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Topic: Another funky proof
Replies: 14   Last Post: Mar 5, 1998 7:54 AM

 Messages: [ Previous | Next ]
 Gerry Myerson Posts: 192 Registered: 12/8/04
Re: Another funky proof
Posted: Feb 26, 1998 6:10 PM

In article <Eoz9qM.FwF@exeter.ac.uk>, rjchapma@exeter.ac.uk (R.J.Chapman) wrote:

=> Peter Ammon writes:
=> > Let S = 1 + 2 + 4 + 8 + 16 + 32....
=> >
=> > Then 2S = 2 + 4 + 8 + 16 + 32 + 64.....
=> >
=> > Thus, S = 2S + 1
=> >
=> > S = -1
=> >
=> > Thus, 1 + 2 + 4 + 8 + 16 + 32... converges to -1.
=> >
=> > Q.E.D.!!! :-)
=> >
=> If you're working in the 2-adic numbers, this is fine!

Even if you're working in the integers, it's fine, as long as you use
the 2-adic valuation. No need to go to the completion.

Gerry Myerson (gerry@mpce.mq.edu.au)

Date Subject Author
2/25/98 Peter Ammon
2/25/98 Frederic Weed
2/25/98 Darrell Ryan
2/25/98 Nat Silver
2/25/98 Gerry Myerson