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

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Posts: 18,076
Registered: 1/29/05
Re: Matheology S 162
Posted: Nov 29, 2012 4:51 AM
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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.
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), and, moreover we can prove that there are
(potentially) infinitely many numbers not in that set.

But a real crackpot stamping with feet and shouting "there is the set
containing all naturals" will impress some other crackpots. No one

Regards, WM

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