Re: infinity

Virgil said:
> In article <MPG.1d88f9918e8b0c0a98a213@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
>
>
> > If the size of a set of all consecutive whole numbers starting at 1
> > is always a member of that set,
>
> It is not. The set of consecutive naturals starting at 1 and BOUNDED by
> some finite natural may have this property, but not all sets of naturals
> are bounded.
It is a fact that NO finite natural can ever have an infinite number of
predecessors, so the set cannot have infinite numbers of members.
>
> If the set of all finite naturals were finite, then it must contain the
> sum of all its members, since finite sums of finite naturals will always
> be finite naturals. But any finite set of two or more natural numbers
> will NEVER have a sum which is a member of the set.
>
> So that the claim that the set of all finite naturals is a finite set
> leads to a contradiction, that it cannot be the set of ALL finite
> natural numbers.
The contradiction is simply derived from the alrgest finite contradiction.
>
> Note that the problem disappears if the finiteness of the set is not
> claimed.
Notice that it doesn't. It only disappears if the values are allowed to contain
infinite wholes.
>

--
Smiles,

Tony
.

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