RE: PDF file conundrum / A way to think about IRs

>....
>Now, for a given entity, let's suppose we have decided how we choose 
>to think of it and consider the three possibilities:
>
>  1. the entity does not have the characteristics of an IR.  It is 
>lacking at least one characteristic of an IR.
>
>  2. the entity has all of the characteristics of an IR, but it also 
>has other characteristics.
>
>  3. the entity has exactly the characteristics of an IR and no more.

I don't think this makes sense. Nothing, except a mathematical 
abstraction defined by axioms (group, commutative algebra, set, etc.) 
has some exact list of characteristics and no others at all.

>In case 1, the entity clearly is not an IR.  In case 3, the entity 
>clearly is an IR.  But what about case 2?  In case 2 we have an 
>entity that is *both* an IR *and* something else: it has 
>characteristics of both.

If it has all the characteristics of an IR, then it's an IR, pretty 
much by the meaning of 'characteristic'. It may be something else as 
well, or it may just be an IR which has some extra properties (such 
as containing precisely 347 characters).

Pat

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Received on Monday, 23 June 2008 01:21:26 UTC