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: Lists
Replies: 7   Last Post: Jan 24, 2013 5:06 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Frederick Williams

Posts: 2,166
Registered: 10/4/10
Re: Lists
Posted: Jan 24, 2013 1:40 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Don Deluise wrote:
>
> This list enumerates all 2 bit binary sequences:
>
> 00
> 01
> 10
> 11
>
> This one enumerates all 3 bit binary sequences:
>
> 000
> 001
> 010
> 011
> 100
> 101
> 110
> 111
>
> Using diagonalization on the first to produce a sequence that is not in the
> list fails. It produces '10' which *is* in the list.
>
> Using diagonalization on the second list also fails. It produces '111'
> which *is* in the list.
>
> Clearly, increasing the length of the sequences does not produce lists in
> which diagonalization will achieve its purpose, i.e. to produce binary
> sequences of a given length which are not already in the list.
>
> So if we were to compile an enumeration of infinite length binary
> sequences, how do we know that diagonalization produces a sequence not
> already in the list?


Infinite things don't behave the same as finite ones.

--
When a true genius appears in the world, you may know him by
this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting



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.