
Re: Matheology S 162
Posted:
Nov 29, 2012 10:11 PM


WM <mueckenh@rz.fhaugsburg.de> writes:
> 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!
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 argued.
> >> 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 welltrod 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."

