Re: infinity

In article <MPG.1d63f0b1e1c61f8398a026@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:


> > I misunderstood your initial comment.
> I believe that was because Virgil keeps lying repeatedly about my positions,
> and is expecially hung up on this "largest finite" objection to actual math.

Since I, or others, have proved to the evident satisfaction of the
mathematicians reading this thread that finite ordered sets MUST have
maximal members, and TO persists is claiming that the set of "finite"
naturals is a finite set, by implication, TO is declaring the existence
of a largest finite natural.

While TO may explicitely deny existence of a largest finite natural, he
keeps insisting on conditions which require its existence.

Given the validity of the Peano postulates for the naturals, it may be
shown that the set of (finite) naturals is not a finite set according to
the Cantor definition.




> You will not find me saying I believe there is a largest finite,

We will often find TO saying things that imply its existence, as
explained above.

> besides
> suggesting that the idea is no different than your smallest infinite, omega.
> They're both figments of an imagination which violates the principles of
> quantity itself.

To suggest that sets which are not finite are incapable of being put
into bijective correspondence is ridiculous.
.

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