Re: Cantor and the binary tree

In article <MPG.1d0656cc97b9a49a989d83@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:


> > Well, positing a "largest finite integer" leads to a contradiction - at
> > least in normal set theory, which is about things existing or not
> > existing, and has no mechanisms looking like "haze" or "indeterminacy".
> > In normal set theory, therefore, there is no largest (finite) integer,
> > and that's it. Because there is always a next (finite) integer after
> > the one you've counted to, the counting ditty never ends, and there are
> > an infinite number of (finite) natural numbers, as Wolf's grandchild
> > could explain to you. There are no contradictions with information
> > theory or anything else.

> Once you have added an infinite number of 1's to a finite number it is no
> longer finite.

Irrelevant to what is still finite.
Every non-empty finite ordered set must have a maximum member.
If the set of naturals, which is obviously non-empty and ordered, were
to be finite, it would have to have a largest member, which means that
adding 1 to that finite number would have to give an infinite number.

Is TO invincibly ignorant or just terminally stupid?
.

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