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

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Shmuel (Seymour J.) Metz

Posts: 3,370
Registered: 12/4/04
Re: distinguishability - in context, according to definitions
Posted: Feb 17, 2013 10:12 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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.

[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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Date Subject Author
2/10/13
Read distinguishability - in context, according to definitions
fom
2/10/13
Read Re: distinguishability - in context, according to definitions
J. Antonio Perez M.
2/10/13
Read Re: distinguishability - in context, according to definitions
fom
2/11/13
Read Re: distinguishability - in context, according to definitions
Shmuel (Seymour J.) Metz
2/11/13
Read Re: distinguishability - in context, according to definitions
fom
2/14/13
Read Re: distinguishability - in context, according to definitions
Shmuel (Seymour J.) Metz
2/14/13
Read Re: distinguishability - in context, according to definitions
fom
2/14/13
Read Re: distinguishability - in context, according to definitions
fom
2/15/13
Read Re: distinguishability - in context, according to definitions
fom
2/15/13
Read Re: distinguishability - in context, according to definitions
Shmuel (Seymour J.) Metz
2/16/13
Read Re: distinguishability - in context, according to definitions
fom
2/17/13
Read Re: distinguishability - in context, according to definitions
Shmuel (Seymour J.) Metz
2/19/13
Read Re: distinguishability - in context, according to definitions
fom
2/21/13
Read Re: distinguishability - in context, according to definitions
Shmuel (Seymour J.) Metz
2/15/13
Read Re: distinguishability - in context, according to definitions
fom
2/15/13
Read Re: distinguishability - in context, according to definitions
fom
2/14/13
Read Re: distinguishability - in context, according to definitions
fom
2/17/13
Read Re: distinguishability - in context, according to definitions
Shmuel (Seymour J.) Metz
2/17/13
Read Re: distinguishability - in context, according to definitions
fom
2/17/13
Read Re: distinguishability - in context, according to definitions
Barb Knox
2/18/13
Read Re: distinguishability - in context, according to definitions
fom
2/19/13
Read Re: distinguishability - in context, according to definitions
Shmuel (Seymour J.) Metz
2/19/13
Read Re: distinguishability - in context, according to definitions
fom
2/21/13
Read Re: distinguishability - in context, according to definitions
Shmuel (Seymour J.) Metz
2/19/13
Read Re: distinguishability - in context, according to definitions
Shmuel (Seymour J.) Metz
2/19/13
Read Re: distinguishability - in context, according to definitions
fom
2/21/13
Read Re: distinguishability - in context, according to definitions
Shmuel (Seymour J.) Metz
2/21/13
Read Re: distinguishability - in context, according to definitions
fom
2/22/13
Read Re: distinguishability - in context, according to definitions
Shmuel (Seymour J.) Metz
2/15/13
Read Re: distinguishability - in context, according to definitions
fom
2/17/13
Read Re: distinguishability - in context, according to definitions
Shmuel (Seymour J.) Metz
2/17/13
Read Re: distinguishability - in context, according to definitions
fom
2/19/13
Read Re: distinguishability - in context, according to definitions
Shmuel (Seymour J.) Metz
2/16/13
Read Re: distinguishability - in context, according to definitions
dan.ms.chaos@gmail.com
2/16/13
Read Re: distinguishability - in context, according to definitions
fom
2/17/13
Read Re: distinguishability - in context, according to definitions
dan.ms.chaos@gmail.com
2/17/13
Read Re: distinguishability - in context, according to definitions
fom
2/17/13
Read Re: distinguishability - in context, according to definitions
dan.ms.chaos@gmail.com
2/18/13
Read Re: distinguishability - in context, according to definitions
Shmuel (Seymour J.) Metz
2/20/13
Read Re: distinguishability - in context, according to definitions
fom
2/21/13
Read Re: distinguishability - in context, according to definitions
Shmuel (Seymour J.) Metz
2/16/13
Read Re: distinguishability - in context, according to definitions
fom
2/19/13
Read Re: distinguishability - in context, according to definitions
Shmuel (Seymour J.) Metz
2/19/13
Read Re: distinguishability - in context, according to definitions
fom

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