Let $x_0, x_1, x_2, \ldots \in [0, 1)$ each be a D993: Real number.

Then \begin{equation} \prod_{n = 0}^{\infty} (1 - x_n) = 0 \quad \iff \quad \sum_{n = 0}^{\infty} x_n = \infty \end{equation}

Let $x_0, x_1, x_2, \ldots \in [0, 1)$ each be a D993: Real number.

Then \begin{equation} (1 - x_0) (1 - x_1) (1 - x_2) (1 - x_3) \cdots = 0 \quad \iff \quad x_0 + x_1 + x_2 + x_3 + \cdots = \infty \end{equation}

Let $x_0, x_1, x_2, \ldots \in [0, 1)$ each be a D993: Real number.

Then \begin{equation} \lim_{N \to \infty} \prod_{n = 0}^N (1 - x_n) = 0 \quad \iff \quad \lim_{N \to \infty} \sum_{n = 0}^N x_n = \infty \end{equation}