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Subject:
From:
Hans Aberg <[log in to unmask]>
Reply To:
Mailing list for the LaTeX3 project <[log in to unmask]>
Date:
Tue, 3 Nov 1998 15:26:07 +0100
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At 07:56 -0600 1998/11/03, Randolph J. Herber wrote:
>I disagree with your second point---with sufficient encoding, any
>semantic can be preserved, possibly with a time penalty (which are
>ignored when discussing such equivalences).  That is one of the
>points of Goedel's Incompleteness (Undecidability) Theorem.

  Provided the semantics that one wants to describe can be expressed by
binary numbers: For example, TeX proper cannot draw a non-straight spline
curve no matter how you apply Turing theorems and Godel theorem, even
though you can define structures simulating that TeX can handle that -- but
that has no practical significance unless you figure out a way to extend
TeX to print it. (In this example, even though the curve itself can be
described by binary numbers, the capacity of printing it cannot.)

  Hans Aberg
                  * Email: Hans Aberg <mailto:[log in to unmask]>
                  * Home Page: <http://www.matematik.su.se/~haberg/>
                  * AMS member listing: <http://www.ams.org/cml/>

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