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Topic: Matheology S 162
Replies: 7   Last Post: Nov 30, 2012 5:00 PM

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Jesse F. Hughes

Posts: 9,776
Registered: 12/6/04
Re: Matheology S 162
Posted: Nov 29, 2012 10:11 PM
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WM <> writes:

> 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!

Boy, are you incoherent. Let's refresh your memory, since you
accidentally snipped the context.

| >> >and the set containing
| >> > both, n and n + 1 ist finite too.
| >>
| >> There is of course no such thing as
| >>  "the set containing both n and n+1".
| >
| > Here it is: {n, n+1}

As everyone can see, what you seem to have prove is that the pair
{n,n+1} is finite.

Of course, it's also true that every proper initial segment of N is
finite, but if you'll simply read the above, that wasn't what you

>> 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.

Yes, yes, same ol' silly disregard for what the principle of induction
actually says. I'm not interested in covering this well-trod ground.

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

Sure. Aside from the fact, you know, that ZFC proves there is a set of
natural numbers.

Jesse F. Hughes.
Me: It's very sad when one's husband or wife dies.
Quincy (Age 4 1/2): Yeah. You might want to tell them something and
you just can't. [Long pause] Like "Take out the trash."

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