SICP习题2.9解答

证明:
设求区间的宽度函数为h(x)
先证区间的加法: 设任意两区间为(a, b) (c, d),那么(a, b) + (c, d) = ( min(a, b) + min(c, d), max(a, b) + max(c, d) )
那么h((a, b) + (c, d)) = ( max(a, b) + max(c, d) - min(a, b) - min(c, d) ) / 2
= ( max(a, b) - min(a, b) + max(c, d) - min(c, d) ) / 2
= ( max(a, b) - min(a, b) ) / 2 + ( max(c, d) - min(c, d) ) / 2
= h( (a, b) ) - h( (c, d) )
即区间加法所得区间的宽度为其参数区间的宽度函数.
证毕.
同理,减法也一样.