ThmDex – An index of mathematical definitions, results, and conjectures.
F12360
Formulation 0
Let $x_0, x_1, x_2, \ldots \in (0, 1]$ each be a D993: Real number.
Then \begin{equation} \prod_{n = 0}^{\infty} x_n > 0 \quad \iff \quad \sum_{n = 0}^{\infty} (1 - x_n) < \infty \end{equation}