Re: How to do magic with infinity

From: Han de Bruijn (Han.deBruijn_at_DTO.TUDelft.NL)
Date: 10/29/04 

Date: Fri, 29 Oct 2004 13:39:32 +0200

Frank Piron wrote:
> Fri, 29 Oct 2004 12:06:25 +0200 Han de Bruijn
> <Han.deBruijn@DTO.TUDelft.NL> wrote:
>> Frank Piron wrote:
>>> But what about numbers for which no generating programs can
>>> be written down?
>>> In what sense do they exist or not exist?
>>
>> Good question! Can you come up with such a number?
>> Examples please.
>
> Of course such a number can not be presented by 10-adic
> expansion. Moreover it can not be presented by any symbolic
> generating code like "10^(10^1000)". But since there is only
> a finite number of programs with a length smaller than the
> volume of our universe such numbers must "exist".
> Let us call such numbers "quasar numbers". [ ... ]

Stop! I'm sorry. But I really don't understand why THIS should
be sufficient reason for such numbers to "exist". What happens
if I simply DENY the existence of your quasar numbers? Does it
have any observable consequences for my universe?

(Hmm, quasar numbers smell a bit like those infinite cardinals)

Han de Bruijn