Re: Absolute value of intervals

On 2009-10-27, Sam Mason <sam@samason.me.uk> wrote:
> On Tue, Oct 27, 2009 at 03:25:02PM +0000, Sam Mason wrote:
>> If the absolute value of an interval was defined to strip out all the
>> negation signs you'd get the "wrong" answers out.
>
> Oops, forgot another reason!  For maths to work (n) and (-(-n)) should
> evaluate to the same value.  Inverting all the signs, as negation does,
> will ensure that these semantics remain.

There not requrement in mathematics that

z be a member of the set  { abs(z) , -abs(z) }

consider the case of z=sqrt(-1)