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



fom
Posts:
1,968
Registered:
12/4/12


Re: distinguishability  in context, according to definitions
Posted:
Feb 17, 2013 2:21 PM


On 2/17/2013 9:12 AM, Shmuel (Seymour J.) Metz wrote: > 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.
I hope my clarification to you regarding your other question shows that we are in agreement on this.
> > [1] I've avoided use of the ellipis since its meaning is not > always clear. >
Good for you.
I realize it is common, and, I try to interpret it as intended, but truly,
2,4,6,8,...
does not permit one to surmise 10 as the next element of the sequence. I will never quite forget how impressed I was by the chaotic nature of mathematics when learning Runge's theorem. There is nothing special about it. I had just not appreciated just how badly "nice" functions could behave until that point in my studies.



