
352 Chapter 9 Sample applications
Definition 9.9. Let x and y be long intervals, then
x ı y :Df ı j 2 x ^ 2 yg,forı2fC, , , =g,
with 0 … y for ıD=.
Of course, in general, this theoretical result is not representable on the computer.
Here the result must be a long interval again. We do not, however, require that it is the
least enclosing long interval of some prescribed length. But we must require that the
computed long interval z is a superset of the result defined in Definition 9.9: x ıy z.
Not to require optimality of the result gives room for a compromise between tightness
of the enclosure and the efficiency of the implementation.
Negation.