From: Christian Szegedy (szegedy@or.uni-bonn.de)
Date: Thu Aug 19 2004 - 03:33:15 MDT
Marc Geddes wrote:
>Well let me turn that around and ask if there is any
>reason why I SHOULDN'T be able to arbitrarily
>approximate any 'uncomputable' functions or
>'undecidable' maths statements?
>
You talk about "approximability" without giving even the
slightest hint what you mean by it. This is not a base for
any fruitable discussion.
Approximation is not a well defined notion. It has
different definitions in a lot of different contexts. The
quality of approximations is an even more complicated issue.
There are some functions which can be approximated well,
there are others that provably cannot. I don't know of any
general notion of approximability that allows for arbitrary
accuracy approximation for any definable functions.
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