Re: Interval comparisons
Nate Hayes wrote:
> John Pryce wrote:
>> (all x in xx) (exist y in yy) E(x) = y,
>> which is the definition of: yy is an enclosure of range(f,xx).
>
> I fully agree. This is my preferred definition of range(f,xx). I wish
> it could be included in our motions and standard.
>
> Furthermore, if and only if
>
> (all x in xx)(exist y in yy) E(x) = y
> (all y in yy)(exist x in xx) E(x) = y
>
> are both true, then range(f,xx) is an exact enclosure (as opposed to
> some outward rounding).
>
> The latter can also define the inner rounding/enclosure, as well.
I suppose to be coherent, in my comments above the two occurences of
"range(f,xx)" should be replaced with "enclosure of range(f,xx)".
Nate Hayes