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Re: Cantor Confusion

Subject: Re: Cantor Confusion
From: Virgil
Date: Sat, 30 Sep 2006 12:44:45 -0600
Newsgroups: sci.math
In article <JguTg.1862$3E2.1091@xxxxxxxxxxxxxxxxxxxxx>,
 "Poker Joker" <Poker@xxxxxxxxx> wrote:

> "Tonico" <Tonicopm@xxxxxxxxx> wrote in message 
> news:1159605340.208078.275580@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

> 
> > Iff you gave a complete list of the reals then the other part would NOT
> > be able to construct a real that is not in it...kid,
> 
> DAH! And any construction of such a number would be flawed.

Only if some flaw could be proved, and PJ has proved nothing.

> Perfectly grammatically correct.  Just like the process that takes
> all reals and produces on that wasn't in its input.  The output LOOKS
> good.  No proof that if you feed it ALL the reals that it actually
> produces as advertised.  It can't.

One does not "feed it all the reals" one feeds it all the lists of 
reals, and by a method independent of which list it is fed, it produces 
a number not listed by that list. In fact, by a suitable modification, 
it can produce one number not in the list for every real number, i.e., 
show a bijection between  the set of all reals and, for any given list, 
the set of unlisted reals.

So in this sense, for any fixed list, you can feed in all the reals and 
get for each real an unlisted real.

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