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Re: distinguishability - in context, according to definitions
Posted:
Feb 19, 2013 7:29 AM
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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
>based on this received paradigm.
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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