Re: abundance of irrationals!)

Randy Poe said:
>
> aeo6 Tony Orlow wrote:
> > *** T. Winter said:
> > > In article <MPG.1ce4531e5377a768989bd0@xxxxxxxxxxxxxxxxxxxxxxxxx>
> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> writes:
> > > ...
> > > > Perhaps an axiom says that a finite set MUST have a greatest
> member. Perhaps
> > > > that is why we INSIST that N is infinite, even though we don't
> want to deal
> > > > with infinite values, because we cannot find an overall largest
> finite
> > > > number. Sure, that's a problem, but do we need the axiom for
> largest
> > > > member? What does that really do for us that we can't do another
> way that's
> > > > better?
> > >
> > > Give me a finite set of numbers and I will supply you with the
> largest.
> > > It is *not* an axiom that finite sets of numbers have a largest
> number.
> > >
> > If there is no such axiom, then why do people keep harping on it?
>
> Because it's a theorem.
>
> > It doesn't
> > prove anything that there is no definite largest element. The set can
> still be
> > finite.
>
> A finite set of numbers, with the usual order relationships,
> has a definite largest elements. A set without a largest
> element can not be finite.
leap alert! Prove your assertion, and define "usual order relationships", and
tell me if that applies to your "set of all finite natural numbers". Axioms,
please, and logic. No leaps.
>
> - Randy
>
>

--
Smiles,

Tony
.

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