sicp exercise 2.9

; Exercise 2.9.  The width of an interval is half of the difference between its upper and lower bounds. The width is a measure of the uncertainty of the number specified by the interval. For some arithmetic operations the width of the result of combining two intervals is a function only of the widths of the argument intervals, whereas for others the width of the combination is not a function of the widths of the argument intervals. Show that the width of the sum (or difference) of two intervals is a function only of the widths of the intervals being added (or subtracted). Give examples to show that this is not true for multiplication or division.


(define (make-interval a b) (cons a b))
(define (upper-bound interval) (car interval))
(define (lower-bound interval) (cdr interval))

(define (width interval)
  (/ (- (upper-bound interval) (lower-bound interval)) 2))


#!

(width (sum a b))
(width ((+ ua ub) , (+ la lb)))
(/ (- (+ ua ub) (+ la lb)) 2)
(+ (/ (- ub lb) 2) (/ (- ua la) 2))

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