Search All of the Math Forum:

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

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: CHAITAN'S POWERSET!
Replies: 3   Last Post: Mar 6, 2013 1:24 AM

 Search Thread: Advanced Search

 Messages: [ Previous | Next ]
 Graham Cooper Posts: 4,495 Registered: 5/20/10
Re: CHAITAN'S POWERSET!
Posted: Mar 6, 2013 1:24 AM
 Plain Text Reply

On Jan 17, 6:48 am, Graham Cooper <grahamcoop...@gmail.com> wrote:
> INPUT  1 2 3 4 5 6 7 8 9 10 ...
> =============================
> TM1    H L H H H L L L L L ...
> TM2    H H H H H H H H H H ...
> TM3    H L L L L L L L L L ...
> TM4    L H L H L H L H L H ...
> ...
> If TM1(1) Halts then 1 e POWERSET_1
> If TM1(2) Loops then 2 !e POWERSET_1
> ...
> If TM2(1) Halts then 1 e POWERSET_2
> If TM2(2) Halts then 2 e POWERSET_2
> ...
>
> 1 <=> {1,3,4,5,...}
> 2 <=> {1,2,3,4,5,...}
> 3 <=> {1}
> 4 <=> {2,4,6,8,10...}
>        | | | | |
> TM4   LHLHLHLHLH ...
>
> Instead of constructing an UN-COMPUTABLE REAL
> And using CHAITANS OMEGA to argue computable reals are UN-COUNTABLE
>
> YOU CAN CONSTRUCT AN ACTUAL SEMI-DECIDABLE
> POWERSET OF N!
>

Fred Williams (and Barny and Betty too?)

wants me to write the above more clearly...

Chaitan's Omega they all get! But a computable PS(N), the list of
all(?) subsets of N, is not interesting (due to poor writing now
apparently).

Herc
--
www.BLoCKPROLOG.com

Date Subject Author
1/16/13 Graham Cooper
3/5/13 Charlie-Boo
3/5/13 Bill Taylor
3/6/13 Graham Cooper

© The Math Forum at NCTM 1994-2018. All Rights Reserved.