My proof said the expected value of all the data points of expectation of all subsets of a larger set which have a true count identical to the true count of the set is a larger value than the value of the expectation of the original set.
Now either the proof is accurate and the expected value is larger or the proof is inaccurate and the expected value is either identical or larger.
While you have ducked the concept of expected value repeatedly, please remember expected value is a specific value. It is not a range of values but a definite mathematical term which cannot have multiple values because it is the mean of the expectation of all possible subsets of size m with a true count the same as the starting set's true count as samples taken of the random variable which is the expectation of all of the subsets approach infinity and since the random variables are finite is one specific ascertainable value.
Yes or no will suffice and then you can explain to your heart's content.
If history is a guide there will be no yes or no answer but a filibuster. But please remember if that occurs the answer will be "no".
