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fom
Posts:
1,030
Registered:
12/4/12
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Re: distinguishability - in context, according to definitions
Posted:
Feb 17, 2013 2:21 PM
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On 2/17/2013 9:12 AM, Shmuel (Seymour J.) Metz wrote:
> In <8O-dnQWE1cztU4DMnZ2dnUVZ_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.
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