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Consider the constant function .
Since g is constant, .
Take any ;
a simple proof by contradiction, which follows, shows that
is an exact bound of g:
Assume there is a point
such that .
Let , so :
Furthermore, and
together imply that .
A quick review of the chart reveals this
situation is impossible, since implies
that . The chart predicts
the sign of since .
So, for any , .
It follows that is a lower and upper bound for g,
over :
The intuitive interval model originally given is now seen to be correct:
since it is equivalent to:
assuming that g is total.
Next: 3.2.5 Optimality
Up: 3.2 Constant Interval Arithmetic
Previous: 3.2.3 Charts