On Mar 18, 2011, at 4:34 PM, DJ Delorie wrote:

>> 
>> In your sense, you have no idea what the "space of the possible" is
>> for the integers.
> 
> Of course I do.  It's aleph null, the set of counting numbers.

That's not the space of the possible, that's only the range of the abstraction. 
To know the space of the possible, in the sense you're arguing, you'd have to 
know every *application* of the integers. You can't know that. But still, you 
can represent the integers used in those applications as strings of digits. You 
don't need to understand the "space of the possible" *at all* to cover it!

John Doty              Noqsi Aerospace, Ltd.
http://www.noqsi.com/
j...@noqsi.com




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