Re: abundance of irrationals!)

*** 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? It doesn't
prove anything that there is no definite largest element. The set can still be
finite. If the naturals are all finite, there's a finite number of them.
--
Smiles,

Tony
.

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