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Virgil
Posts:
4,479
Registered:
1/6/11
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Re: Matheology S 162
Posted:
Nov 29, 2012 3:26 PM
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In article
<3d568ac0-15e2-4b3f-a125-535c7a0114e8@s14g2000vba.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 28 Nov., 19:46, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
>
> > So, your conclusion is that, for every n, the set {n,n+1} is finite?
>
> My conclusion is that for every set {1, ..., n} also the set {1, ...,
> n, n+1} is finite!
>
> > If so, surely we agree. And from this, we infer that every set of
> > natural numbers is finite, er, how?
>
> Every set, that is formed by induction beginning with {1}, is finite.
The only set, S, that I know of which starts with 1 and is defined by
induction says that for every member, s, of S , s+1 is also a member.
But every finite ORDERED set can be shown to have a last member.
So WM claims existence of inductive sets which are not inductive.
> For every set of natural numbers we can prove that all numbers are
> finite, hence the set is finite (for completed infinity an infinite
> number would be required)
As a cardinality, perhaps, but not as a member.
But then WM has never been able to tell the difference between such
things anyway.
> and, moreover we can prove that there are
> (potentially) infinitely many numbers not in that set.
While there are an actual infinity of non-natural-number-things which
are not in the set of natural numbers, that in no way limits the number
of natural numbers which can be members of the set of actual natural
numbers.
>
> But a real crackpot stamping with feet and shouting "there is the set
> containing all naturals" will impress some other crackpots. No one
> else.
While WM is certainly able to speak for "real" crackpots and from real
crackpotism, he is not competent to speak for anyone else.
--
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