ThmDex – An index of mathematical definitions, results, and conjectures.
F10969
Formulation 1
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^{-1 / 2^n} \end{equation}
Then
(1) \begin{equation} x_1, x_2, x_3, \ldots \in (0, 1) \end{equation}
(2) \begin{equation} \lim_{N \to \infty} \prod_{n = 1}^N x_n = \frac{1}{e} \end{equation}