# Number of elements

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• November 30th 2009, 07:32 AM
Sampras
Number of elements
Suppose $R(k) = \{(i,j): a_{i,j} \leq k \}$. Why does $|R(k)|= \left \lfloor \frac{k}{1} \right \rfloor + \left \lfloor \frac{k}{2} \right \rfloor+ \cdots + \left \lfloor \frac{k}{k} \right \rfloor$, where $k$ is a positive integer?