[std-interval] Mathematical relations and default initialization

[George Corliss]

Guillaume,

Thank you for your response.

>> * Default initialization
>> I see on page 15 that the default constructor creates an empty interval.
>>  At some point in the discussion, Sylvain gave 6 possible ways of
>> implementing this constructor:
>> 
>> 1- no default constructor at all
>> 2- [0,0]
>> 3- empty
>> 4- whole
>> 5- uninitialized tag
>> 6- see below (something a la "singular iterator")
>> 
>> Possibility 4 was brushed away from the start, and the remaining
>> possibilities heavily debated. In my opinion, it makes sense to have the
>> default constructor return "whole" since interval arithmetic is often
>> used in processes that try to gain some information on the possible
>> value of a variable (that is, we start from a wide interval and narrow
>> it down to some reasonably small one).
> 
> I don't remember 4 being brushed right away (proposition 1 was). As a
> matter of fact, propositions 3 and 4 have reached a point in my opinion
> where I consider them to be equally useful. So, at least on my side, it
> is still 4 in the proposal, only because of inertia.
P. 15, 26.6.4, par. 1 & 2 says empty, which is #3.

As I discussed in an earlier message, I favor <whole>

Dr. George Corliss
Electrical and Computer Engineering
Marquette University
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