ThmDex – An index of mathematical definitions, results, and conjectures.
F12361
Formulation 1
Let $x_0, x_1, x_2, \ldots \in (0, 1]$ each be a D993: Real number.
Then \begin{equation} x_0 x_1 x_2 x_3 \cdots > 0 \quad \iff \quad (1 - x_0) + (1 - x_1) + (1 - x_2) + (1 - x_3) + \cdots < \infty \end{equation}