Re: Numbers we cannot talk about

[paul@fatmans.demon.co.uk]

> > 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.

 

  Datacomms Technologies web authoring and data security
       Paul Bradley, Paul@fatmans.demon.co.uk
  Paul@crypto.uk.eu.org, Paul@cryptography.uk.eu.org    
       Http://www.cryptography.home.ml.org/
      Email for PGP public key, ID: 5BBFAEB1
     "Don`t forget to mount a scratch monkey"