Re: Undefined behaviour (Was: Definition of intervals as subsets...)

[Dan Zuras Intervals <intervals08@xxxxxxxxxxxxxx>]

	This was intended for the entire group.  - Dan

To: Nate Hayes <nh@xxxxxxxxxxxxxxxxx>,
    "R. Baker Kearfott" <rbk@xxxxxxxxxxxxx>
Cc: Dan Zuras Intervals <intervals08@xxxxxxxxxxxxxx>
From: Dan Zuras Intervals <intervals08@xxxxxxxxxxxxxx>
Subject: Re: Undefined behaviour (Was: Definition of intervals as subsets...) 
Date: Mon, 16 Mar 2009 08:13:51 -0700

> Date: Mon, 16 Mar 2009 08:40:10 -0500
> From: "R. Baker Kearfott" <rbk@xxxxxxxxxxxxx>
> To: stds-1788 <stds-1788@xxxxxxxxxxxxxxxxx>
> Subject: Re: Undefined behaviour (Was:  Definition of intervals as subsets...)
> 
> Dear Michel, et. al.,
> 
> > . . .
> >
> 
> For example, the Kaucher interval addition
> 
>     [a,b]+[c,d]=[a+c,b+d]
> 
> is the same as the classical formula except it
> relaxes the constraint a <= b and c <=d, i.e.,
> 
>     [5,2]+[3,9]=[8,11]
> 
> is the correct modal result.
> 
> . . .
> 
> Sincerley,
> 
> Nate Hayes
> Sunfish Studio, LLC

	Nate,

	Am I missing something here?

			[5,2]+[3,9]=[8,11]

	Can it really be that the sum of {x | 5 <= x or x <= 2}
	and {y | 3 <= y <= 9} is {x+y | 8 <= x+y <= 11}?

	Stated another way, can it really be that the sum of a
	bifurcated interval of infinite width & an ordinary
	interval of width 6 is an ordinary interval of width 3?

	This appears non-intuitive at best or wrong at worst.

	Can you explain this result?

	Thanks,

				Dan