Re: How to do magic with infinity

From: Frank Piron (empty_at_zero.nil)
Date: 10/29/04 

Date: Fri, 29 Oct 2004 13:04:03 +0200

Fri, 29 Oct 2004 12:06:25 +0200 Han de Bruijn
<Han.deBruijn@DTO.TUDelft.NL> wrote:

> Frank Piron wrote:
>
>> In fact you didn't show me the program because the library function
>> "random" comes from outer space in your listing. For this function
>> there are two origins possible
>>
>> 1)
>> It is a pseudo random generator and thus an ordinary number
>> function.
>
> No doubt. It IS a pseudo random number generator.
>
>> 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". Now if quasar numbers
"exist" there must be a minimum quasar number. Let us call it
Q. Q is the example you wanted. Be careful with it.

Interesting - there may be greater numbers than Q which are not
quasar. Also the sum Q_1 + Q_2 of two quasar numbers may be not
quasar. 

-- 
Frank Piron,
etfrankatkonaddotn
(leftrotate two)