for any y in L, there must be a z in L' (trimmed list) satisfy y/(1+delta) <= z <=y. for delta = 0.1: when y = 50, we put 50 in L' to satisfy the inequality. L' = {50} when y = 51, 46.4 <= z <=51, 50 satisfies. when y = 55, we need z s.t 50 <= z <=55, 50 satisfies. when y = 70, we need z s.t. 63.6 <= z <= 70, so we put 70 in L'. L' = {50, 70} when y = 71, we need z s.t. 64.5 <= z <= 71, 70 satisfies. when y = 82, we need z s.t. 74.5 <= z <= 82, we put 82 in L'. L' = {50, 70, 82} when y = 83, we need z s.t. 75.45 <= z <= 83, 82 satisfies. when y = 84, we need z s.t. 76.36 <= z <= 84, 82 satisfies. when y = 99, we need z s.t. 90 <= z <= 99, we put 99 in L'. Finally L' = {50, 70, 82, 99}

Given L=⟨50,51,55,70,71,82,83,84,99⟩

and δ=0.1.

Using the inequality from the slides,

L'=⟨50,55,70,82,99⟩

L = <50,51,55,70,71,82,83,84,99>

L' = (50) ----- 50 x 1.1 = 55

L' = (50,70) ----- 70 x 1.1 = 77

L' = (50,70,82) ----- 82 x 1.1 = 90.2

L' = (50,70,82,99) <---- trimmed list

A δ trimmed list for L is such that for each value y in L, there is a value z also in L that is greater than 1/(1+δ) but also smaller than y itself. In this case, δ is 0.1, so z has to be between y/1.1 and y.

For L=⟨50,51,55,70,71,82,83,84,99⟩, L' would be ⟨50,70,82,99⟩

With list (50,51,55,70,71,82,83,84,99) and trimming parameter = 0.1, the trimmed list is 50,55,72,82, 99

Given the list, L=⟨50,51,55,70,71,82,83,84,99⟩. and δ=0.1

The trimmed list would be L' = <50, 70, 82, 99>

L = <50, 51, 55, 70, 71, 82, 83, 84, 99>

45.45 <= z <= 50

46.36 <= z <= 51

50 <= z <= 55

63.64 <= z <= 70

64.55 <= z <= 71

74.55 <= z <= 82

75.45 <= z <= 83

76.36 <= z <= 84

90 <= z <= 99

Every inequality must be satisfied by some z in L' L' = <50, 70, 82, 99>