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Re: Cantor's diagonalization argument

Subject: Re: Cantor's diagonalization argument
From: "Jesse F. Hughes"
Date: Tue, 31 Oct 2006 14:49:51 -0500
Newsgroups: sci.math, sci.logic
"David R Tribble" <david@xxxxxxxxxxx> writes:

> glennlieding wrote:
>> There is no such thing as "the countable list of all reals", no matter
>> what the encoding.  There is, however, a sequence (countable set) of
>> all rational numbers.
>
> A nice little sequence I recently (re)discovered which enumerates the
> rationals:
>   S(0) =    0
>   S(2n) =   S(n)+1, for n > 0
>   S(2n+1) = 1/S(2n)
>
> This maps all the naturals to all the positive rationals.
> It's fairly trivial to extend the sequence to include the negative
> rationals as well.

What am I missing?  Which n maps to 2/3?  Or 3/4?  Or 2/1157?


-- 
Jesse F. Hughes

"The Hammer has arrived."
  -- James S. Harris, Feb. 14 2006

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