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Topic: Peer-reviewed arguments against Cantor Diagonalization
Replies: 23   Last Post: Nov 2, 2012 1:46 AM

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Graham Cooper

Posts: 4,348
Registered: 5/20/10
Re: Peer-reviewed arguments against Cantor Diagonalization
Posted: Nov 1, 2012 12:22 AM
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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:
>
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> > "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 conspiracy-tinged
> > 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 non-cranks "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



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