Re: infinity

*** T. Winter said:
> In article <MPG.1d8a1b9fa478af6e98a22c@xxxxxxxxxxxxxxxxxxxxxxxxx> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> writes:
> ...
> > 1) The size of any set of naturals from 1 through n is equal to n, the
> > largest element.
> > 2) The set of naturals only contains finite elements.
> > 3) the size of the set of naturals is aleph_0, an infinite number and
> > NOT a natural.
> >
> > Do you resolve this by simply denying the existence of a valid inductive
> > proof, or do you admit a contradiction?
>
> What *is* the contradiction?
>
> (1) is about particular sets of naturals with a last element, (3) is about
> sets of naturals *without* a last element. Your induction is always for
> sets with a last element, so the conclusion can not follow for sets
> without a last element.
>
My induction is about the set defined by each n in N. All n are largest members
of a finite set. There is no n with an infinite number of predecessors.
--
Smiles,

Tony
.

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