Re: Well Ordering the Reals

boink said:
> On Mon, 21 Nov 2005 15:42:07 -0500, Tony Orlow wrote:
>
>
> > How is this proof different than the inductive proof of the finiteness of the
> > values of the natural numbers?
>
> How does what you just said contradict what I said?
>
> Any finite set of finite numbers is finite. (Duh.)
>
> The set of _all_ finite numbers is infinite.
>
>
But, you cannot get an infinite set by starting with 1 root element, and
successively adding individual successors, since any finite set will still be
finite after the addition of a new element. This is the same argument given for
the finiteness of the natural numbers, that adding 1 to a finite natural will
never give an infinite value, so therefore all successors in the naturals are
finite. So, you either accept both proofs and have a finite set of finite
naturals, or reject them and have an infinite set with infinite values in it.
So, what's it going to be, boinky.
--
Smiles,

Tony
http://www.people.cornell.edu/pages/aeo6/WellOrder/
.

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