
Re: Peerreviewed arguments against Cantor Diagonalization
Posted:
Nov 1, 2012 12:22 AM


On Nov 1, 2:15 pm, Graham Cooper <grahamcoop...@gmail.com> wrote: > On Nov 1, 8:38 am, "Jesse F. Hughes" <je...@phiwumbda.org> wrote: > > > > > > > > > > > "LudovicoVan" <ju...@diegidio.name> writes: > > > "Jesse F. Hughes" <je...@phiwumbda.org> wrote in message > > >news:87mwz2qu53.fsf@phiwumbda.org... > > >> "LudovicoVan" <ju...@diegidio.name> writes: > > >>> "Jesse F. Hughes" <je...@phiwumbda.org> wrote in message > > >>>news:87txtaqxih.fsf@phiwumbda.org... > > > <snip> > > > >>>> I never said you thought that set theory was a root of evil, but, near > > >>>> as I can figger, you said that it was a symptom of a lying culture which > > >>>> lies just 'cause it can. > > > >>> You could say because it wants, not because it can: anyway, you rephrase > > >>> it > > >>> as a 13 year old would, but yes, let's say you almost got it, son, though > > >>> not quite. OTOH, I am pretty sure you could do better, if only you could > > >>> be > > >>> any little more honest. > > > >> Sorry, I've studied too much set theory to be honest, I guess. > > > > Set theory is not responsible for your honesty, big boy. > > > >>>> In an honest culture, we would all admit that > > >>>> set theory is a plain falsehood. > > > >>> No, I have never said that: there are indeed things that I find are > > >>> patently > > >>> wrong, the standard theory of cardinality being one of them, but that > > >>> does > > >>> not mean I'd discard the baby too. Not to mention that we all have > > >>> "search" > > >>> strategies, and a world of fools and criminals means just do not expect > > >>> that > > >>> I be a gentlemen. It's a war, mate. > > > >> See, here's the weird thing. The theorems of ZFC can be confirmed by > > >> anyone. > > > > Apart from the fact that proof by consensus is not a valid argument, that's > > > not even true. > > > Who the fuck said anything about proof by consensus? > > > And, surely, if the argument is invalid, perhaps you can point out the > > invalid step. > > > For that, of course, we should be clear on what argument we are > > discussing. There are various arguments that go by the name "Cantor's > > theorem". The easiest to analyze, of course, is the proof that, for all > > sets X, X < PX. Are you prepared to show me how that argument is > > invalid? If so, we can discuss it. > > > But I'm not going on some vague, meandering and conspiracytinged > > rantfest. If you want to claim that the proof is invalid, you have to > > show me the step which is invalid. > > > >> At best, you can complain that either the axioms are false > > >> (I'm sure I don't know what that would mean) > > > > At best? Anyway, try and ask Aatu about that: to you he might even > > > reply. > > > >> or that the logic we use is > > >> mistaken (and that's a mighty hard sell). But it is undeniable that ZFC > > >> proves for all X, X < PX. Anyone can confirm that the proof is a > > >> valid argument. > > > > Again, proof by consensus is not a proof, but that is not even true: as you > > > should know even too well, not anyone would confirm, and this is not just > > > the cranks. > > > And, again, to say that "anyone can confirm the validity" is not proof > > by consensus, you tedious twat. > > > And, as far as noncranks "not confirming" the validity, well, that is > > the subject of this discussion. Can you name a single, reputable source > > that disputes whether ZFC proves Cantor's theorem? (NOTE: I'm talking > > about a particular formal theory here, so the various mathematicians who > > gave philosophical disputes over Cantor's informal argument are > > irrelevant to our purposes here, unless those disputes can explicitly > > show an invalid step in this very simple proof.) > > Can you state explicitly what it proves? > > I don't see how MODUS PONENS might make this deduction. > > LHS>RHS & LHS > RHS > > where RHS = "X > size({1,2,3...})" > > nor how the enumeration of a set and it's index inclusion or not has > anything to do what's in the superset. > > Herc >  > if( if(t(S),f(R)) , if(t(R),f(S)) ). > if the sun's out then it's not raining > ergo > if it's raining then the sun's not out
Let's construct the missing set.
Here's is my purported P(N) 1st 20 subsets.
f(1) = { 2 3 4 5 6 7 10 12 14 16 17 18 20 } f(2) = { 1 2 3 4 6 7 9 11 12 13 14 16 18 } f(3) = { 1 4 5 6 10 12 13 18 } f(4) = { 1 2 3 9 10 14 15 18 19 } f(5) = { 4 5 6 9 14 } f(6) = { 2 3 5 7 8 10 12 19 20 } f(7) = { 1 2 5 6 7 8 14 } f(8) = { 1 2 3 4 6 7 10 11 12 13 } f(9) = { 2 6 8 10 15 } f(10) = { 5 7 15 17 19 20 } f(11) = { 1 2 7 8 10 12 19 } f(12) = { 5 6 8 13 19 } f(13) = { 1 2 4 5 8 11 } f(14) = { 1 3 11 15 20 } f(15) = { 2 4 5 6 9 12 } f(16) = { 1 3 4 8 12 14 15 19 } f(17) = { 9 13 15 } f(18) = { 2 3 4 5 7 9 13 17 } f(19) = { 1 2 3 5 7 12 13 19 } f(20) = { 1 2 4 5 8 20 }
HERE'S THE MISSING SET! { x  ~x e f(n) }
{ 1 3 4 6 8 9 10 11 12 13 14 15 16 17 18 }
BWAHAHAHAHAHA!!
MISSING!???
We don't need to show a flaw in stupidity!
Herc

