikipedia article has the solecism you mention? I can't see a trace of such a claim in the article "Harmonic Series (mathematics)", which was my first guess.
On Wed, Sep 9, 2015 at 2:27 PM, Dan Asimov <dasimov@earthlink.net> wrote:
This is trivial to do, so you don't need a web-reference.
But please don't label a justification for
1 - 1/2 + 1/3 - 1/4 + ... = 0.
a "proof".
People have already deeply bewildered by the recent kerfuffle about whether
1 + 1/2 + 1/3 + 1/4 + ... = -1/12
(following a YouTube video purporting to prove this) to the point that the Wikipedia article on this will not budge on the point that this is merely "true", and Terry Tao remained steadfastly ambiguous on the subject.
—Dan
On Sep 9, 2015, at 10:03 AM, James Propp <jamespropp@gmail.com> wrote:
Can anyone provide a favorite web-reference?
For my upcoming Mathematical Enchantments column, I composed a proof that 1 - 1/2 + 1/3 - 1/4 + ... is both positive and zero, but it really doesn't fit into the (already over-long) article, so I'd like to outsource the job of showing "You can get nonsensical results by rearranging conditionally convergent series" to some website that already exists.
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