ThmDex – An index of mathematical definitions, results, and conjectures.
F10968
Formulation 0
Let $x_1, x_2, x_3, \ldots \in \mathbb{R}$ each be a D993: Real number such that
(i) \begin{equation} x_n = e^{-2^{-n}} \end{equation}
Then
(1) \begin{equation} x_1, x_2, x_3, \ldots \in (0, 1) \end{equation}
(2) \begin{equation} \prod_{n = 1}^{\infty} x_n = e^{-1} \end{equation}