Re: Cantor and the binary tree
- From: Virgil <ITSnetNOTcom#virgil@xxxxxxxxxxx>
- Date: Thu, 02 Jun 2005 17:32:20 -0600
In article <1117743718.175728.184440@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:
> Robert Kolker wrote:
> > Tony Orlow (aeo6) wrote:
> > >
> > > You are being retarded. If the range of values is infinite, that means
> > > there is
> > > a value in the set that is infinitely greater than another value in the
> > > set. A
> > > value that is infinitely greater than a finite value is infinite. I am
> > > not
> > > conflating anything inappropriately.
> >
> > Consider the identity map from the natural numbers to the natural
> > nubers. There is no infinite natural number.
>
> Consider the mapping
>
> 1 --> {1}
> 2 --> {1,2}
> 3 --> {1,2,3}
> ...
> n --> {1,2,3,...,n}
> ...
> ? --> {1,2,3,...} = N
>
> Do you see the contradiction arising from the "infinite set of finite
> numbers"?
NO!
Your mapping is like
Card(S) --> S for "initial" subsets of N
I see no problem ar all.
.
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