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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 >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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