Drexel dragonThe Math ForumDonate to the Math Forum


Math Forum
 Ask Dr. Math
 Discussions
 Internet Newsletter
 MathTools
 Problems of the Week
 Teacher2Teacher
 Teacher Exchange
 Workshops

Search All of the Math Forum:
Browse our Internet Mathematics Library

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: CANTORS PROOF DEMO the Reals are UN-COUNTABLE
Replies: 2   Last Post: Jan 22, 2013 9:00 PM

Advanced Search
Reply to this Topic Reply to this Topic

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Graham Cooper

Posts: 4,237
Registered: 5/20/10
CANTORS PROOF DEMO the Reals are UN-COUNTABLE
Posted: Jan 9, 2013 7:34 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

A SUBLIST OF REALS IN [BASE 4]

R1 0.0000...
R2 0.3333...
R3 0.3210...
...

DIAGONAL = 0.031...

DEFINE
AD(d) = 2 IFF DIAGONAL(d) < 2
AD(d) = 1 IFF DIAGONAL(d) > 1

AD=0.212... is MISSING FROM THE LIST

PROOF
DIGIT 1 (2) IS DIFFERENT TO LIST[1,1] (0)
DIGIT 2 (1) IS DIFFERENT TO LIST[2,2] (3)
DIGIT 3 (2) IS DIFFERENT TO LIST[3,3] (1)
AND SO ON

So AD is DIFFERENT to EVERY ROW
since This Holds For Any Arbitrary List Of Reals
there is a missing Real for any List Of Reals
therefore Reals are Un-Countable!

Herc

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.