We takes two intervals represented by a double similarly to the representation in our program:
Now we can do the sum of the two intervals:
We can see that the width function is a linear map so the same thing works for the difference of two intervals.
It’s not true for the multiplication as for example:
\(c = (0,1)(c)=\)
\(d = (-1,1)(d)=1\)
But we have \(cd=(-1,1)\) using the
mul-interval function and \((cd)=1\)
Using the same \(c\) and \(d\) and the
div-interval function we show as example:
\((c)/(b)=1 = (c/d)\)
Therefore the width of the division of two intervals is not equal to the division of the width of the two intervals.