I am reading this algorithm in these notes for counting the number of distinct items in a stream.
From my understanding, the basic idea is that if such number is big enough, the distance between the numbers generated by the hash function will be, on average, the same and equal to $1/(k+1)$, where $k$ is the number of distinct element. Hence, one can derive $k$ from that. However, I don't follow the reasoning in slide 6. Why would $2^R$ be "around" $m$?