From: paul@fatmans.demon.co.uk
Date: Tue, 21 Jan 1997 12:15:41 -0800 (PST)
To: ichudov@algebra.com
Subject: Re: Numbers we cannot talk about
Message-ID: <199701212015.MAA11107@toad.com>
MIME-Version: 1.0
Content-Type: text/plain



> > I know that Standard mathematical axioms yields lots of interesting
> > results, but when it talks of the infinite and we are dealing
> > with a practical subject like cryptography or even physics it
> > should not be taken too seriously. (With respect to uncountable sets.)
> 
> Some of the applications of these theories are very relevant. For
> example, a theorem that proves that it is impossible to write a program
> that would determine if any other program would stop or loop forever, is
> very relevant and interesting.

Absolutely, something does not have to be practical to be 
interesting, Igor`s example of Cantors double slash argument (useful 
for example in AI research) is something that seems very abstract 
until we find a use for it, and most abstract mathematical concepts 
and theorems of this kind do eventually come into use by some other 
class of scientists.

 

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