in 35.5 of CLRS i have read about algorithm to find sum as large as possible, but not larger than $t.$
Essential part of this algorithm is trimming. On every step you delete all numbers which close one to another, but one to represent them all. Good explanation of the algorithm.
At page 7 from provided link or at page 1133 of ClSR 3rd edition you can find such a statement: $z'/z>1+\epsilon/2n.$ I think $z'$ and $z$ is numbers of elements before and after trimming. But i can't understand how they got such estimation. For example at first step trimming don't actually trim any element. We can devise example of sequence and epsilon to have no trimmed elements even at second step.
Can somebody, please, explain how they got such an estimation? Thanks.