A few weeks ago, I was mindlessly browsing the Mathematics Stack Exchange when I came across a really interesting question (that I unfortuntately can no longer locate); how do you sort a real-valued continuous function?

The initial naive approach is straightforward: take some $f: \mathbb{R} \to \mathbb{R}$ that’s continuous and, just like in typical countable sets, create a sequence $\mathcal{F}$ where $\mathcal{F}_0 = \inf(f)$ and