Virgil
Posts:
8,833
Registered:
1/6/11


Re: Matheology S 162
Posted:
Nov 30, 2012 12:43 AM


In article <87pq2vbx8v.fsf@phiwumbda.org>, "Jesse F. Hughes" <jesse@phiwumbda.org> wrote:
> 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.
And note that neither WM nor anyone else has yet been able to show that ZFC contains any selfcontradictions or internal inconsistencies. 

