Meaning of decorations
John Pryce wrote:
> >> I think "Hmm" on this one. What does "any defined and continuous (dac)
interval
> range
> >> of floor([0,6])" mean? The only meaning I can see is "since floor()
isn't dac on the
> >> input [0,6], such a range doesn't exist; and if we insist on treating
this nonexistent
> >> thing as a set, it must be the empty set".
> > That is exactly my view... so why the "Hmmm"?
>
> Precisely because I think the argument I stated above, with which you are
agreeing,
> makes no sense.
> Above, a certain kind of set does not exist: that is, the class of sets
having a certain
> property P is empty. You are arguing from that that you can take the empty
set as
> being a set that has property P.
No.
Decorations describe a property that is true about the evaluation of a
function over an interval box.
Two examples:
sqrt(Empty) = Empty (1)
sqrt([-4,-1]) = Empty (2)
Both (1) and (2) are Empty, but the Empty result is obtained for different
reasons:
-- in (1), the restriction of sqrt to Empty is defined and
continuous (DAC), but the result is Empty because the input was Empty; and
-- in (2), the restriction of sqrt to [-4,-1] is not defined (NDF)
so the result is Empty even though the input was nonempty.
Decorations describe a property that is true about the evaluation of a
function over an interval box:
-- (Empty,DAC) is a property that is true about evaluation of (1)
-- (Empty,NDF) is a property that is true about evaluation of (2)
Nate