\begin{definition}[Definition:Harmonic Numbers]
The '''harmonic numbers''' are denoted $H_n$ and are defined for positive integers $n$:
:$\ds \forall n \in \Z, n \ge 0: H_n = \sum_{k \mathop = 1}^n \frac 1 k$
From the definition of vacuous summation it is clear that $H_0 = 0$.
\end{definition}