A Sequence is a Net

Last updated Nov 1, 2022

Let $X$ be a Set and let ${x_n}{n=1}^{\infty} \subset X$ be a Sequence. Then ${x_n}{n=1}^{\infty}$ is a Net.

This follows by simply noting that $\mathbb{N}$ is Archimedean with its natural Well-Ordering. Thus it is a Directed Partial Ordering.