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Re: A question Level 1 <---> level 2 mappings; arithmetic versus applications

Yes.
Possibly semi-infinite intervals can be considered invalid construction for mid-rad types, similar to how [-Inf,-Inf] is invalid construction for inf-sup. So there may be connections to the exception handling mechanism for these cases. 
Nate
----- Original Message ----- From: "Michel Hack" <hack@xxxxxxxxxxxxxx> 
To: "stds-1788" <stds-1788@xxxxxxxxxxxxxxxxx>
Sent: Wednesday, June 30, 2010 3:25 PM
Subject: Re: A question Level 1 <---> level 2 mappings; arithmetic versus applications 



Nate Hayes wrote:

For example, any given Level 1 interval [a,b] has the property:
    [a,b] = (m;r)
where (m;r) is a mid-rad interval and m=(a+b)/2, r=(b-a)/2.


Any *bounded* Level 1 interval.  At level 1 a+b and a-b don't exist
when either a or b is infinite.  At level 2 the only possible mid-rad
result is Entire, which loses almost all information unless the level 1
interval was Entire too (in which case a+b does not exist at level 2,
so a special rule would be followed).

Michel.
---Sent: 2010-06-30 20:31:49 UTC