Re: Well Ordering the Reals

boink said:
> On Mon, 21 Nov 2005 16:34:20 -0500, Tony Orlow wrote:
>
> > Did you just add one element to a finite set and pretend it's infinite? Oh, by
> > the way, I don't believe in omega. If you can't deal with that, you might want
> > to drop this hot potato.
>
> I missed this part.
>
> Mathematics is not about "believing". Mathematics is about proving. _At_
> least_, it is a game that follows rigorous rules. You're not playing
> along. You should try finding different playmates...perhaps in the
> humanities.
>
>
Ah, but what you don't understand, Mr. Boink, is that I have other ideas about
these things. You see, as far as I am concerned, there is no smallest infinite,
as one can subtract a finite, or divide by a finite, and get a smaller infinite
number, just like you say there is no largest finite. So, omega means nothing
to me. I deal with a unit infinity which I generally call N, which represents,
not some definite number, but the 1-1 correspondence between element count and
element value, 1 element per unit of value, across the infinite real line. It
can be thought of as the length of the infinite line, and the number of unit
segments and natural numbers in the line, but isn't really a particular number.
It's more of a variable which can take on infinite values.

Anyway, when I say I don't believe in omega, more specifically I mean that the
system of limit ordinals and the axiom of infinity as stated which is at its
root, are unnecessary kludges and lead to wrong results, and I prefer not to
adhere to such definitions with their faulty implications. When you say math is
not about "believing", you have to admit that axioms are assumed to be true,
and believed for the sake of argument within a system, at least for the
duration of any given proof.
--
Smiles,

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

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