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Topic: On the diagonal argument again
Replies: 199   Last Post: Jun 10, 2012 10:12 AM

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 Guest
Re: On the diagonal argument again
Posted: Jun 1, 2012 10:32 AM

"Graham Cooper" <grahamcooper7@gmail.com> wrote in message

> Here is an alternate take that seems to fall on deaf ears.
>
> The list of computable reals contains every digit sequence of ALL
> LENGTHS.
>
> Good 'nuff!

Good for what? By the diagonal argument, it is simply false:

The anti-diagonal of an effective list of computable reals is, apparently, a
computable real itself; OTOH, the anti-diagonal is, as a direct consequence
of its definition, not on the list. Hence, any effective list of computable
reals must be incomplete (not enumerate all the computable reals). --
Standardly, when we say that a list does not contain this or that entity, we
mean that for no n in N that entity appears at position n.

I am thinking that the best we can get when talking of effective
enumerations of strings is (modulo remapping) the dyadic rationals, i.e.
strings that end with period "0", namely all and only the finite strings.

Please correct me if I am mistaken.

-LV

Date Subject Author
5/15/12 LudovicoVan
5/15/12 LudovicoVan
5/15/12 William Hughes
5/15/12 LudovicoVan
5/15/12 Virgil
5/16/12 Graham Cooper
5/15/12 Shmuel (Seymour J.) Metz
5/15/12 LudovicoVan
5/15/12 Virgil
5/16/12 mueckenh@rz.fh-augsburg.de
5/16/12 Daryl McCullough
5/16/12 LudovicoVan
5/16/12 LudovicoVan
5/16/12 Virgil
5/16/12 LudovicoVan
5/16/12 Virgil
5/17/12 LudovicoVan
5/17/12 Virgil
5/17/12 LudovicoVan
5/17/12 Virgil
5/17/12 Graham Cooper
5/18/12 Michael Stemper
5/18/12 Daryl McCullough
5/18/12 Shmuel (Seymour J.) Metz
5/18/12 LudovicoVan
5/16/12 Graham Cooper
5/16/12 Shmuel (Seymour J.) Metz
5/16/12 LudovicoVan
5/16/12 Virgil
5/17/12 LudovicoVan
5/17/12 Virgil
5/17/12 LudovicoVan
5/17/12 Virgil
5/17/12 LudovicoVan
5/18/12 Virgil
5/18/12 Graham Cooper
5/18/12 David Bernier
5/18/12 Graham Cooper
5/18/12 K_h
5/18/12 |-| E R C
5/18/12 K_h
5/18/12 Graham Cooper
5/18/12 Graham Cooper
5/19/12 K_h
5/19/12 Graham Cooper
5/19/12 Graham Cooper
5/19/12 David Bernier
5/19/12 Graham Cooper
5/19/12 Graham Cooper
5/20/12 K_h
5/20/12 Graham Cooper
5/21/12 K_h
5/21/12 Graham Cooper
5/29/12 mueckenh@rz.fh-augsburg.de
5/29/12 Virgil
5/19/12 K_h
5/19/12 Graham Cooper
5/18/12 LudovicoVan
5/18/12 LudovicoVan
5/18/12 Shmuel (Seymour J.) Metz
5/17/12 Graham Cooper
5/17/12 Shmuel (Seymour J.) Metz
5/18/12 LudovicoVan
5/19/12 Shmuel (Seymour J.) Metz
5/19/12 LudovicoVan
5/20/12 Shmuel (Seymour J.) Metz
5/19/12 LudovicoVan
5/19/12 LudovicoVan
5/20/12 Shmuel (Seymour J.) Metz
5/19/12 LudovicoVan
5/19/12 LudovicoVan
5/16/12 Graham Cooper
5/16/12 Virgil
5/18/12 K_h
5/15/12 dilettante
5/16/12 LudovicoVan
5/16/12 dilettante
5/16/12 LudovicoVan
5/16/12 dilettante
5/16/12 Graham Cooper
5/16/12 dilettante
5/16/12 Graham Cooper
5/16/12 dilettante
5/16/12 Graham Cooper
5/16/12 LudovicoVan
5/16/12 dilettante
5/16/12 LudovicoVan
5/16/12 Virgil
5/17/12 William Hughes
5/17/12 LudovicoVan
5/17/12 William Hughes
5/17/12 LudovicoVan
5/17/12 Virgil
5/17/12 LudovicoVan
5/17/12 Virgil
5/17/12 LudovicoVan
5/16/12 Graham Cooper
5/16/12 Virgil
5/16/12 |-| E R C
5/16/12 LudovicoVan
5/16/12 Virgil
5/16/12 LudovicoVan
5/16/12 Jim Burns
5/16/12 LudovicoVan
5/16/12 Graham Cooper
5/16/12 Jim Burns
5/16/12 LudovicoVan
5/16/12 Jim Burns
5/16/12 |-| E R C
5/17/12 LudovicoVan
5/17/12 Jim Burns
5/17/12 Virgil
5/17/12 LudovicoVan
5/17/12 LudovicoVan
5/17/12 Virgil
5/17/12 LudovicoVan
5/16/12 Virgil
5/17/12 LudovicoVan
5/17/12 Virgil
5/17/12 LudovicoVan
5/17/12 Virgil
5/17/12 LudovicoVan
5/17/12 Virgil
5/17/12 LudovicoVan
5/18/12 Virgil
5/17/12 |-| E R C
5/18/12 Shmuel (Seymour J.) Metz
5/19/12 LudovicoVan
5/16/12 Virgil
5/17/12 LudovicoVan
5/17/12 Virgil
5/17/12 Graham Cooper
5/18/12 Daryl McCullough
5/18/12 Graham Cooper
5/18/12 Virgil
5/17/12 LudovicoVan
5/17/12 Virgil
5/17/12 LudovicoVan
5/17/12 YBM
5/17/12 LudovicoVan
5/18/12 Virgil
5/18/12 Shmuel (Seymour J.) Metz
5/19/12 LudovicoVan
5/17/12 Shmuel (Seymour J.) Metz
5/19/12 LudovicoVan
5/20/12 Shmuel (Seymour J.) Metz
5/16/12 Virgil
5/29/12 Aatu Koskensilta
5/29/12 Graham Cooper
5/30/12 K_h
5/30/12 Virgil
5/30/12 Curt Welch
5/30/12 Graham Cooper
5/30/12 ross.finlayson@gmail.com
5/30/12 Graham Cooper
5/30/12 K_h
6/1/12 ross.finlayson@gmail.com
6/8/12 Albert van der Horst
5/29/12 Aielyn
5/29/12 Aielyn
5/29/12 Graham Cooper
5/29/12 Aielyn
5/29/12 Mike Terry
5/31/12 Aielyn
5/31/12 Virgil
5/31/12 Aielyn
5/31/12 Virgil
5/31/12 Aielyn
5/31/12 Shmuel (Seymour J.) Metz
5/31/12 Shmuel (Seymour J.) Metz
5/31/12 Mike Terry
6/1/12 Graham Cooper
6/1/12 Guest
6/1/12 LudovicoVan
6/1/12 LudovicoVan
6/1/12 LudovicoVan
6/1/12 LudovicoVan
6/1/12 Graham Cooper
6/1/12 Virgil
6/1/12 Graham Cooper
6/1/12 LudovicoVan
6/1/12 |-| E R C
6/10/12 Aielyn
6/10/12 Shmuel (Seymour J.) Metz
5/29/12 Tim Little
5/31/12 LudovicoVan
6/5/12 Shmuel (Seymour J.) Metz
6/4/12 Aatu Koskensilta
6/4/12 Graham Cooper
6/4/12 ross.finlayson@gmail.com
6/4/12 ross.finlayson@gmail.com
6/4/12 Graham Cooper
6/4/12 ross.finlayson@gmail.com
6/4/12 |-| E R C