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Topic: distinguishability - in context, according to definitions
Replies: 43   Last Post: Feb 22, 2013 10:04 AM

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Shmuel (Seymour J.) Metz

Posts: 3,335
Registered: 12/4/04
Re: distinguishability - in context, according to definitions
Posted: Feb 18, 2013 10:27 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

In <hd-dnfiTht7VboLMnZ2dnUVZ_r6dnZ2d@giganews.com>, on 02/16/2013
at 02:59 PM, fom <fomJUNK@nyms.net> said:

>In the logical construction of the real numbers system
>using Dedekind cuts, one must fix a choice as to which
>kind of rational cut will be taken as canonical.


It's more convenient to do so, but it's not actually necessary.

>> In general , machines can't decide the equality or inequality of real
>> numbers ,or infinite strings in general ,without the 0.(9) = 1
>> equivalence of real numbers.


Programs capable of proving theorems have been available for decades.

>So, in the hierarchy of logical definition, one obtains the real
>numbers from Dedekind cuts relative to a logical identity
>relation. Then, a definition of least upper bound and greatest
>lower bound for that system may be defined. Then, provided that
>the nature of relations used in the metrization lemma are
>satisfiable, one uses the function constructed in that proof to
>put a metric on the system of Dedekind cuts.


It's the other way around; one needs the Reals to define a metric, and
once one has the Reals the standard metric is a trivial construction,
the details of which don't depend on whether one used Axioms, Cauchy
sequences of rational or Dedekind cuts of rationals.

--
Shmuel (Seymour J.) Metz, SysProg and JOAT <http://patriot.net/~shmuel>

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Date Subject Author
2/10/13
Read distinguishability - in context, according to definitions
fom
2/10/13
Read Re: distinguishability - in context, according to definitions
J. Antonio Perez M.
2/10/13
Read Re: distinguishability - in context, according to definitions
fom
2/11/13
Read Re: distinguishability - in context, according to definitions
Shmuel (Seymour J.) Metz
2/11/13
Read Re: distinguishability - in context, according to definitions
fom
2/14/13
Read Re: distinguishability - in context, according to definitions
Shmuel (Seymour J.) Metz
2/14/13
Read Re: distinguishability - in context, according to definitions
fom
2/14/13
Read Re: distinguishability - in context, according to definitions
fom
2/15/13
Read Re: distinguishability - in context, according to definitions
fom
2/15/13
Read Re: distinguishability - in context, according to definitions
Shmuel (Seymour J.) Metz
2/16/13
Read Re: distinguishability - in context, according to definitions
fom
2/17/13
Read Re: distinguishability - in context, according to definitions
Shmuel (Seymour J.) Metz
2/19/13
Read Re: distinguishability - in context, according to definitions
fom
2/21/13
Read Re: distinguishability - in context, according to definitions
Shmuel (Seymour J.) Metz
2/15/13
Read Re: distinguishability - in context, according to definitions
fom
2/15/13
Read Re: distinguishability - in context, according to definitions
fom
2/14/13
Read Re: distinguishability - in context, according to definitions
fom
2/17/13
Read Re: distinguishability - in context, according to definitions
Shmuel (Seymour J.) Metz
2/17/13
Read Re: distinguishability - in context, according to definitions
fom
2/17/13
Read Re: distinguishability - in context, according to definitions
Barb Knox
2/18/13
Read Re: distinguishability - in context, according to definitions
fom
2/19/13
Read Re: distinguishability - in context, according to definitions
Shmuel (Seymour J.) Metz
2/19/13
Read Re: distinguishability - in context, according to definitions
fom
2/21/13
Read Re: distinguishability - in context, according to definitions
Shmuel (Seymour J.) Metz
2/19/13
Read Re: distinguishability - in context, according to definitions
Shmuel (Seymour J.) Metz
2/19/13
Read Re: distinguishability - in context, according to definitions
fom
2/21/13
Read Re: distinguishability - in context, according to definitions
Shmuel (Seymour J.) Metz
2/21/13
Read Re: distinguishability - in context, according to definitions
fom
2/22/13
Read Re: distinguishability - in context, according to definitions
Shmuel (Seymour J.) Metz
2/15/13
Read Re: distinguishability - in context, according to definitions
fom
2/17/13
Read Re: distinguishability - in context, according to definitions
Shmuel (Seymour J.) Metz
2/17/13
Read Re: distinguishability - in context, according to definitions
fom
2/19/13
Read Re: distinguishability - in context, according to definitions
Shmuel (Seymour J.) Metz
2/16/13
Read Re: distinguishability - in context, according to definitions
dan.ms.chaos@gmail.com
2/16/13
Read Re: distinguishability - in context, according to definitions
fom
2/17/13
Read Re: distinguishability - in context, according to definitions
dan.ms.chaos@gmail.com
2/17/13
Read Re: distinguishability - in context, according to definitions
fom
2/17/13
Read Re: distinguishability - in context, according to definitions
dan.ms.chaos@gmail.com
2/18/13
Read Re: distinguishability - in context, according to definitions
Shmuel (Seymour J.) Metz
2/20/13
Read Re: distinguishability - in context, according to definitions
fom
2/21/13
Read Re: distinguishability - in context, according to definitions
Shmuel (Seymour J.) Metz
2/16/13
Read Re: distinguishability - in context, according to definitions
fom
2/19/13
Read Re: distinguishability - in context, according to definitions
Shmuel (Seymour J.) Metz
2/19/13
Read Re: distinguishability - in context, according to definitions
fom

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