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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: 3,473 Registered: 12/4/04
Re: distinguishability - in context, according to definitions
Posted: Feb 19, 2013 7:29 AM

In <x_-dnZNsYePggrzMnZ2dnUVZ_rydnZ2d@giganews.com>, on 02/17/2013
at 12:20 PM, fom <fomJUNK@nyms.net> said:

>This is not how I understand mathematics.

There are two very different issues; structure and presentation. It is
cumbersome to always write proofs out in full, so working
mathematicians use a set of informal shorthand notations.

>Almost every reputable mathematics department is
>giving courses in "mathematical logic," presumably

I believe that such courses fo into more than just the logical
machinery needed in Mathematics, and that they cover, e.g.,
independence, consistency, models.

>But, in the "logical" sense,
>1.000... = 0.999...
>is merely a stipulation of syntactic equality
>between distinct inscriptions that is prior
>to any mathematical discourse.

There is no syntactic identity there. There is, instead, an identity
based on a specific[1] definition of the notation and a specific set
of axioms.

[1] Well, some of the posters seem to be unable to formulate what
they mean by, e.g., "0.999...".

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

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Date Subject Author
2/10/13 fom
2/10/13 J. Antonio Perez M.
2/10/13 fom
2/11/13 Shmuel (Seymour J.) Metz
2/11/13 fom
2/14/13 Shmuel (Seymour J.) Metz
2/14/13 fom
2/14/13 fom
2/15/13 fom
2/15/13 Shmuel (Seymour J.) Metz
2/16/13 fom
2/17/13 Shmuel (Seymour J.) Metz
2/19/13 fom
2/21/13 Shmuel (Seymour J.) Metz
2/15/13 fom
2/15/13 fom
2/14/13 fom
2/17/13 Shmuel (Seymour J.) Metz
2/17/13 fom
2/17/13 Barb Knox
2/18/13 fom
2/19/13 Shmuel (Seymour J.) Metz
2/19/13 fom
2/21/13 Shmuel (Seymour J.) Metz
2/19/13 Shmuel (Seymour J.) Metz
2/19/13 fom
2/21/13 Shmuel (Seymour J.) Metz
2/21/13 fom
2/22/13 Shmuel (Seymour J.) Metz
2/15/13 fom
2/17/13 Shmuel (Seymour J.) Metz
2/17/13 fom
2/19/13 Shmuel (Seymour J.) Metz
2/16/13 dan.ms.chaos@gmail.com
2/16/13 fom
2/17/13 dan.ms.chaos@gmail.com
2/17/13 fom
2/17/13 dan.ms.chaos@gmail.com
2/18/13 Shmuel (Seymour J.) Metz
2/20/13 fom
2/21/13 Shmuel (Seymour J.) Metz
2/16/13 fom
2/19/13 Shmuel (Seymour J.) Metz
2/19/13 fom