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Math  /  Discrete

QuestionFind the norm of the partition P={−2.1,−1.3,−0.1,0.2,0.8,1.5}\mathrm{P}=\{-2.1,-1.3,-0.1,0.2,0.8,1.5\}. ||P ∥=\|= □\square (Type an integer or a decimal.)

Studdy Solution

STEP 1

1. The partition P={−2.1,−1.3,−0.1,0.2,0.8,1.5}\mathrm{P} = \{-2.1, -1.3, -0.1, 0.2, 0.8, 1.5\} is a set of points on the real number line.
2. The norm of the partition, denoted as ∥P∥\|P\|, is the length of the largest subinterval formed by consecutive points in the partition.

STEP 2

1. Identify consecutive subintervals in the partition.
2. Calculate the length of each subinterval.
3. Determine the largest subinterval length.

STEP 3

Identify the consecutive subintervals in the partition P\mathrm{P}. The partition points are −2.1,−1.3,−0.1,0.2,0.8,1.5-2.1, -1.3, -0.1, 0.2, 0.8, 1.5. The subintervals are:
1. [−2.1,−1.3][-2.1, -1.3]
2. [−1.3,−0.1][-1.3, -0.1]
3. [−0.1,0.2][-0.1, 0.2]
4. [0.2,0.8][0.2, 0.8]
5. [0.8,1.5][0.8, 1.5]

STEP 4

Calculate the length of each subinterval:
1. Length of [−2.1,−1.3][-2.1, -1.3] is −1.3−(−2.1)=0.8-1.3 - (-2.1) = 0.8.
2. Length of [−1.3,−0.1][-1.3, -0.1] is −0.1−(−1.3)=1.2-0.1 - (-1.3) = 1.2.
3. Length of [−0.1,0.2][-0.1, 0.2] is 0.2−(−0.1)=0.30.2 - (-0.1) = 0.3.
4. Length of [0.2,0.8][0.2, 0.8] is 0.8−0.2=0.60.8 - 0.2 = 0.6.
5. Length of [0.8,1.5][0.8, 1.5] is 1.5−0.8=0.71.5 - 0.8 = 0.7.

STEP 5

Determine the largest subinterval length from the calculated lengths:
- 0.8,1.2,0.3,0.6,0.70.8, 1.2, 0.3, 0.6, 0.7
The largest length is 1.21.2.
The norm of the partition ∥P∥\|P\| is:
1.2 \boxed{1.2}

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