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In article <454762d8@xxxxxxxxxxxxxxxxxxx>,
Tony Orlow <tony@xxxxxxxxxxxxx> wrote:
> David R Tribble wrote:
> > David R Tribble wrote:
> >>> Every member of N has a finite successor. Can you prove that your
> >>> "infinite naturals" are members of N?
> >
> > Virgil wrote:
> >>> The property of not being an infinite natural holds for the first
> >>> natural, and holds for the successor of each non-infinite natural, so
> >>> that it must hold for ALL naturals.
> >
> > Tony Orlow wrote:
> >> It holds for all finite naturals, but if there are an infinite number of
> >> naturals generating using increment, then there are naturals which are
> >> the result of infinite increments, which must have infinite value.
The naturals are naturally well ordered, which means that any non-empty
subset of them must have a first element.
So either the set of infinite naturals is empty or it has a first
element. Which is it TO?
> >
> > Can you show us one of those infinite naturals?
> >
> >
>
> I meant an infinite number of increments, each being a successive
> difference of +1 in measure.
So what is the first infinite natural, TO? And which finite natural is
it the successor of?
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