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Topic: Matheology S 162
Replies: 3   Last Post: Nov 29, 2012 3:26 PM

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Posts: 8,833
Registered: 1/6/11
Re: Matheology S 162
Posted: Nov 29, 2012 3:26 PM
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In article
WM <> wrote:

> On 28 Nov., 19:46, "Jesse F. Hughes" <> 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
> 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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