Re: Well Ordering the Reals

In article <MPG.1deba3b0d0814dc998a729@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow <aeo6@xxxxxxxxxxx> wrote:


> You have asked what axioms of set theory I disagree with? I guess I will have
> to say, in the light of the above, if it is correct, that I choose to reject
> the axiom of infinity as it stands, and perhaps suggest replacing it with the
> something that doesn't call the finite set infinite.

It is only in TO's misrepresentation that any TO-finite set is called
infinite. The axiom of infinity does no such thing, at least outside
TOamtics.
> >
> > Note: Some posters have said that the axiom of infinity is that the set
> > of natural numbers exists. There may be treatments of the subject in
> > which that is how the axiom is stated, but, as far as I know, the axiom
> > is usually stated as that there exists an inductive set, from which the
> > existence of the set of natural numbers is proven as a corollary.
>
> That's basically what I had said, when you responded: "I don't know what your
> definition is of 'inductive definition', but the axiom of infinity is not a
> definition". It defines a an inductive set, does it not?

NO! It merely says one exists. Inductive sets are defined elsewhere.

It
> may
> take some time, so I'll try not to be too obnoxious in the meantime. ;)

You will fail!
.

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