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: UNCOUNTABILITY
Replies: 59   Last Post: Dec 24, 2012 2:06 PM

 Search Thread: Advanced Search

 Messages: [ Previous | Next ]
 Graham Cooper Posts: 4,495 Registered: 5/20/10
Re: UNCOUNTABILITY
Posted: Dec 20, 2012 6:28 PM
 Plain Text Reply

On Dec 21, 7:14 am, Virgil <vir...@ligriv.com> wrote:
>
> > > Thus the set of all parameter free definable reals is UNCOUNTABLE!
> > > QED

>
> > And it is countable by the simple proof that there is a bijection
> > between all finite words an the natural numbers.

>
> In order to claim that the set of reals is countable reals, WM must show
> that the set of reals satisfies the definition of countability.
>
> I.E.,WM  must show a surjection from N to R, or an injection from R to N.
>

For the UMPTEENTH TIME!!!!

http://tinyurl.com/blueprints-powerset

Use a Universal Turing Machine to generate POWERSET(N)
Every <algorithm, input> pair that terminates populates a
value into P(N).

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 H H H H H H H H H H ...
...

TM1(1) Halts => 1 e POWERSET_1
TM1(2) Loops => 2 !e POWERSET_1
TM1(3) Halts => 3 e POWERSET_1

TM2(1) Halts => 1 e POWERSET_2
TM2(2) Halts => 2 e POWERSET_2
TM2(3) Halts => 3 e POWERSET_2
...

POWERSET(N) = { {1,3,...} {1,2,3...} ... }

ANYBODY READING YET!!!!

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 ...

SEE WHERE THOSE SETS CAME FROM???? ANYONE??? BUELLER???

IF IT HALTS THEN THE INPUT VALUE
IS AN ELEMENT OF THAT SUBSET OF N

FFS! P(N)

You can't fng read Virgil!

Herc

Date Subject Author
12/19/12 george
12/20/12 Zaljohar@gmail.com
12/20/12 Barb Knox
12/20/12 ross.finlayson@gmail.com
12/20/12 Zaljohar@gmail.com
12/20/12 ross.finlayson@gmail.com
12/20/12 Graham Cooper
12/21/12 mueckenh@rz.fh-augsburg.de
12/21/12 Virgil
12/20/12 Graham Cooper
12/20/12 mueckenh@rz.fh-augsburg.de
12/20/12 Zaljohar@gmail.com
12/21/12 mueckenh@rz.fh-augsburg.de
12/21/12 Zaljohar@gmail.com
12/21/12 mueckenh@rz.fh-augsburg.de
12/21/12 Virgil
12/21/12 William Hughes
12/22/12 mueckenh@rz.fh-augsburg.de
12/22/12 William Hughes
12/22/12 Virgil
12/22/12 William Hughes
12/22/12 Graham Cooper
12/23/12 Virgil
12/23/12 William Hughes
12/24/12 Graham Cooper
12/24/12 mueckenh@rz.fh-augsburg.de
12/24/12 Virgil
12/23/12 mueckenh@rz.fh-augsburg.de
12/23/12 Virgil
12/23/12 mueckenh@rz.fh-augsburg.de
12/23/12 William Hughes
12/24/12 mueckenh@rz.fh-augsburg.de
12/24/12 Virgil
12/23/12 Virgil
12/22/12 Virgil
12/21/12 Zaljohar@gmail.com
12/22/12 mueckenh@rz.fh-augsburg.de
12/22/12 William Hughes
12/22/12 Virgil
12/21/12 Zaljohar@gmail.com
12/21/12 mueckenh@rz.fh-augsburg.de
12/21/12 Virgil
12/22/12 Zaljohar@gmail.com
12/22/12 Virgil
12/22/12 Zaljohar@gmail.com
12/22/12 mueckenh@rz.fh-augsburg.de
12/22/12 Virgil
12/22/12 mueckenh@rz.fh-augsburg.de
12/22/12 Virgil
12/23/12 mueckenh@rz.fh-augsburg.de
12/23/12 Virgil
12/21/12 Virgil
12/20/12 Virgil
12/20/12 Graham Cooper
12/20/12 Graham Cooper
12/21/12 mueckenh@rz.fh-augsburg.de
12/21/12 Virgil
12/21/12 Graham Cooper
12/21/12 Graham Cooper

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