Re: infinity

stephen@xxxxxxxxxx said:
> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> > David Kastrup said:
> >> But there is no largest natural number. There is an axiom against that.
> > (sigh) And yet, if you have ANY infinite set of whole numbers, each being at
> > least one greater than the last, the greatest one in whatever set you have must
> > be infinitely greater than the smallest in the set. There must be an infinite
> > difference between at least two elements, and one of them must therefore be
> > infinite.
>
> But there is not necessarily a greatest one in whatever set
> you have!!! You keep assuming that in a set there must
> be a greatest (or largest) element, despite denying it whenever
> anyone points it out.
>
> If I have an infinite set of whole numbers, each being at
> least one greater than the last, there is not going to be
> a greatest one. Do you really not understand that?
>
> As someone else has pointed out, you really do not
> understand the concept of infinity. To you infinity
> is just a really big but essentially finite number.
>
> Stephen
>
That is entirely wrong. It does not matter whether there is a largest or not,
although I can give you an infinite set with a largest member, given infinite
whole numbers. The fact remains that it is impossible to fit an infinite number
of unit line segments end to end in a finite distance. Do you really not
understand that? Why is this not completely obvious? It is like saying you can
put an infinite number of finite balls in your finite vase.

Personally, I am sick to death of the Cantorian hangup on whether there is a
first or last element. It's irrelevant almost every time it is brought up. Do
you really think you can fit an infinite number of units in a finite number of
units? I am not the confused one here.
--
Smiles,

Tony
.

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