Let $x, y : \mathbb{N} \to \mathbb{R}$ each be a D4685: Real sequence such that

(i)	\begin{equation} \lim_{N \to \infty} \sum_{n = 0}^N x_n \neq \emptyset \neq \lim_{N \to \infty} \sum_{n = 0}^N y_n \end{equation}

Then \begin{equation} x \leq y \quad \implies \quad \sum_{n = 0}^{\infty} x_n \leq \sum_{n = 0}^{\infty} y_n \end{equation}