Warp wrote:
> Darren New <dne### [at] sanrrcom> wrote:
>> It also is interesting to consider things like Chaitin's number or "the 
>> smallest uninteresting number" or other finite descriptions that name a 
>> number but you can't tell which number they name.
> 
>   Well, not all numerical concepts have an actual numerical value because
> there simply isn't a number that represents the concept. For example,
> "the smallest real number which is larger than zero" does not exist.

Sure. But Chaitin's number *does* have a value. It's just defined in a way 
that you can't compute it.  (Basically, "the probability that an arbitrarily 
selected program will halt", along with of course all the definitions and 
such to make that meaningful mathematically.)

And "the smallest uninteresting number" doesn't exist because the definition 
is self-contradictory.

-- 
Darren New, San Diego CA, USA (PST)
   Serving Suggestion:
     "Don't serve this any more. It's awful."

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