Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Hercules ofZeus

Posts: 27
Registered: 9/19/11
Re: Peer-reviewed arguments against Cantor Diagonalization
Posted: Nov 1, 2012 4:03 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Nov 1, 8:38 am, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:

> > irrelevant to our purposes here, unless those disputes can explicitly
> > show an invalid step in this very simple proof.)

>

it DOES NOT HOLD UP TO INDUCTION!!!!!


Examine the lower level Decimal Proof Technique...


ROW1_1=/=AD_1 -> AD=/=ROW1
ROW2_2=/=AD_2 -> AD=/=ROW2
ROW3_3=/=AD_3 -> AD=/=ROW3
...
AND SO ON!


THIS IS THE INDUCTIVE STEP

P(n) -> P(S(n))


---------------

But P(1) DOESNT HOLD BY ITSELF!!!

Proviging a single digit of the diagonal is WORTHLESS, even for ROW 1!

---------------

If you claim this is a proof in PREDICATE CALCULUS
then the only Proof Method in PREDICATE CALCULUS
about infinite sets is INDUCTION!

p(1) & p(n)->p(s(n))
-> ALL(n) p(n)


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




Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.