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Re: distinguishability  in context, according to definitions
Posted:
Feb 17, 2013 10:12 AM


In <8OdnQWE1cztU4DMnZ2dnUVZ_oydnZ2d@giganews.com>, on 02/14/2013 at 11:57 PM, fom <fomJUNK@nyms.net> said:
>It would make no sense to treat the presentation >of the "math trick" and its corresponding algebraic >variant in any semantically meaningful way since >that particular proof was not the subject of analysis.
Strings such as '9.(9)'[1] are not real numbers, but denote real numbers; specifically, they denote the limits of sequences derived from them. Deriving numerical equalities by manipulating such strings is only valid to the extent that it can be justified by analysis. What you describe as a trick is at best a heuristic. In
> 9.999... >0.999... > > 9.000...
What matters is not the syntactic similarity of the first two strings, but that they can be proven to denote 10 and 1.
[1] I've avoided use of the ellipis since its meaning is not always clear.
 Shmuel (Seymour J.) Metz, SysProg and JOAT <http://patriot.net/~shmuel>
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