Question

Let i=[0,4] then the norm of the partition p=(0,0.5,2.5,3.5,4) is ​

Answer 1

the norm of the partition p=(0,0.5,2.5,3.5,4) is 2

1: The norm of a partition is merely the length of the largest subinterval into which the partition divides [a,b]. Clearly many partition have the same norm, so partition is not a function of the norm.

2: for i=[a,b] where a<x1,x2,x3,....xn<b, partition p={x1,x2,x3,....xn} for above condition norm=max{x2-x1,x3-x2,....xn-x(n-1)}

3: i=[0,4] where a<0,0.5,2.5,3.5,4<b, partition p={0,0.5,2.5,3.5,4}

4: Therefore,

x2-x1=0.5-0=0.5

x3-x2=2.5-0.5=2

x4-x3=3.5-2.5=1

x5-x4=4-3.5=0.5

5: Hence,

norm=max{x2-x1,x3-x2,x4-x3,x5-x4}

norm=max{0.5,2,1,0.5}

norm=2

6: Hence the norm of the partition p=(0,0.5,2.5,3.5,4) is 2.