I knew about it when I had bright teachers more than 80 years ago! R. On Sat, 12 Sep 2015, James Propp wrote:
That's it! THAT'S the bogus proof Mr. Brenner showed me forty years ago!
Thanks, Dan!
Can anyone give a reference? (I assume that if a high school math teacher knew about it forty years ago, someone must have written about it in print or on the web.)
By the way, I was entering the bathroom last night, and at the moment when I put my foot on the doorstep, the idea came to me, without anything in my previous thoughts having prepared me for it, that I had in the very first paragraph of my essay made a ludicrous arithmetic error, exchanging the number of bottles with the number of drinkers, so that the story problem I proposed corresponded not to the fractions I wished to compare, but rather to their reciprocals. I did not verify this, I did not have the time for it. On returning to the bedroom I verified my hunch and fixed the error to spare myself embarrassment. :-)
Jim
On Saturday, September 12, 2015, Dan Asimov <dasimov@earthlink.net> wrote:
One very bogus analysis is that
1 - 1/2 + 1/3 - 1/4 + ...
equals the difference
(1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + ...) - 2(1/2)(1 + 1/2 + 1/3 + . . .) _____________________________________________
= (1 + 1/2 + 1/3 + ...) - (1 + 1/2 + 1/3 + ...)
= 0
—Dan
On Sep 11, 2015, at 12:48 PM, James Propp <jamespropp@gmail.com <javascript:;>> wrote:
P.S. I'm sure I've seen a slicker and easier-to-follow bogus analysis of 1 - 1/2 + 1/3 - 1/4 + ... than the one I give in the End Notes; my high school math teacher Mr. Brenner showed it to me forty years ago, but for some reason I'm unable to reconstruct it. I'm sure it's out there, in print if not on the web. Can anyone provide a lead?
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