Re: sci.math FAQ and Cantors proof

From: Arturo Magidin (magidin_at_math.berkeley.edu)
Date: 09/23/04 

Date: Thu, 23 Sep 2004 15:03:51 +0000 (UTC)

In article <4152319c$0$4310$afc38c87@news.optusnet.com.au>,
Peter Webb <webbfamily@DIESPAMDIEoptusnet.com.au> wrote:
>Both sci.math and sci.logic receive many posts concerning Cantors diagonal
>proof. Many of these are common misunderstandings, which could be considered
>FAQs.

   [.snip.]

>
>Let us imagine you have a list of Real numbers that you claim has every Real
>number between 0 and 1 on it. It might look as follows:

I would suggest avoiding a proof by contradiction. Why not show that
any function f:N->R is not surjective?

   [.snip.]

>However, it doesn't. For example, 0.333. isn't on the list.

I would suggest writing "1/3" or "0.333..." rather than "0.333."; or
explain that the period at the end is meant to signify an infinite
repetition of the digit 3?

Otherwise, looks good! 

-- 
======================================================================
"It's not denial. I'm just very selective about
 what I accept as reality."
    --- Calvin ("Calvin and Hobbes")
======================================================================
Arturo Magidin
magidin@math.berkeley.edu

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